Knowledge Check Section II
If a sample variance is 9, what is the standard deviation 1. 81 2. 3 3. 9 4. 6
2. 3
You are asked to collect data to help with the decision of switching suppliers of a critical component to your company's product. What level of significance should you set beforehand so you have a high degree of confidence in your decision? 1. 0.01 2. 0.5 3. 0.95 4. 0.05
1. 0.01... By selecting a small significance level as your threshold for decision making, you help ensure that the data will provide a proven decision.
A process produces a part tht is 5 inches wide on average, with a standard deviation of 0.06 inches. The customer is accept parts 5 =/- 0.15 inches. What percentage of product will be scrapped? 1. 1.24 % 2. 0.62 % 3. 99.38 % 4. 98.76 %
1. 1.27 %... Z lower = (4.85-5.00)/(0.06) = -2.5 Z upper + (5.15-5.00)/(0.06) = 2.5 Z of -2.5 (from the table) = 0.0062 Z of 2.5 from the table = 0.9938. Since we want the upper tail, 1 - 0.9938 or 0.0062. Adding the lower percentage scrapped (0.0062) = 0.0124, therefor 1.24 % of product will be scrapped.
Determine the mean of the following data set: 26, 25, 52, 2, 31, 7, 24, 31, 27 1. 25 2. 31 3. 26 4. 27
1. 25... 26+25+52+2+31+7+24+31+27/9 = 25
A set of gauges contains 34 blocks. How many four -stack combination sets exist? 1. 1,113,024 2. 46,376 3. 1.23 X 10 to the 37th power 4. 136
1. 46,376... lower 34Clower4 = 34! = 46376 4!(34-4)
If the quality characteristic plotted on an attributes control charts became less important to the customer, which management action would most likely be taken first? 1. Change the corrective action plan for out-of-control points 2. Eliminate the control chart 3. Reduce the sampling/measurement frequency 4. Reduce the control chart with periodic process audit
1. Change the corrective action plant for out-of-control points.
Which of the following represents a data plotting technique? 1. Control charts 2. A check sheet used by a quality inspector 3. Estimating measure of central tendency of a data set 4. Estimating measure of dispersion of a data set.
1. Control charts
If you increase the sample size n when constructing a confidence interval estimate, what happens to the width of the interval? 1. it decreases in size 2. It increases in size 3. It changes the confidence level 4. It remains unchanged
1. It decreases in size... Since n is in the denominator, the width of the interval decreases as the sample size increases.
A technician is asked to collect data on a product for vendor qualifications along with some parameter estimates. What would be one of the first things that technician has to decide in order to get a good sample of product? 1. Level of significance 2. Confidence level 3. Confidence interval 4. Confidence coefficient
1. Level of significance... The level of significance is used in hypothesis testing
Which of the following is a continuous distribution that can be used for both positive and negative values of a continuous variable? 1. Normal distribution 2. Weibull distribution 3. Poisson distribution 4. Binomial distribution
1. Normal distribution
A manufacturer inspects one in every 20 units produced. which of the following would best describe those units that are being pulled for inspection? 1. Sample 2. Statistic 3. Parameter 4. Population
1. Sample
Which of the following is likely to be true if the variance is large? 1. Several data points in the set are distant from the mean 2. The standard deviation in the data set is small 3. The mean of the data set is large 4. The sum of squared differences is divided by the number of values in the set
1. Several data points in the set are distant from the mean. Part of the formula is (xi-funny m)squared, so if several of the points are distant from the mean, the variance will be larger.
Which of the following best describes the mean? 1. The mathematical average of a data set 2. The most frequently occurring value in a data set 3. The middle value in a ordered data set 4. The highest point in a distribution
1. The mathematical average of a data set
Why might the Poisson distribution be a good choice for modeling accident data? 1. The occurrences of accidents are independent of each other 2. Some accidents result in more serious injuries that others 3. The probability of an accident is at least 70% 4. The record system for accidents contains errors
1. The occurrences of accidents are independent of each other... The Poisson distribution assumes the occurrences of events are independent of each other. This is the most critical assumption.
A technician measures calls and then plots them on a chart over the week to identify call times that are longer than normal. Plotting the calls to identify abnormal conditions is an example of which of the following statistical terms? 1. Population 2. SPC 3. Parameter 4. Statistic
2. SPC... SPC uses the idea of a visual control to plot abnormal conditions.
What would be a common Z-value that is used in the creation of a confidence interval estimate? 1. 1.96 2 . a/2 3. 95 % 4. 3sigma or funny looking o
1. 1.96... This is a very common value for Z.
What is the standard deviation of the following data set? 54, 44, 74, 10, 48, 51, 50, 55 1. 64 2. 48.5 3. 322.86 4. 17.97
4. 17.97 look at this closer does not match with doing it on the computer
A technician would like to create a confidence interval around the length of a part. What does the confidence level denote? 1. The percentage of created confidence intervals from repeated sampling that would contain the true mean 2. The percentage of samples to take from the population to estimate the confidence interval 3. How certain the technician can be that the true mean is in the calculated confidence interval 4. How confident the technician can be about the limits of the confidence interval
1. The percentage of created confidence intervals from repeated sampling that would contain the true mean.
What is the intent of measuring the range or the standard deviation when using control data? 1. To measure process variability 2. To ensure constant subgroups 3. To study the average of the ranges 4. To measure process output
1. To measure process variability
How might an attributes control chart be used to best assess the performance of auditors? 1. To provide evidence of consistent judgment between auditors 2. To prove the effectiveness of corrective actions 3. To prove new trainees are qualified as auditors 4. To support the claim that proper safety rules were observed on audits.
1. To provide evidence of consistent judgment between auditors...the basic purpose of a control chart is to provide evidence of a consistent process over time.
Which of the following situations describe a "hugging" pattern control chart? 1. Various points on a control chart sticking close to the control limits. 2. Seven or more consecutive points increasing or deceasing 3. One or more points outside the control limits 4. Several consecutive points either above or below the mean
1. Various points on a control chart sticking close to the control limits.... various points sticking around the mean or the control limits is called a hugging pattern.
A quality technician takes a sample of products produced over a period of a week and measures them. The aggregated result from this inspection is best described as.. 1. a statistic 2. a parameter 3. a population 4. statistical process control (SPC)
1. a statistic
A part hisortically has an average diameter of 10.5 inches with a standard deviation of 0.25 inches. What percentage of parts will measure less that 9.8 inches? 1. 75.80 % 2. 0.26% 3. 0 24.2% 4. 99.81%
2. 0.26% You need to first calculate the z-value. Looking up the z-vailue in the tables, -2.8+0.00026. There is a 0.26% probability of a part measurein less that 9.8 inches Z = (938-10.5)/0.25 = -2.8
Determine the mode of the following data set: 0, 7, 6, 10, 11, 9, 14, 21, 3, 13, 25, 16, 14, 8, 23 1. 13 2. 14 3. 12 4. 11
2. 14... ..since 14 occurs more that once, while none of the other values do
Determine the median of the following data set: 19, 17, 13, 19, 25, 35, 48, 20 1. 20 2. 19.5 3. 19 4. 24.5
2. 19.5... When we put the values in numerical order, we get 13, 17, 19, 19, 20, 25, 35, 48. Since the data set has an even number of values, we take the mid point between the two values in the middle, 19 and 20 which is 19.5.
An ice cream manufacturer is analyzing a sample of 200 cartons for E. colie contamination. In the sample, three cartons have tested positive for E. Coli growth over the industry safe limits. If five cartons are randomly selected from the sample, what is the probability that texactly one carton contains dangerous E.colie colony counts? 1. 7,423,481.04 2.2535,650,040.00 3 0.0015 4. 4.183x10 to the neg 9th power
2. 2,535,650,040.00
Select which answer is the mode given the data set below: 0, 2, 2, 4, 5, 6, 7, 8, 9, 11 1. 5 2. 2 3. 6 4. 4
2. 2... 2 is the most often occurring number, which is the mode
What three color set combinations (arrangement matters) can be formed from a bin containing 30 pegs of three colors, each color represented by 10 pegs. 1. 720 2. 24,360 3. 27,000 4. 4,060
2. 24, 360 nP to the lower 1 = n!/(n-r)! lower 30Plower = 30!/(30-3)! = 24,360
What is the variance of the following data set? 23, 56, 64, 48, 47, 30 1. 15.5 2. 240.7 3. 41 4. 44.7
2. 240.7 look at this closer--not matching up with internet calculator
If the confidence coefficient is 10%, then the confidence level is: 1. 80 % 2. 90 % 3. 10% 4. 0.1%c
2. 90 %... The confidence level is the complement of the confidence coefficient (1-0.1 = 0.90, or 90 %)
A company instates 100 % inspection of critical space program part. All the parts inspected are best described as 1. a paramter 2. a population 3. a statistic 4. a sample
2. A population
Of the following process capability measures, which best represents a process capable of meeting customer specifications with a value of less than 1? 1. Cpm 2. CR 3. Cpk 4. Cp
2. CR....the Capability Ratio is the inverse of Cp. This is an indication of less area between the specification limits being consumed by random variation.
Which of the following describes a limitation of data plotting? 1. Data plotting techniques are not easy to implement in day to day work 2. Charts and graphs can only provide a general idea about process behavior and trends 3. data plots have to be made to similar scales for all process 4. Data plots cannot be used to communicate business performance
2. Charts and graphs can only provide a general idea about process behavior and trends.
What is the term used for the highest and lowest calculated value of a process capability? 1. Specification limits 2. Control limits 3. Process constraints 4. Sigma Level
2. Control Limits---they depict the normal operating capability of the process.
Which of the following describes an advantage of data plotting? 1. It can be used regardless of user objective 2. It can help in predicting future performance of processes 3. Non of these 4. It can be implemented with out specialized software
2. It can help in predicting future performance or processes
Which of the following words best describes special cause variation? 1. Natural 2. Sporadic 3. Predictable 4. Inherent
2. Sporadic... Special causes appear every now and then in the process and are not constantly present in the process.
What is the name given to the set of general rules used in interpreting variable chart data? 1. The End Zone Rules 2. The Western Electric Zone Rules 3. The Constants Rules 4. The Control Chart End Zone Rules
2. The Western Electric Zone Rules
A delivery company states they will deliver pizza within 30 minutes. They take a sample of 40 deliveries and determine the average timer of a delivery is 25.6 minutes with a standard deviation of 1.7 minutes. What are the lower and upper confidence limits for the true average delivery time at a 95 percent confidence level? 1. (24.91, 26.29) 2. (25.52, 25.68) 3. (25.07, 26.13) 4. (22.2, 29)
3. (25.07, 26.13)... Looking up 0.025 and 0.975 in the Z tables, we come up with a coefficient of 1.96. The formual to calculate a confidence interval is: located in the book!
The specification for a part is 5.5 inches+/-. An engineer uses a control chart to confirm the process is in statistical process control, and then takes 30 samples from the process three items at a time. Then sample avg is calculated as 5.5 inches and average range is calculated as 0.06 inches. What is the capability ratio of this process? 1. 1.77 2. 4.76 3. 0.21 4. 0.36
3. 0.21... SD= R-bar/d2 SD= 0.6/1.693 (d2 where subgroup size is 3) SD = 0.0354 CR = (6*SD)/(USL-LSL) CR = (6*0.0354)/(6-5) CR = (0.2126)/(1) CR = 0.2126
A process is producing 2.4 % defective parts on average. What is the probability of detecting one of more defective parts in a sample of 30 items? 1. 0.4825 2. Cannot be calculated since the process average is not binomial. 3. 0.5175 4. 0.3559
3. 0.5175... The formula to calculate this is P(0 defects) = 30!/0!(30-0)! 0.024the the 0 power (1-0.024) to the 30-0 power = 0.4825 The question is asking for 1 or more, so we need to subtract this from 1 (100%): 1.-0.4825 = 0.5175
What is the range of the following data set: 25, 45, 45, 67, 33, 28, 45 1. 41 2. 14.4 3. 43 4. 207.7
3. 43... Identify the largest and smallest numbers in the dat set and subtract the smallest from the largest. (67-24 = 43)
Which confidence level will most likely contain the true parameter on repeated samplings. 1. 90 % 2. 5 % 3. 95 % 4. 10 %
3. 95%
A confidence interval is an estimate of the interval between tow statistics that includes the true value of a parameter. Which interval below would have a better chance of including the true value of a parameter within? 1. 90 % confidence interval 2. 95 % confidence interval 3. 99 % confidence interval 4. 5 % confidence interval
3. 99 % confidence interval... The higher the confidence interval the wider the confidence is to potentially contain the true value of a parameter.
The Cpk for a process cannot be computed because the process is not in control. The process has produced no defective product for an extended period of time. What is the best action to do next? 1. The process should be brought in control so Cpk can be calculated. 2. The process should be watched for signs of possible future problems 3. Attention should move to a process producing defective product 4. The process should be brought into control to make it easier to manage
3. Attention should move to a process producing defective product.... Taking care of that next is a good idea while still devoting time and resources to the longer-term options.
What probability distribution would be used to test whether a coins is fair? 1. Normal 2. Weibul 3. Binomial 4. Poisson
3. Binomial... binomial distribution is a model for binary events like a coin toss.
What attribute chart type is used to track the number of defects per unit versus the number of defective units? 1. u chart 2. np chart 3 c chart 4. p chart
3. C chart... it tracks the number of defects versus the number of defective units as in a p chart.
Which of the following is anther reference for data plot? 1. Gauge R&R 2. Analysis of variance 3. Graph 4. Least squares regression
3. Graph... A graph is also a visual representation of data
What is a characteristic of a parameter? 1. It is likely to be exactly the same value as a statistic 2. It is an estimate of the true value of the parameter 3. It is calculated using all of the data from the population 4. It is often less expensive to capture than the statistic
3. It is calculated using all of the data from the population... In order to calculate the parameter, we would have to take a census of the population. A statistic is not calculated based on the underlying perameter, but is an estimate for the parameter.
Which of the following words best describes common cause variation? 1. Sporadic 2. External 3. Stable 4. Unpredictable
3. Stable.... A process is called stable if it has only common cause variation.
The height of a an average man in the US is 5 feet 9 1/2 inches. A scientist measures the height of 300 randomly selected people and calculates an average height of 5 feet 8 inches. Which of the following statistical terms best describes the avg. height the scientist calculated. 1. Parameter 2. Sampling error 3. Statistic 4. Sample
3. Statistic
Which of the responses below is the best definition of the grand average (X double bar)? 1. The average of tall the data put together 2. The largest average of the subsets 3. The average of all the subset averages 4. The average of the range and x-bar
3. The average of all the subset averages.
A process has a Cp of 1.13. Which of these describes the most likely interpretation of this value? 1. The process is not centered on the target specification. 2. The process has a standard deviation of 1.13 3. The process is not capable of consistently meeting specifications 4. The process is not within statistical process control
3. The process is not capable of consistently meeting specifications.
Which of the following applies to specification limits? 1. Used to demonstrate whether the process is in statistical control 2. Calculated from data collected through the process 3. Used to determine if the parts meet conformance limits 4. Consider the range of variation between each part produced
3. Used to determine if the parts meet conformance limits.
How many subsets of the data are typically necessary to consider a study to be statistically significant? 1. >11 2. It depends on the process 3. 20 4. n=4
3.20.....this is not a fast rule but is accepted by most.
An arrival rate at a toll both is eight cars every 10 minutes on average. What is the probability of two cars arriving within four minutes? 1. 0.2707 2. 0.0107 3. 0.1465 4. 0.2087
4. 0.2087... To get the correct answer, we need to compare the process average ( eight cars per 10 min) to the same rate as the question ( how many cars per four mins): (8cars)/(10mins) = funny looking m/(4 min) funny looking m = 3.2 P(x) = (funny mto the x power times e to the neg funny power/x! P to the lower (x) = 2 = (3.2 squared * e to the -3.2 power) / 2! = 0.2087
Which is the following is an example of special cause variation? 1. Arrival rates of cars at a toll both 2. Changes in daily mileage or a car 3. Fluctuations in the pulse rate of a healthy person 4. A computer crash
4. A computer crash... This is a sporadic event caused by an eternal factor.
Which of the following cases indicates an out-of-control process? 1. A control chart showing all points within upper and lower control limits 2. A hugging pattern of points in a control chart 3. A control chart showing points increasing and decreasing alternately 4. A single point outside the upper control limit of a control chart
4. A single point outside the upper control limit of a control chart... A point outside control limits indicates the presence of special causes, which means the process is out of control.
What is another term that can be used for putting a range around the estimate of the population mean? 1. Point estimate 2. Hypothesis testing 3. Significance level 4. Confidence interval estimate
4. Confidence interval estimate
If a process has a Cp of 1.60, what is the value of Cr and what does it mean? 1. Cr = 1.60 and extensive product inspection is required 2. Cr = 1.60 and extensive product inspection should not be required 3. Cr = 0.625 and extensive productions inspection should not be required. 4. Cr = 0.625 and extensive product inspection should not be required.
4. Cr = 0.265 & extensive product inspection should not be required... The natural process variation consumes 62.5% of the distance between the spec. limits. There is considerable room for drift without risking out-of-specification product. Extensive product inspection to screen out defects should not be required.
Which is most likely a source of common cause of variation? 1. New machine operator 2. Equipment part change 3. Undefined product requirements 4. Gauge drift up and down
4. Gauge drift up and down... Common cause variation is the remaining variation after removing the special causes (non-normal causes) due to one or more of the 6Ms (manpower, Mother Nature, materials, method, measurements, or machine).
What is the fastest way to design a corrective plan for an attributes control chart? 1. Refer to government regs and company policy statements. 2. Read about lessons learned in past audit reports. 3. Benchmark similar processes at other companies 4. Hold a brainstorming session between production and engineering.
4. Hold a brainstorming session between production and engineering...this takes less time than benchmarking and can focus immediately on the possible causes of problems and possible corrective actions.
Which of the following best describes the mean? 1. It is the most frequently occurring value in a data set 2. It should not be used for normally distributed data 3. It is a robust measure of central tendency. 4. It can be skewed by extreme values
4. It can be skewed by extreme values.
Which statement is true about the standard deviation? 1. It provides no indication about the observation's distance from the mean 2. It is in a different unit measurement than the original observation 3. It requires you identify the largest and smallest values in the data set 4. It is the square root of the squared sums of the differences between each observation and the mean
4. It is the square root of the squared sums of the differences between each observation and the mean
You are monitoring a series of machines performing the same operations on x-bar and R charts. Your most recent sample set from one of the machines resulted in an average that is outside the lower control limit on the x-bar chart. Which of the following responses would be the best course of action? 1. No nothing because control limits are always smaller that specification limits. 2. Change the limits on the chart to ensure that the point is within specification limits. 3. Shut down the machine and scrap the production run. 4. Notify the supervisor and quarantine the produced units until an analysis can be completed and parts are dispositioned.
4. Notify the supervisor and quarantine the produced units until an analysis can be completed & parts are dispositioned.
What quality characteristic would most likely be tracked on an attributes control chart? 1. Density 2. On-time delivery 3. Brightness 4. Severity of scratches on a product
4. Severity of scratches on a product....is not a measurement that is easily and economically automated. It is highly dependent on visual inspection. This is the characteristic most likely requiring tracking on an attributes chart.
An engineer has created a drawing of a moto with the shaft diameter dimension of 1.0257 inch. What is this an example of? 1. Control Limit 2. Outer limit 3. Linear Limit 4. Specification Limit
4. Specification limit...establishes the acceptable limits of the characteristic and provides criteria for determining acceptance of the feature.
Select the response below that best describes the use of specification limits? 1. define the use of the product 2. are the same a control limits 3. Set process parameters and x-bar and R chart zones 4. The acceptable limits of a product or process characteristic or feature
4. The acceptable limits of a product or process characteristic or feature.
Which of the following best describes variable data charts? 1. Tables are always used to calculate the data. 2. The chard is characterized by specification limits. 3. The data are either good or bad and are normally in electronic format. 4. The data can be any value based on the measurements made.
4. The data can be any value based on the measurements made. Variable data are indeed variable and can be any value as opposed to discreet data that can be only one of two outcomes.
An auditor wishes to summarize the deficiency results across several plants on a wide array of characteristics. What would be the appropriate attributes control chart to use? 1. np chart 2. c chart 3. p chart 4. u chart
4. u chart....handles defects where the opportunities for defects vary across sample points.
Which of the following charts would typically be used in situations in which sample sizes are relatively small (<6) and the data are variable? 1. x-bar and s chart 2. X and MR chart 3. P chart 4. x-bar and R chart
4. x-bar and R chart
