Six Sigma Practice Test 8 (Indiana Council--Measure & Analyze Stage)
Most widespread use of F distribution?
Most widespread use of F distribution? To test for equality of variances from 2 normal populations
Calculate standard deviation of the population for the 5 samples: 1.5, 1.2, 11.1 1.0. 1.6
Calculate standard deviation of the population for the 5 samples: 1.5, 1.2, 11.1 1.0. 1.6 Answer= 0.259
Calculate the performance ration for the process with spread of 20-30 and lower and upper specification limits of 15 and 35 respectively.
Calculate the performance ration for the process with spread of 20-30 and lower and upper specification limits of 15 and 35 respectively. P(R)= 6 sigma / (USL -LSL) P(R)= 10 / (35 -15) = 10/20 = 0.5
Calculation of reproducibility results in value of zero while repeatability yeilds a positive number. Conclusion?
Calculation of reproducibility results in value of zero while repeatability yeilds a positive number. Conclusion? Reproducibility =0 means operator has no effect on the measurement --aka no appraiser effect
1,000 gamblers start rolling dice under the condition that if they roll 6 they can stay in the game. After 3 roles, how many gambler will stay?
1,000 gamblers start rolling dice under the condition that if they roll 6 they can stay in the game. After 3 roles, how many gambler will stay? Each roll of teh dice is mutually exclusive ecent with odds of 1/ 6. So after 3 rolls, the odd are : (1/6) (1/6) (1/6) = 1/ 216 Thus, 1000/ 216= 4.63 gamblers are left
What is the effect of management tampering with process capability?
What is the effect of management tampering with process capability? Answer= Process capability will deteriorate if management mandates frequent adjustments. Excess adjustments will increas the variation and decrease capable processes
Non-locational data might be found on which data sheets? a. defect diagram check sheet b. measles chart c. concentration chart d. recording check sheet
Non-locational data might be found on which data sheets? a. defect diagram check sheet b. measles chart c. concentration chart d. recording check sheet D= correct: A, B, C are types of check sheets that indicate location.
Number derived from sample data, which describes the data in some useful way is called?
Number derived from sample data, which describes the data in some useful way is called? Statistic
Most accurate methods of quantifying Gage R& R?
Most accurate methods of quantifying Gage R& R? ANOVa
Error variance in an R&R study means?
Error variance in an R&R study means? Measurement error or repeatability
Repeatability of R & R study is most similar to?
Repeatability of R & R study is most similar to? Accuracy of measurements
When would Cp and Cpk be equal?
When would Cp and Cpk be equal? When the process is perfectly centered.
Which type of distribution is closely related to expotential distribution?
Which type of distribution is closely related to expotential distribution? Poissian distribution
A combined calculation of repeatability and reporducibility using the average and range method produces a ration of 7.42% of process tolerance. What ca be stated about the 7.2% value?
A combined calculation of repeatability and reporducibility using the average and range method produces a ration of 7.42% of process tolerance. What ca be stated about the 7.2% value? Answer= Measurement system is acceptable Acceptability criteria states that a combined R&R value: (1) less than 10% is considered acceptable. (2) Between 10% and 30% is considered marginal ( good but suitable to improvement) and (3) over 30% is not accepetable.
A comparison between Cp and Cpk for a process would find which of the following to be true? a. Cpk value is often larger than Cp b. Denominator of Cp calculation is half that of Cpk c. Cp value does not account for centering d. Neither calculation requires a sable process.
A comparison between Cp and Cpk for a process would find which of the following to be true? a. Cpk value is often larger than Cp b. Denominator of Cp calculation is half that of Cpk c. Cp value does not account for centering d. Neither calculation requires a sable process. C= correct Because Cpk corrects for centering, Cpk cannot be greater than Cp. Cp denominator is 6S and Cpk denominator is 3S
A gage should be sensitive enough to discriminate in measurement base don total tolerance speicification or process spread, whichever is smaller. What should the sensitivity be?
A gage should be sensitive enough to discriminate in measurement base don total tolerance speicification or process spread, whichever is smaller. What should the sensitivity be? Gage should be sensitive enough to detect differences in measurement as slight as 1/10 of the total tolerance specificaiton or spread, which ever is smaller
A lot of 50 pieces has 5 defectives. A sample of 2 is drawn without replacement. Probability that both will be defective is: ??
A lot of 50 pieces has 5 defectives. A sample of 2 is drawn without replacement. Probability that both will be defective is: ?? Answer= 0.0082 Use multiplicative law of probability: P ( A ∩ B) = P (A) * P (B) P ( A ∩ B) = (5/50) (4/ 49) = 0.0082
A lot of parts is found to be rejected and is 20% defective. What is the probability that the lot would have been accepted by the following sampling plan--when N= 10 and accept no defectives if the one or more defectives?
A lot of parts is found to be rejected and is 20% defective. What is the probability that the lot would have been accepted by the following sampling plan--when N= 10 and accept no defectives if the one or more defectives? 0.20= defects; 0.8 is no defects S= 10 Binomial Probability calculation Equation: ---- P(r) = C r= No. of defectives= 0 N= sample size = 10 P= proportion defective Solution = P(0) = 10!/ [0! (10-0)!] * (0.2 ^0) (1-02) ^ 10-0) P(0) = 0.1074 Section VII---14
A number resulting from manipulation of some raw data according to certain specified procedures is called?
A number resulting from manipulation of some raw data according to certain specified procedures is called? Statistic
A process is producing material which is 20% defective. Five pieces are selected at random for inspection. What is the probability of exactly 3 good pieces being found in the samples?
A process is producing material which is 20% defective. Five pieces are selected at random for inspection. What is the probability of exactly 3 good pieces being found in the samples? Answer= 0.205 This is a binomial probability . n= samples; r= number of defectives ; p= proportional defective n! ______ (p ^x) (1-p) ^ n-x x! (n-x)! = 5! ___ (0.2 ^2) (1-0.2) ^ 5-2 2! (5-2) ! = [5*4/ 2] (0.04) (0.8 ^3) = 10 * 0.04 * 0.512 = 0.2048
A process shows lack of stability but yesterday's capability index was so great (1.77) that your supervisor decides to use it as a benchmark for all future process capabilities. What should your advise your supervisor?
A process shows lack of stability but yesterday's capability index was so great (1.77) that your supervisor decides to use it as a benchmark for all future process capabilities. What should your advise your supervisor? Answer= Don't use 1.77 value, first get the process to statistical stability. If the process shows a lack of stability, the process capability index is not valid. One should first get the process to statistical stability by eliminating special cause variation.
A product's USL = 7.3 lbs & LSL= 7 lbs. Actual data indicates that the product is currently running at an average of 7.465 lbs. with standard deviation of 0.03039 lbs. Calculations indicates Cp= 1.645 and Cpk=1.81. What conclusions can be made about the process. a. there is something wrong with the calcalations b. specifications are unrealistically set c. process is close to 6 sigma; negative Cpk is irrelevant d. Cp and Cpk values indicate that the proces is not centered.
A product's USL = 7.3 lbs & LSL= 7 lbs. Actual data indicates that the product is currently running at an average of 7.465 lbs. with standard deviation of 0.03039 lbs. Calculations indicates Cp= 1.645 and Cpk=1.81. What conclusions can be made about the process. a. there is something wrong with the calculations b. specifications are unrealistically set c. process is close to 6 sigma; negative Cpk is irrelevant d. Cp and Cpk values indicate that the process is not centered. D= correct. Negative Cpk is rate but possible. If the process is so out of center that all measures fall outside both limits, then one of the Cpk values must be negative Cp= (USL -LSL ) / 6 sigma Cp= (7.3 - 7) / (6 * 0.03039)= 1.645 Cpk= min [ (x-bar - LSL)/ (3 *sigma) , (USL - X-bar)/ (3 *sigma) Cpk = min [ 7.465 -7 / (3 * 0.03039) , (7.3 - 7.465/ (3 * 0.03039) = -1.81 Cp= 1.645 and Cpk= -1.81
A scoop samples 100 units/ trial. What must be the average number of defects for there to be an 80% chance that more than one defect will be found in the sample?
A scoop samples 100 units/ trial. What must be the average number of defects for there to be an 80% chance that more than one defect will be found in the sample? Question requires the backward use of the Poisson table. Note that more than one defect is desired. For the sample to contain more than one defect with 80% probability, the table must be used to determine a 20% probability of 0 or 1 np= 3.0 Aswer= 3.0
ASQ sectional history indicates 70% of all candidates successfully pass the CSSGB certification exam. A total of 12 company employees will take the upcoming CSSGB exam. Area manager promised a big bonus to all 12 people who pass the exam. What is the probability of getting the promised bonus?
ASQ sectional history indicates 70% of all candidates successfully pass the CSSGB certification exam. A total of 12 company employees will take the upcoming CSSGB exam. Area manager promised a big bonus to all 12 people who pass the exam. What is the probability of getting the promised bonus? Answer = 0.013841 Problem is clearly a bionomial situation. The probability of exactly 12 of all 12 CSSGB candidates passing the exam is given by the following formula, with n= 12, p-0.70, X=12 P (x= X) = [N! / X! (n-X!)] [p^x * (1-p) ^ n-X] P (x= 12) = [12! / 12! (12-12!)] [0.7^12 * (1-0.7) ^ 12-12 = 0.013841 The big bonus is very unlikely
ASQ sectional history indicates that 70% of all candidates successfully pass the CSSGB certification exam. A total of 12 company employees (including your) take the upcoming CSSGB exam. The area manager has promised a big bonus if all 12 you pass the exam. What is the probability of getting promised bonus.
ASQ sectional history indicates that 70% of all candidates successfully pass the CSSGB certification exam. A total of 12 company employees (including your) take the upcoming CSSGB exam. The area manager has promised a big bonus if all 12 you pass the exam. What is the probability of getting promised bonus. Answer = 0.013841 This is a binomial situation. The probability of exactly 12 of all 12 CSSGB candidates pass the exam is given by the following formula, with n=12, p=0.7, and x=12 P (x= X) = [n! / X (n- X)! ] * p^x * (1-p) ^ n-x P (x= 12) = [12! / 12 (12- 12! ] * 0.70^12 * (1-0.70) ^12-12 P (x= 12) = 0.013841 Big bonus unlikely
Advantage of R& R range method compared to the average and range or ANOVA methods is that is is quick way to ____?
Advantage of R& R range method compared to the average and range or ANOVA methods is that is is quick way to ____? Quantify the total R &R portion of the measurment. Repeatability can only be qualified via ANOVA only.
Advantage of using ANOVA over average and range method for Gage R& R?
Advantage of using ANOVA over average and range method for Gage R& R? ANOVA can measure interactions. But both have the ability to partition variation into component parts
After attending SPC classes, a second shift production supervisor implements a mean chart for an important quality characteristic. The supervisor said " I'm happy to annouce that out of 24 samples means (sample size 5 units, taken every 20 minutes) none were found outside of the specification limits. The process is running falwlessly. What can be stated about the supervisor's conclusion> a. supervisor is wrong, there is no measure of the confidence level b. supervisor is wrong, two different populations are being compared. c. supervisor is right, for the wrong reasons d. supervisor is right, all values are within specifications.
After attending SPC classes, a second shift production supervisor implements a mean chart for an important quality characteristic. The supervisor said " I'm happy to annouce that out of 24 samples means (sample size 5 units, taken every 20 minutes) none were found outside of the specification limits. The process is running falwlessly. What can be stated about the supervisor's conclusion> a. supervisor is wrong, there is no measure of the confidence level b. supervisor is wrong, two different populations are being compared. c. supervisor is right, for the wrong reasons d. supervisor is right, all values are within specifications. B= correct The world of the sample means and the world of individual values are completely different. Only individual values can be compared with specifications. Sample means will concentrate closer to the center. The relationship between 2 population spreads is given by the formula: Sigma (x-bar) = Sigma (x) / Square root of N samples
After attending SPC classes, a second shift production supervisor implements a mean chart of an important quality characteristics. Superviors says " I'm happy to announce that out of 24 samples (sample size 5 units taken every 20 minutes) now were outside the specification limits. Conclusion?
After attending SPC classes, a second shift production supervisor implements a mean chart of an important quality characteristics. Superviors says " I'm happy to announce that out of 24 samples (sample size 5 units taken every 20 minutes) now were outside the specification limits. Conclusion? Supervisor are wrong, two different populations are being compared World of sample means and work of individual values are completely different. Only individual values can be compared with specifications. Sample means will concentrate closer to the center. Relationship between two population Sigma (X-bar ) = Sigma (X) / (Square root of sample size)
As a new green belt in the company, you are given the following data: X-double bar = 4.241 mm, S- x bar = 0.565mm, n=5 You decide to estimate the process parameters but discover that the original data was lost and all you have are these 3 numbers. What is the best estimate that can be made of the process parameter under the current circumstances?
As a new green belt in the company, you are given the following data: X-double bar = 4.241 mm, S- x bar = 0.565mm, n=5 You decide to estimate the process parameters but discover that the original data was lost and all you have are these 3 numbers. What is the best estimate that can be made of the process parameter under the current circumstances? Answer= X-double = 4.241 and Sigma (x-bar)= 1.263 The information given refers the average and standard error of the mean for sample size. Using the central limit theorem, an estimate can be made for the population parameters as follows: Sigma (x- double bar) = Sigma (x-bar) * Square root of sample size = 0.565 * Square root of 5 = 1.263
Assume in a R & R study, using the ANOVA method, that the technician - to - technician error was noted to be very low. this value is defined as?
Assume in a R & R study, using the ANOVA method, that the technician - to - technician error was noted to be very low. this value is defined as? Reproducibility error = answer
Assuming that repeatability and reporducibility variance are known from R & R study, what can be determined?
Assuming that repeatability and reporducibility variance are known from R & R study, what can be determined? Measurement variation By taking the square root of the combined variances, the standard deviation can also be found. Not enough information to find the total or partial variation.
Batch with 2% defectives. N= 30 and batch accepted if 1 or less defects found. What is the probability that batch is rejected?
Batch with 2% defectives. N= 30 and batch accepted if 1 or less defects found. What is the probability that batch is rejected? Approximate using Poisson Table. ---> (np= 0.6) and it can been seen that probability of getting 1 or fewer defects si 0.878. thus the probability of rejecting the lot = 1- 0.878 = 0.122 or 12.2%
Bias in R& R Study is reported as:
Bias in R& R Study is reported as: percentage of process variation or tolerance.
Binomial distribution is a discrete distribution and may be used to describe: a. sampling without replacement from finite population b. case of n independent trails with probabilities constant from trial-to-trial c. case of n independent trials with several outcomes for each trial d. Sampling without replacement where there are several potential outcomes
Binomial distribution is a discrete distribution and may be used to describe: a. sampling without replacement from finite population b. case of n independent trails with probabilities constant from trial-to-trial c. case of n independent trials with several outcomes for each trial d. Sampling without replacement where there are several potential outcomes B= correct; Hypergeometric distribution--"without replacement" and "finite population"
Box has 27 black and 3 red balls. What is the probability that the ball is picked is red?
Box has 27 black and 3 red balls. What is the probability that the ball is picked is red? Black = 27/ 30=0.9 Red= 3/ 30 = 0.1 Answer = 0.1000
Calculation of reproducibility using the average and range method comes from ???
Calculation of reproducibility using the average and range method comes from ??? Examining the variation between the average of the appraisers for all parts measured Reproducibility is commonly referred to as "between appraisers" variability. Measuring the variation between the average of the appraisers for all parts measured will give an assessment of the reproducibility
Calibration of measuring instruments is necessary to maintain accuracy. How does calibration affect precision?
Calibration of measuring instruments is necessary to maintain accuracy. How does calibration affect precision? Calibration has minimum impact on precision.
Central location, width, spread, and shape can visualized on which tool? a. p-chart b. affinity diagram c. pareto diagram d. histogram
Central location, width, spread, and shape can visualized on which tool? a. p-chart b. affinity diagram c. pareto diagram d. histogram D= histogram
Correlation coifficents are generated from which type of graph?
Correlation coifficents are generated from which type of graph? Scatter diagram
IDs of a certian peice of tubing are distributed with mean of 1.00. Proportion of tubing with ID's less than 0.9 is:
IDs of a certian peice of tubing are distributed with mean of 1.00. Proportion of tubing with ID's less than 0.9 is: Answer= less than the proportion of IDs greater than 1.0
Data points: 64.7, 37.5 28.9, 55.6, 42.5, Calculate coifficient of variation
Data points: 64.7, 37.5 28.9, 55.6, 42.5, Calculate coifficient of variation Mean is 45.84. St. deviation = 12.976 COV= mean/ St. dev= 27.9% Note that using a standard deviation of 14.306 will give COV-31.2% the wrong answer
Define the sample space S (rock, book, cigar, guitar, dog), What is the compliment of (Cigar, dog) ? a. rock, book, cigar, guitar, dog b. cigar, guitar, dog c. dog d. rock, book, guitar
Define the sample space S (rock, book, cigar, guitar, dog), What is the compliment of (Cigar, dog) ? a. rock, book, cigar, guitar, dog b. cigar, guitar, dog c. dog d. rock, book, guitar D= answer Compliment of an envet is a set of all the elements not in the event. The sample space S has 5 elements: (rock, book, cigar, guitar, dog. Elements rock, book, guitar are not in the event (cigar , dog)
Determine the coefficient of variation for the last 500 pilot plant test runs of high temperature film having a mean of 900 degrees Kelvin with standard deviation of 54 degrees. a. 6% b. 16.7% c. 0.6% d. 31%
Determine the coefficient of variation for the last 500 pilot plant test runs of high temperature film having a mean of 900 degrees Kelvin with standard deviation of 54 degrees. a. 6% b. 16.7% c. 0.6% d. 31% A= Correct % Coefficient of Variation = S/ (X-bar) * 100 54/ 900 * 100 = 6%
Identify the data conversion that would be most difficult to accomplish: a. attribute data converted to variable data b. variable data converted to attribute data c. Accumulated "go/ no-go" data converted to variables data d. Variables data converted to go/ no-go data
Identify the data conversion that would be most difficult to accomplish: a. attribute data converted to variable data b. variable data converted to attribute data c. Accumulated "go/ no-go" data converted to variables data d. Variables data converted to go/ no-go data C= correct. Variable data can easily be converted to attribute data. Attribute data can be converted to attribute COUNTED data
Diameter of a population of ball bearings is normally distributed with a mean of 75 and sigma of 8. What is the average diameter of 10 randomly selected ball bearings being greater than 77?
Diameter of a population of ball bearings is normally distributed with a mean of 75 and sigma of 8. What is the average diameter of 10 randomly selected ball bearings being greater than 77? N= 10 sigma = 8 mean= Standard deviation of sample of 10 is equal tot he standard deviation of the individuals divided by the square root of the sample size. Standard deviation of the average with a sample of 10 is 2.53. Transform to standard normal using (mean= 0 and standard deviation =1) Z= (X - mean) / sigma Z= (77 - 75) / 2.53 = 0.7906. Area under the standard normal curve to the right of 0.7906 is 0.2146 Answer= 0.2146
Distribution of average approach a normal distribution with sample sizes of 25 are taken. Statement applies to: a. only normal distribution, according to the central limit theorem b. only triangular distribution, according to the central limit theorem c. only uniform distribution, according to the central limit theorem d. All distributions, according to the central limit theorem
Distribution of average approach a normal distribution with sample sizes of 25 are taken. Statement applies to: a. only normal distribution, according to the central limit theorem b. only triangular distribution, according to the central limit theorem c. only uniform distribution, according to the central limit theorem d. All distributions, according to the central limit theorem D= correct. Regardless of shape of the original distribution of the means from the samples (n= 25) will follow normal distribution Section VII --11/12
Expression below is formula for which distribution? n! ______ (p ^x) (1-p) ^ n-x x! (n-x)!
Expression below is formula for which distribution? n! ______ (p ^x) (1-p) ^ n-x x! (n-x)! Answer= t- distribution Knowing the relationships between reliability distributions and tests, this question implies sampling distribution. that eliminates the normal and exponential continuous modeling distributions. The chi-square test deals with variances, while the t-test is a sample means test VII- 23/23
For a process with normal distribution, that is centered on the specification limits, assuming no process shift, what is the process capability index, if the non-conformance level is 6.8 ppm a. Cp=1 b. Cp= 1.33 c. Cp= 1.5 d. Cp= 2
For a process with normal distribution, that is centered on the specification limits, assuming no process shift, what is the process capability index, if the non-conformance level is 6.8 ppm a. Cp=1 b. Cp= 1.33 c. Cp= 1.5 d. Cp= 2 C= Correct With no process shift, a ppm= 6.8 has a Cp= 1.5 for a nomral distribution. This can be cound from the table where ppm= 6.8 and z= 4.5 Cp = USL - LSL / 6 SIMGS = 4.5 - (-4.5) / 6 = 1.5
For process with normal distribution, that is centered on specification limits, assuming no process shift, what is the process capability index, if the non-comformance level is 6.8 ppm?
For process with normal distribution, that is centered on specification limits, assuming no process shift, what is the process capability index, if the non-comformance level is 6.8 ppm? Cp = 1.5 is the correct answer The capability index failure rate is shown in the talbe. With no process shift, a ppm = 6.8 has Cp= 1.5 for a normal distribution A ppm= 6.8 is a z-value of 4.5. Cp= (USL - LSL) / 6 SGMA = (4.5 - (-4.5) / 6 = 1.5
For two events, which of the following is a true probability statement? a. P (A or B) = P (A) + P (B) if A and B are independent b. P (A or B) = P (A) + P (B) if A and B are mutually exclusive c. P (A or B) = P (A) * P (B) if A and B are mutually exclusive d. P (A or B) = P (A) * P (B) if A and B are independent
For two events, which of the following is a true probability statement? a. P (A or B) = P (A) + P (B) if A and B are independent b. P (A or B) = P (A) + P (B) if A and B are mutually exclusive c. P (A and B) = P (A) * P (B) if A and B are mutually exclusive d. P (A or B) = P (A) * P (B) if A and B are independent B= correct The question requires a comparison of the answers with the additive and multiplicative laws of probabiliy. (C and D) would be correct if it stated: P (A AND B) = P (A) * P (B) if A and B are independent
Given a Cp of 1.7 for a process and the same standard deviation and specification limits for the calculation of Cp indices one would not be surprised to fine what?
Given a Cp of 1.7 for a process and the same standard deviation and specification limits for the calculation of Cp indices one would not be surprised to fine what? Standard deviation is fairly low compared to specification limits
Given the following information : Probability of 1 or more defects = 0.69 Probability of 1 or more defects = 0.34 Probability of 1 or more defects = 0.12 Probability of 1 or more defects = 0.03 What is the probability of 2 or fewer defects?
Given the following information : Probability of 1 or more defects = 0.69 Probability of 1 or more defects = 0.34 Probability of 1 or more defects = 0.12 Probability of 1 or more defects = 0.03 What is the probability of 2 or fewer defects? Answer= 0.88 The question presents typical Poisson data in a slightly different light. However, it boils down to a basic probability question. Probability of 3 or more defects is 0.12, the probability of 2 or fewer defects: 1- 0.12 = 0.88
Graphical display of total percentage of results below a certain measurement value if called: a. histogram b. probability density function c. cumulative density function d. Expected Value
Graphical display of total percentage of results below a certain measurement value if called: a. histogram b. probability density function c. cumulative density function d. Expected Value C= Correct; (A) and (B) display probabilities over a range of values. Expected value means the average outcome.
Histogram is also called?
Histogram is also called?---Relative Frequency graph Cumulative frequency graph is called an ogive---this differs from ordinary frequency polygon or histogram in that the frequencies are cumulative. That is, each class frequency is added to the total of all previous class frequency is added to total of all previous class frequenices. Histogram displays distribution of sample, not a population function and is part of relative frequency graph
Histogram used to plot the number of voids found verses the weight of the plastic injection molded part. One would expect the shape of distribution to be: a. normally distributed b. binomial distributed c. decreasing slope d. bimodal
Histogram used to plot the number of voids found verse the weight of the plastic injection molded part. One would expect the shape of distribution to be: a. normally distributed b. binomial distributed c. decreasing slope d. bimodal C- Correct. Not all histograms have normal distribution. In this case, the as the weight of the part increases, there would be fewer voids, or a decreasing slope. The number of voids is the X-axis and the part weight on the Y-asiz. Section VI-31 and logic
Historically, the number of flaws in the finish of surface has an average of 0.45. What is the probability of a randomly selected item having more than 1 defect in the surface finish?
Historically, the number of flaws in the finish of surface has an average of 0.45. What is the probability of a randomly selected item having more than 1 defect in the surface finish? Poisson distribution is used to model rates. The probability of r events occuring is computed: P (r) = ( mean ^ r) (e ^ -mean) / ( r !) r= 0 and mean = 0.45 give the probability of exactly zero defects: 0.6376 Entering r=1 and mean= 0.45 give probability of exactly 1 defects: 0.2869 Entering r=2 and mean= 0.45 give probability of exactly 2 defects: 0.6376 + 0.2869 = 0.9245 Probability of more than one defect is 1 - ( 0.9245 ) = 0.0755
Identify the distribution that presents the most difficulty in using tables directly to determine either probabilities or critical values: a. Posisson distribution b. Standard normal (z) values c. t-distribution d. binomial distribution
Identify the distribution that presents the most difficulty in using tables directly to determine either probabilities or critical values: a. Posisson distribution b. Standard normal (z) values c. t-distribution d. binomial distribution D= correct; Table for binomial distribution gets volunminous very rapidly. The other 3 options have tables that can provide proabilities or critical values for almost any conditions in one, tow, or three pages.
If 87 data observations from a process were to be plotted on a histogram, the rule of thumb would suggest how many intervals across the range of data?
If 87 data observations from a process were to be plotted on a histogram, the rule of thumb would suggest how many intervals across the range of data? Answer= 9 intervals Rule of Thumb= No. of Data intervals = square root of number of data observations Square root of 87 = 9.32
If X can be any random variable mean (mu) and standard deviation. (n) - random samples. As n increases, and as results of central limit theorem.... what happens to the distribution?
If X can be any random variable mean (mu) and standard deviation. (n) - random samples. As n increases, and as results of central limit theorem.... ---> Distribution of X-bar approaches a normal distribution with a mean (mu) and standard deviation (sigma / square root of n)
If a engineer or technician were to select samples from a mixture in a vat that is suspected of separation, what sampling technique would be advisable?
If a engineer or technician were to select samples from a mixture in a vat that is suspected of separation, what sampling technique would be advisable? Stratified sampling because the vat is suspected of not being homogenous.
If events A and B are independent, then: a. P (B/ A) = P (A) b. P ( A/B) = P (B) c. P (B/ A) = P (B) d. P (B/ A) = P (A) + P (B)
If events A and B are independent, then: a. P (B/ A) = P (A) b. P ( A/B) = P (B) c. P (B/ A) = P (B) d. P (B/ A) = P (A) + P (B) Answer= C If 2 events are independent, gaining information about one provides no information about the probability of the other event occurring. Thus, the probability of event B occurring given event A has occurred P (B/A) is the equal to the probability of event B occurring
If events cannot occur simultaneously they are called: a. Randomly selected b. Mutually exclusive c. Independent d. Statistically
If events cannot occur simultaneously they are called: a. Randomly selected b. Mutually exclusive c. Independent d. Statistically B= correct Random selection means that all elements available for selection have the same chance of being chosen. Independent events are those in which the occurrence of one does not affect the probability of the other. A process which yields 8 consecutive values above or below the mean is not considered statistically stable. Events are mutually exclusive if that can't happen at the same time.
If one were to compare short-term capability with long-term capability for the same process, what would be observed?
If one were to compare short-term capability with long-term capability for the same process, what would be observed? Short-term Cp is better Both the average and the variability changes over time
If process improvement ideas have been submitted for project selection. Unknown to the team, two of these ideas have the potential for breakthrough improvement. If your team selects 2 projects at random, what is the chance of picking both winners?
If process improvement ideas have been submitted for project selection. Unknown to the team, two of these ideas have the potential for breakthrough improvement. If your team selects 2 projects at random, what is the chance of picking both winners? Answer= 0.0095 P ( A ∩ B) = (2/ 15) (1/ 14) = 2/ 210 = 0.0095
If specification limits are wider than control limits, then : a. process is capable b. process capability index greater than 1.0 c. specification limits replace the control limits on chart d. none of above
If specification limits are wider than control limits, then : a. process is capable b. process capability index greater than 1.0 c. specification limits replace the control limits on chart d. none of above D= correct; No conclusion can be draw if sample size is unknown. ---see the formula for process capability which requests for sample size
If the probability of a car starting on a cold morning is 0.6, and we have two such cars, what is the probability of at least on of the cars starting on a cold morning?
If the probability of a car starting on a cold morning is 0.6, and we have two such cars, what is the probability of at least on of the cars starting on a cold morning? (A ∪ B) = P (A) + P (B) - P ( A ∩ B) (A ∪ B) = 0.6 + 0.6 - (0.6 * 0.6) = 1.2 - 0.36= 0.84 Answer = 0.84
If the probability of success on a single trial is 0.3 and two trials are performed, what is the probability of at least one success?
If the probability of success on a single trial is 0.3 and two trials are performed, what is the probability of at least one success? VII- 14/15 P= 0.3 P(r) = C ( 1-0) Classical binomial problem since the number of trials is small and probability is greater than 10%.....the above formula can be solved for zero occurrences and subtracted from one. Use the binomial table where the answer for zero occurences is listed as 0.490. Subtracting the value from 1 gives you 0.520 Sectin VII- 14/15
If the variance of a distribution of readings is 16. the standard deviation of the distribution is: ?
If the variance of a distribution of readings is 16. the standard deviation of the distribution is: ? S= Square root (variance) = Square root of 16= 4
In determining a process average fraction defective using inductive or inferential statistics, which of the following would be used. a. Statistics, computed from samples, to to make inferences about populations b. Populations, computed from samples, to to make inferences about populations c. Samples, computed from statistics ,to to make inferences about populations d. Samples, computed from populations, to to make inferences about populations
In determining a process average fraction defective using inductive or inferential statistics, which of the following would be used. a. Statistics, computed from samples, to to make inferences about populations b. Populations, computed from samples, to to make inferences about populations c. Samples, computed from statistics ,to to make inferences about populations d. Samples, computed from populations, to to make inferences about populations A= correct Question requires the review of answer options. In inferential stations, one is always making inferences about the populations. From the wording of the question, statistics computed from samples is a more logical choice.
In most cases, data should be collected in: a. statistical cormat b. Homoenous layers c. Time sequence.
In most cases, data should be collected in: Homogenous layers
In normal distribution, what is the area under the curve between 0.7 and 1.3 standard deviation units?
In normal distribution, what is the area under the curve between 0.7 and 1.3 standard deviation units? Z-value of o.7 and 1.3 must be looked up. 0.242 - 0.0968 = 0.1452
In order to calculate a performance index, what two factors must be known about the process?
In order to calculate a performance index, what two factors must be known about the process? Answer= Specification limits and standard deviation . Calculation of Performance Index: Pp = ( USL - LSL) / 6 *Sigam
In performing an analytical study, Which of the following statistical values would seldom be known? a. true critical value b. sample statistic c. true population parameter d. degree of uncertainty.
In performing an analytical study, Which of the following statistical values would seldom be known? a. true critical value b. sample statistic c. true population parameter d. degree of uncertainty. C= correct Person doing the analytical study would use sample statistic for comparison against the critical value for a predetermined degree of risk.
In the control stage of DMAIC, critical stains have been reduced from 73 to 1 per fabric roll. Which control chart should be used?
In the control stage of DMAIC, critical stains have been reduced from 73 to 1 per fabric roll. Which control chart should be used? Control chart based on Poisson distribution such as u-chart. Critical stains are defect counts which describes Poisson distribution
Interaction term in an R & R ANOVA indicates interaction between?
Interaction term in an R & R ANOVA indicates interaction between? Technician and part (Not technician and measurement error)
It is suspected that a process requiring a capability determination is not normal, but appears to be stable. The last action to , at this point would be to: a.advise the customer and request specification changes b. reduce variation to the point that it doesn't matter c. transform data to that of a normal distribution d. test the normality assumption using a chi-square test.
It is suspected that a process requiring a capability determination is not normal, but appears to be stable. The last action to , at this point would be to: a.advise the customer and request specification changes b. reduce variation to the point that it doesn't matter c. transform data to that of a normal distribution d. test the normality assumption using a chi-square test. A= correct. (B) is expenseive
How would one determine the ppm failure rate for normal distribution?
Look it up in a table such as standard normal table or six sigma failure rate
Define machine capability
Machine Capability = the inherent variation of the machine
Main purpose of Gage R & R is?
Main purpose of Gage R & R is? To determine how much of the total variation is due to measurement errors
Manufacturer of children's wagaons would like to visualize where the defects occur on the wagons. Defects encountered so far include missing bolts, paint, peeling, missing decals, cracked wood, bent metal parts. A useful tool would be: a. X Y matrix b. Measles chart c. Regression Plot d. Scatter diagram
Manufacturer of children's wagaons would like to visualize where the defects occur on the wagons. Defects encountered so far include missing bolts, paint, peeling, missing decals, cracked wood, bent metal parts. A useful tool would be: a. X Y matrix b. Measles chart c. Regression Plot d. Scatter diagram B= Measles cahrt
Measure for central location for nominal scale is called?
Measure for central location for nominal scale is called? Mode B/c the nominal scale is a very low level statistic
On average, a company hires 4 people per month. In a given month, what is the probability that exactly 7 people will be hired?
On average, a company hires 4 people per month. In a given month, what is the probability that exactly 7 people will be hired? Answer= 0.0595 This is Poisson Distribution. P (X) = ( e ^-u) (mean) ^x _______________ X! x= 7 and m=4 gives the probability that 7 people will be hired, 0.0595. Can also get this answer from Poisson table. In this case, np= 4. The probability of 7 or less minus the probability of 6 or less (0.889) yields teh answer 0.06
One would expect to capture measured quantitative data with which of the following tools? a. pareto b. cWQC c. histogram d. P-chart
One would expect to capture measured quantitative data with which of the following tools? a. pareto b. cWQC c. histogram d. P-chart A= correct; CWQC= company wides quality control
Pilot run of 100 units, indicated the Cpk upper value of 1.8 and lower value 0.9. Customer requires Cpk minimum value of 1.25. What action should be taken?
Pilot run of 100 units, indicated the Cpk upper value of 1.8 and lower value 0.9. Customer requires Cpk minimum value of 1.25. What action should be taken? Center the process.
Plus and minus 3 standard deviations includes 99.73% of all points of a normal distribution. How many standard deviations would include 99% of all points of a normal distribution?
Plus and minus 3 standard deviations includes 99.73% of all points of a normal distribution. How many standard deviations would include 99% of all points of a normal distribution? Area under the curve of 99% implies that 1% is not under the curve---> 1% split into two tails is 0.5% Z-value that corresponds to 0.5% is 2.575
Precision can be defined as
Precision can be defined as Agreement or closeness of the measurement of the same item
Probability of Steve passing Math is 0.7. Probability of passing History is 0.8. Probabily of passing both classes i 0.56. What of probability of passing either math or history?
Probability of Steve passing Math is 0.7. Probability of passing History is 0.8. Probabily of passing both classes i 0.56. What of probability of passing either math or history? 0.7 + 0.8 - (0.56)= 0.94
Probability that at least one defective in a random sample size of 10 drawn from a population that has been producing on the average. 10% defective units is?
Probability that at least one defective in a random sample size of 10 drawn from a population that has been producing on the average. 10% defective units is? Binomial probability calculation N= 10 r= 0 p= 0.1 P (r) =[ 10! / 0! (10-0 )! ] [ (0.1^0) (1- 0.1)^ 10-0] = 1 * 1 * (0.9 ^ 10) = Answer= 1 - (0.9^ 10)
Process capability analysis is defined as: a. ability to make the process reliable and maintainable b. inherent variability of items produced by the process c. Variability allowed by the specification limits d. The determination that the process can meet the product specifications as intended
Process capability analysis is defined as: a. ability to make the process reliable and maintainable b. inherent variability of items produced by the process c. Variability allowed by the specification limits d. The determination that the process can meet the product specifications as intended D= correct
Process capability index calculated for stable, non-automated process. then, operatior is told to check samples at random and making centering adjustments to the process. Results?
Process capability index calculated for stable, non-automated process. then, operatior is told to check samples at random and making centering adjustments to the process. Results? Process Capability got worse.
Why is process capability called a comparison between 2 independent worlds?
Process capability is the comparison between the world of specifications and the world of process spread Cp = (USL -LSL) / 6sigma = Specifications / Process Spread
Process is centered and Cp is 0.8. This indicates that the specification range is what % of process width?
Process is centered and Cp is 0.8. This indicates that the specification range is what % of process width? 80%
Process is turning out end items that have no defects of type A, type B, or both. If the probability of type a defect is 0.1 and type B is 0.2, the probability that end item will have no defects: a. 0.7 b. 0.3 c. 0.72 d. .68
Process is turning out end items that have no defects of type A, type B, or both. If the probability of type a defect is 0.1 and type B is 0.2, the probability that end item will have no defects: a. 0.7 b. 0.3 c. 0.72 d. .68 C= correct P (AUB) = P(A) + A(B) - P(A*B) P(success) = 1- (Pfailure) type A= 0.1 Type b= 0.2 Both= (0.1 * 0.2) = 0.02 Probability of defects = 0.1 + 0.2 - (0.2) = 0.28
Process map is used to accomplish which of the following? a. display dynamic picture of process performance behavior b. focus attention on process problems in priority order c. diagram possible problem causes in a process d. track products, operator actions, or administrative procedures
Process map is used to accomplish which of the following? a. display dynamic picture of process performance behavior b. focus attention on process problems in priority order c. diagram possible problem causes in a process d. track products, operator actions, or administrative procedures D= correct Process map is a graphical depiction of a process.---Used to track products, operator actions, or administrative procedures (A)= control Chart (B) = Pareto chart (C) = Fish diagram
Process map know as SIPOC provides team members an understanding of the process from the view of: a. floor level b. very high level c. customer d. very detailed level
Process map know as SIPOC provides team members an understanding of the process from the view of: a. floor level b. very high level c. customer d. very detailed level B= correct; SIPOC has high level view of only 4-7 stpes.
Process mapping of activities and systems is most helpful in detecting: a. ways to eliminate written procedures b. deficiencies in the organizational structure c. Holes or gaps in the control system d. Improper use of statistical methods
Process mapping of activities and systems is most helpful in detecting: a. ways to eliminate written procedures b. deficiencies in the organizational structure c. Holes or gaps in the control system d. Improper use of statistical methods C= Correct Process mapping is good to visualize the process and find weaknesses. Organizational chart is a better source for determining organizational deficiencies. Flow chart does not identify improper statistical methods.
Process specification limits are unknown and the Standard deviation = 1.0, which of the capabilities can be determined? A. Cr B. Cp C. Pr D None of above
Process specification limits are unknown and the Standard deviation = 1.0, which of the capabilities can be determined? A. Cr B. Cp C. Pr D None of above D= correct
Refer to the Venn Diagram in the answer side: If the probability of event A is 20%, the probability of event B is 30%, and the probability of event A intersecting event B is 8%, what is the probability of neither event?
Refer to the Venn Diagram in the answer side: If the probability of event A is 20%, the probability of event B is 30%, and the probability of event A intersecting event B is 8%, what is the probability of neither event? Answer= 58 % (A ∪ B) = P (A) + P (B) - P ( A ∩ B) (A ∪ B) = 0.2 + 0.3 - 0.08 = 42% Probability of neither event= 100% -42% = 58%
Referring from the equation below, if U and V are independent chi-square random variables with m and n degrees of freedom, then A: A= [ U/m] / [V / n]
Referring from the equation below, if U and V are independent chi-square random variables with m and n degrees of freedom, then A: A= [ U/m] / [V / n] If U and Va are independent chic-square random variables, the A follow F-distribution A= F distribution
Relationship between process capability target and product specifications?
Relationship between process capability target and product specifications? Process capability target is usally tighter than product specifications
Repeatability of an R & R study can be determined by examining the ?
Repeatability of an R & R study can be determined by examining the ? Variation between individual inspector and within their measurement readings
Reproducibility in an R & R study would be considered the variability introduced into the measurement system by:
Reproducibility in an R & R study would be considered the variability introduced into the measurement system by: Bias difference of different operator (change in instrument differences over the operating range, which actually defines linearity) Total measurement system variation include BOTH reproducibility and repeatability
When a single gage is checked by comparing the results of different operators taken at different times.....Term?
Reproducibility.
SIPOC process map provides a view of the process that contains how many steps?
SIPOC process map provides a view of the process that contains how many steps? 4-7 steps
Sample of means approaches normal distribution when: a. original distribution in normal b. Random sample variance approaches the population variance c. Sample size increases d. mean control chart demonstrates control
Sample of means approaches normal distribution when: a. original distribution in normal b. Random sample variance approaches the population variance c. Sample size increases d. mean control chart demonstrates control C= Correct
Sample of n observation has mean X-bar and standard deviation S(x) >0. If a single observation, which equals the value of the sample mean X-bar, is removed from teh sample, what is true. a. X-bar and S(x) both change b. X-bar and S(x) both stay same c. X-bar stays same and S(x) increases d. X-bar stays same and S(x) decreases
Sample of n observation has mean X-bar and standard deviation S(x) >0. If a single observation, which equals the value of the sample mean X-bar, is removed from teh sample, what is true. a. X-bar and S(x) both change b. X-bar and S(x) both stay same c. X-bar stays same and S(x) increases d. X-bar stays same and S(x) decreases Answer C---X-bar will not change when an observation equal to the average is removed. Sx must increase slightly according to the following formula: Sx= Square root of [sum of (X- mean) ^2] / Sample size minus 1) Number will not be affected in the above equation bu the denominator will become smaller (n-2) which causes S (x) to get larger
Scatter diagram used to plot the number of defects produced in a day verses the number of coffee the supervisor had that day. What can be concluded a. Supervisor should drink more coffee b. Supervisor will drink tea c. Nothin
Scatter diagram used to plot the number of defects produced in a day verses the number of coffee the supervisor had that day. What can be concluded a. Supervisor should drink more coffee b. Supervisor will drink tea c. Nothing One risk with scatter diagrams is that a relationship between two variables may appear to exist when in fact no relationship exists. Unless there is another information as to why the coffee consumptions has an influences on defects, we should not make any conclusions Section VI-- 31
Look up the formal for proabability of B occurring given that event A has occurred
See primer
Sequential sampling plans and ASN
Sequential sampling plans and ASN Sequential sampling plan have low ASN (average sample number) and samples are taken one item at a time. However, these plan are more complex and difficult to administer
Six sigma mean 3.4 ppm considering a shift in the mean of 1.5 standard deviations. What is the value of 6 sigma without the 1.5 standard deviations shift in the mean.
Six sigma mean 3.4 ppm considering a shift in the mean of 1.5 standard deviations. What is the value of 6 sigma without the 1.5 standard deviations shift in the mean. answer= 0.002 ppm A shift in the mean of 1.5 standard deviation s is an assumption that considers any processes natural tendency to loose capability over time. Using a normal disbribution tale, six sigma , without the 1.5 process shift, is 0.002
Some 10 production units are known to contain 3 defective units. If 2 units are inspected, what is the probability that both will be good?
Some 10 production units are known to contain 3 defective units. If 2 units are inspected, what is the probability that both will be good? N= 10 r= 3 defective units P= 0.3 of being defective P= 0.7 of being good P (A ∩ B ) = P (A) * P (BIA) P (A ∩ B) = ( 7/10) (6/9) = 42/ 90 = 0.467
See the curve for Standard normal distribution.---VII- 18
Standard normal distribution is a special case of normal distribution with mean of 0 and standard deviation of 1. Normal distribution is transformed into standard normal disbution using the formula--- Z= (X- mean) / Sigma
Student t-test is applicable when a. collecting attribute data b. limited measured data c. sample sizes of 100 or greater d. comparing population variances
Student t-test is applicable when a. collecting attribute data b. limited measured data c. sample sizes of 100 or greater d. comparing population variances B- correct; (D) = F-distribution t- distribution deals with small samples of measured data. For measured data with large sampe sizes, the standard normal Z-table is ussed.
Suppose that 5 bad electron tubes are mixed with 8 good tubes. If 2 tubes are drawn simultaneously, what is the probability that both are good?
Suppose that 5 bad electron tubes are mixed with 8 good tubes. If 2 tubes are drawn simultaneously, what is the probability that both are good? Answer= 14/ 39 Multiplicative Law of Probability: P ( A ∩ B) = P (A) * P (B) Although both samples are drawn simultaneously, the two events are dependent and analyzed as if the tubes were drawn sequentially. P ( A ∩ B) = ( 8/ 13) * (7/ 12) = 56/ 156 = 14/ 39
The Poisson distribution can be used to approximate the binomial distribution under which of the following conditions?
The Poisson distribution can be used to approximate the binomial distribution under which of the following conditions? When p is equal or small than 0.1 and the sample size is large..
The average number of flows in a large plate glass is 0.25 per pane. Standard deviation of the Poisson distribution is: ??
The average number of flows in a large plate glass is 0.25 per pane. Standard deviation of the Poisson distribution is: ?? Answer= 0.5 _ C = Poisson average _ Poisson sigma= square root of C = square root of 0.25= 0.5
The care you drive to work has a 90% chance of starting in the morning . It is blocked by your spouse's car which has an 80% chance of starting. Both cars are blocked by your son's car which has 70% chance of starting. What is the probability of getting to work in your car?
The care you drive to work has a 90% chance of starting in the morning . It is blocked by your spouse's car which has an 80% chance of starting. Both cars are blocked by your son's car which has 70% chance of starting. What is the probability of getting to work in your car? Answer= 0.504 P ( A ∩ B ∩ C ) = P (A) * P (B) * P (C) 0.504 = 0.9 * 0.8* 0.7
The distribution of a characteristic is negatively skewed. The sampling distribution of the mean for large samples, taken from the same distribution is_____?
The distribution of a characteristic is negatively skewed. The sampling distribution of the mean for large samples, taken from the same distribution is_____? Approximately Normal = Answer Question requires a review of the answers in light of the central limit theorem. The central limit theorem states that the sample means will be more normally distributed around the mean than individual readings (X's). As n increases, the X means approach a normal distribution with mean "mu"
The distribution that has a mean equal to the variance is the: ???
The distribution that has a mean equal to the variance is the: ??? Answer= Poission _ Poisson Average= mu = (N * P) = C _ Poisson Variance = σ2= u = (n * p-bar) = C
The equation for joint probability , of 2 accident events under any circumstance is given by " P (A I B) = P (AIB) X (P(B) If fault A does not enhance occurrence of fault B in any way, the probability of accident, when P(A) = 0.1, P(B) = 0.05 is given by?
The equation for joint probability , of 2 accident events under any circumstance is given by " P (A I B) = P (AIB) X (P(B) If fault A does not enhance occurrence of fault B in any way, the probability of accident, when P(A) = 0.1, P(B) = 0.05 is given by? Example of multiplicative law of probability where event A and event B are independent. P (A ∩ B ) = (PA) (PB) = 0.1 * 0.05= 0.005
Three types of checklists
Three types of checklists? 1) Measles chart--locational data 2) checklists---counted data 3) Recording checklist---measured data
Two constant values are often used to calculate P/T AND P/TV ratios. What is the origin of the values 6 and 5.15 in the ratio calculations ?
Two constant values are often used to calculate P/T AND P/TV ratios. What is the origin of the values 6 and 5.15 in the ratio calculations ? They represent 99.73% and 99% of total population of measurements, assuming normality. Assuming normality, 6 represents 3 standard deviations or 99.73% and 5.15 represents +/- 2.575
Two micrometers are used to measure the same quality characteristic (thickness in this case). The mircometer at headquarters has ore decimal places than the one being used at the plant. The mircrometer at headquarters is more: a. accurate b. precise c. advanced d. sensitive
Two micrometers are used to measure the same quality characteristic (thickness in this case). The mircometer at headquarters has ore decimal places than the one being used at the plant. The mircrometer at headquarters is more: a. accurate b. precise c. advanced d. sensitive C= correct; Accuracy refers to the comparison with a standard making (a) wrong. Precision refers to the ability to repeat measurements making (b) wrong.
Use the data below Raw data= 307, 309, 310, 315, 310 Coded data = 7,9,10,15,9, 10 What is the X-bar?
Use the data below Raw data= 307, 309, 310, 315, 310 Coded data = 7,9,10,15,9, 10 What is the X-bar? Average of the raw data is 10. Average of coded data is 10. True X-bar should be expressed in the same terms as the raw data. Considered the coded data average to be X-bar- C (where C is consant) Answer= 310 Section VI-17
Variances given" Tech = 0.05 Part= 0.4 Error= 0.15 Waht si the ratio of the total gage R &R variation? Use straight ANOVA
Variances given" Tech = 0.05 Part= 0.4 Error= 0.15 Waht si the ratio of the total R &R variation? Use straight ANOVA Answer -= 0.333 Total gage R &R variation is technician variance (0.05) which is the reproducibility added to measurement error of 0.15 (repeatability) divided by the toatl variance of 0.6
What distribution is normally used to model rates?
What distribution is normally used to model rates? Poisson Distribution
What graphical data method can show the value of all individual readings?
What graphical data method can show the value of all individual readings? Stem-and- leaf plot Histogram has grouped data. Complex box plot show many data features but individual readings is not among them
What is an improper action when ensuring data accuracy and integrity?
What is an improper action when ensuring data accuracy and integrity? Removing data based on a firm hunch that is false
What is mandatory when conducting a process capability study consistent with PPAP requirements?
What is mandatory when conducting a process capability study consistent with PPAP requirements? Data collected from a significant production run of 300 or more or consecutive pieces.
What is the danger of using the formula: sigma (t) = R-bar / d2 to determine standard deviation to use in calculating capability index?
What is the danger of using the formula: sigma (t) = R-bar / d2 to determine standard deviation to use in calculating capability index? Factor d2 works when the process is in control and most processes aren't
What is the difference between Coifficient of determination and correlation coifficent?
What is the difference between Coifficient of determination and correlation coifficent? Regression analysis == correlation coifficient.
What is the difference between central tendency statistics and Dispersion statistics?
What is the difference between central tendency statistics and Dispersion statistics? Dispersion statistics----how precise data is Central tendency statistics ----how accurate data is
What is the practical difference between the precision/ tolerance ration (P/T ration) and the precision/total variation ration ( P/TV ration) a. P/T ratio and P/TV are practically same. b. P/T ratio gives a better picture of the measurement precision for internal improvement studies while P/TV ratio is better for evaluations relative to specifications. c. P/T ratio gives a better picture of the measurement precision relative to specifications while the P/TV ratio is better fro internal improvement studies. d. The combined P/T and P/TV ratios should equal one in order to achieve a better understanding of the measurement system analysis results.
What is the practical difference between the precision/ tolerance ration (P/T ration) and the precision/total variation ration ( P/TV ration) a. P/T ratio and P/TV are practically same. b. P/T ratio gives a better picture of the measurement precision for internal improvement studies while P/TV ratio is better for evaluations relative to specifications. c. P/T ratio gives a better picture of the measurement precision relative to specifications while the P/TV ratio is better fro internal improvement studies. d. The combined P/T and P/TV ratios should equal one in order to achieve a better understanding of the measurement system analysis results. C= correct----- The denominators of both ratios have different origins. Only in those cases where the capability index is 1 will the P/T ratio be the same. P/T ratio provides better analyses of the measurement system relative to specifications, with the P/TV ratio is more of an internal measure.
What is the practical result of combining a normal random variable and chi-square variable?
What is the practical result of combining a normal random variable and chi-square variable? Small samples can be used to make robust inferences about population means---which describes the t-distribution and its ability to make robust conclusions using small samples
What is the practical use of F-distribution?
What is the practical use of F-distribution? To study the equality of two variances
What is the probability of finding no defective items in a random sample of 100 items taken from the output of a continuous process which averages 0.7% defective items?
What is the probability of finding no defective items in a random sample of 100 items taken from the output of a continuous process which averages 0.7% defective items? S= 100 r= 0 P (0.03) The answer can be determined with Poisson table (n) (p)= (100) (0.7)= 0.487
What is the relationship among mean, median, and mode for normal distribution curve?
What is the relationship among mean, median, and mode for normal distribution curve? Mean= Median= Mode
What is the relationship between the sum of the exponents and binomial equation?
What is the relationship between the sum of the exponents and binomial equation? Answer----> Sum of the exponent sof each term after expansions equal to sample size
What percentage of the area under the standard normal curve is included under the curve within 1.5 deviation from zero?
What percentage of the area under the standard normal curve is included under the curve within 1.5 deviation from zero? Area between z= 1.5 and z= -1.5 is 0.9332 - 0.0668 = 0.8664 Answer = 0.8664
When P (A | B) = P (A) , then : a. Event A and B are independent b. Event A and B are dependent c. Event A and B are mutually exclusive d. Event A and B are compliments
When P (A | B) = P (A) , then : a. Event A and B are independent b. Event A and B are dependent c. Event A and B are mutually exclusive d. Event A and B are compliments B= correct Probability shorthand in the question states the proability of event A, given that event B has occurred, no longer equals the probability of A. this must mean that event B an dthe two evens
When a process is not centered relative to specifications, how is the Cpk affected?
When a process is not centered relative to specifications, how is the Cpk affected? Answer= Cpk is the smalled value of the either Cpk upper or Cpk lower
When comparing short term machine capability indexes to long term process capability indexes, what can one expect?
When comparing short term machine capability indexes to long term process capability indexes, what can one expect? Answer= Process capability will be a loer number. This question is referring to capability index. In this calculation, a higher number indicates greater capability. The long term process capability would be expected to be a lower number than short term capability
When considering a quality characteristic for process capability calculations, a green belt should consider which of the following: a. Chose the characteristics with the highest process capability index ratios b. Chose a small number of customer defined CTQ characteristics c. Choose only normal characteristics to comply with the normality assumption d. choose all characteristics defined in these procedures and work instructions.
When considering a quality characteristic for process capability calculations, a green belt should consider which of the following: a. Chose the characteristics with the highest process capability index ratios b. Chose a small number of customer defined CTQ characteristics c. Choose only normal characteristics to comply with the normality assumption d. choose all characteristics defined in these procedures and work instructions. B= correct. The chosen characteristic should reflect key product or process quality factors.
When performing calculation on sample data: a. continuous relative frequency graph is created b. rounding the data has no effect on the mean and standard deviation c. coding the data has no effect on the mean and standard deviation d. coding the data has effect on both mean and standard deviation
When performing calculation on sample data: a. continuous relative frequency graph is created b. rounding the data has no effect on the mean and standard deviation c. coding the data has no effect on the mean and standard deviation d. coding the data has effect on both mean and standard deviation D= correct. Coding data will affect the mean to the extent that mean must be uncoded fro reporting purposes.
When the natural process limits are greater than the specification range, which of the actions involves the customer? a. changing the specifications b. centering the process c. reducing the variability d. accepting the losses
When the natural process limits are greater than the specification range, which of the actions involves the customer? a. changing the specifications b. centering the process c. reducing the variability d. accepting the losses A= correct. All are good options but accepting looses is not desirable.
When using Poisson as an approximation to the binomial, which of the following conditions apply for the best approximation?
When using Poisson as an approximation to the binomial, which of the following conditions apply for the best approximation? Poisson is an approximation to the binomial distribution when the probability of occurrence is equal to or less than 0.1 and the sample size is large. Smaller the fraction defective and the larger the sample size, the better the approximation.
Which MSA methods allows the interaction between operators and parts to be determined? a. ANOVA method b. Average and Range method c. Interaction method d. Range method
Which MSA methods allows the interaction between operators and parts to be determined? a. ANOVA method b. Average and Range method c. Interaction method d. Range method A= correct; ANOVA method is the most accurate method for calculating repeatability and reproducibility. Not only doe it include the other two formal methods (Range method and Average and Range method) but it also allows for a determination ofthe interaction between appraisers and parts. Interaction method is a distractor
Which distribution is most appropriate for modeling the number of surface defects on a drive?
Which distribution is most appropriate for modeling the number of surface defects on a drive? Poissian distribution--because it modls rates such as the number of defects per disk drive or number of defect per autonobile and is a discret distribution with its expected value equal to its variance
Which measure of variability is independent of exact value of every measurement? a. Mean deviation b. variance c. range d. standard deviation
Which measure of variability is independent of exact value of every measurement? a. Mean deviation b. variance c. range d. standard deviation C= correct; Variance, mean, deviation, and st. deviation requires the exact value for every measurement. Range requires the exact values for highest and lowest measurements only.
Which of the distribution models events have 2 possibilities on each trial? a. normal b. poisson c. binomial d. Gamma
Which of the distribution models events have 2 possibilities on each trial? a. normal b. poisson c. binomial d. Gamma C- correct; Outcome from a Bernoullie trial has 2 possibilities, usually success or failure, as shown in bionomial distribution
Which of the following distribution have their x- axis starting at zero a. normal and t b. normal and chi-square c. chi-square and F d. F and t
Which of the following distribution have their x- axis starting at zero a. normal and t b. normal and chi-square c. chi-square and F d. F and t C= correct. Negative values have no meaning in either of these two distributions.
Which of the following is likely to create process shifts? a. new measuring device b. gradual tool wear and heat build up c. reduction in defective level due to kaizen technique d. small increase in state gasoline taxes
Which of the following is likely to create process shifts? a. new measuring device b. gradual tool wear and heat build up c. reduction in defective level due to kaizen technique d. small increase in state gasoline taxes A= correct; Process shift is due to rapid shifts in the process pattern being plotted like a change in crew (machine setting) or change in method/ measuring device
Which of the following is necessary assumption to validate the meaning of the standard deviation of the measurement variability? a. Measurement errors are independent b. Measurement scale is normally distributed c. Measurement errors are independent of the operators involved in the study d. Measurement errors are skewed in the direction of nornality
Which of the following is necessary assumption to validate the meaning of the standard deviation of the measurement variability? a. Measurement errors are independent b. Measurement scale is normally distributed c. Measurement errors are independent of the operators involved in the study d. Measurement errors are skewed in the direction of normality A= correct The valid assumptions for standard deviation due to the measurement variability are: (1) Measurement errors are independent (2) Measurement errors is normally distributed (3) Measurement errors are independent on the magnitude of the measurement.
Which of the following statement is most applicable to trend analysis? A. experience is required for proper interpretation b. bar charts are more informative than run charts c. most applications should be reflected as an improvement percentage d. An improving trend is an indication of corporate survival
Which of the following statement is most applicable to trend analysis? A. experience is required for proper interpretation b. bar charts are more informative than run charts c. most applications should be reflected as an improvement percentage d. An improving trend is an indication of corporate survival A= correct b and C may be correct or incorrect dependent upon the subject being charted. (D) is correct but not ALWAYS true. Experience and recognition of fallacies are important in trend analysis. VI--33/34
Which of the following statements is true about a sample of 10 units taken from a population? a. standard deviation is greater than the variance b. range is greater than standard deviation c. sigma estimate cannot be determined d. no estimate of population average is possible
Which of the following statements is true about a sample of 10 units taken from a population? a. standard deviation is greater than the variance b. range is greater than standard deviation c. sigma estimate cannot be determined d. no estimate of population average is possible B= correct C and D are untrue Variance is standard deviation squared
Which of the following statistical term statements is correct? a. parameters come from samples b. samples come from statistics c. statistics come from samples d. populations comes from statistics
Which of the following statistical term statements is correct? a. parameters come from samples b. samples come from statistics c. statistics come from samples d. populations comes from statistics C= correct. Parameters are tur population values, most often unknown, while statistics are population estimates that come from samples.
Which of the number sets are mutually exclusive? a. 1,2,3, and 2,4,6, b. 2,4,6 and 1,3,5, 7 c. 1,3,5,7 and 5,7,8.9 d. 1,2,3,4,5,6,7,8, snf 3,8
Which of the number sets are mutually exclusive? a. 1,2,3, and 2,4,6, b. 2,4,6 and 1,3,5, 7 c. 1,3,5,7 and 5,7,8.9 d. 1,2,3,4,5,6,7,8, and 3,8 B= correct; Mutually exclusive is when they have no elements in common
Which quality tool displays large amounts of numeric data to show a static picture of process behavior?
Which quality tool displays large amounts of numeric data to show a static picture of process behavior? Histogram
Why are scatter diagrams useful in problem solving?
Why are scatter diagrams useful in problem solving? They show relationships between variables
Why is the normality assumption essential to the interpretation of the capability index?
Why is the normality assumption essential to the interpretation of the capability index? Answer= Because the normal distribution always has a mean equal to zero The meaning of the capability index comes from the fact that the specification limits is being compared with 99.73% of all possible outputs for the process represented by a process spread of 6 standard deviations. The comparison is meaningless if the process distribution is not normal.
With Gage R & R, the error is usually due to what?
With Gage R & R, the error is usually due to what? Error can be determined if they are due to measurement errors.
