Quality Engineering: Final Review
Upper and lower control limits for a control chart are customarily what?
+/- 3 Sigma
The Shewhart control chart is effective in detecting shifts in the process if the magnitude of the shift is what?
1.5 Sigma or larger
The percentage of specification band used up by the process is calculated as what?
1/Cp x100%
90% of values are above the following?
10th Percentile
The most common type of factorial experiment that considers two levels for each variable is a what?
2 Level Experiment
The simplest two factor design with A and B each at two levels is called what?
2 level, 2 factor
In general a 2^k design may be run with fractional factors called what type of design?
2^k-p design
When constructing a histogram, what is the rule of thumb for selecting the number of bins?
5 to 20
The rule characterizing processes less than 3 sigma is generally referred to as?
68-95-99.7
The Process Capability Ratio Cp, which for a quality characteristic with both upper and lower specification limits are provided, is defined as CP = (USL-LSL)/Denominator, what is the Denominator?
6Sigma
A 2X4 factorial design that is divided into a one half fraction has how many runs?
8
If 100 Units enter a process, and 95 good units are produced as a an output, what is the First Time Yield?
95%
What percentage of the values fall within + or - 3 sigma?
99.73%
In the design matrix, the product of any two columns results in what?
A column in the table
The statistical summary to determine which factors in the factorial experiment are significant is called what?
ANOVA
What statistical analysis technique is used two compare the means when there are more than two levels of a single factor?
ANOVA
We often say that Cp captures the potential capability in the process, whereas Cpk takes into account centering and is a measure of what?
Actual Capability
Two or more effects that have the same effect are know as what?
Aliases
A fixed significance level of testing is often used in reporting the results of the hypothesis test, what is this level called?
Alpha Value
In the lean six-sigma approach, Failure Mode Effects Analysis (FMEA) is a tool used to prioritize potential sources of variability, failures, errors or defects in of what DMAIC phase?
Analyze
Statistical methods such as hypothesis testing, control charts, ANOVA, Regression, etc. are extremely important tools that a primarily used in this DMAIC phase.
Analyze
In experimental design we usually experiment sequentially and do all of the following except what?
Answer all questions up front
A control chart will detect what type of out of control cause?
Assignable Cause
Quality characteristics classifying the product as conforming or nonconforming are what type?
Attributes
Which of the following is not one of the 8 primary dimensions of quality discussed in class?
Average Quality
The main effect of a factor A is the difference between what?
Average Response at High Level and Average Response at the low level
What does the visual appearance of a normal distribution look like?
Bell Shaped Curve
What is a trial called where the outcome of each trial is a success or failure?
Bernoulli
Any regression model is a linear model so long as it is linear in what parameters?
Betas
In acceptance testing a useful approximation for the Hypergeometric distribution when the ratio of n/N < 0.1 is what?
Binomial
Suppose a random sample of n observations, x1, x2, ... , xn is taken from a Bernoulli process with constant probability of success p, then the sum of the same observations x = x1 + x2 + ... + xn has what distribution?
Binomial
The distribution that is used to describe acceptance sampling from an infinitely large population, where p represents the fraction of defective in the population is called?
Binomial
The statistical principles underlying the control chart for fraction nonconforming are based on what distribution?
Binomial
What distribution is used to model the random variable of the sample fraction defective?
Binomial
Which one of the following is not a recognized Six Sigma belt?
Blue
Tables of the standard normal distribution can be used to obtain P-values for a Z-test, so long as the computed value of the Z statistic are in the body of the table. For example if the Z value computed is between -3.99 to 3.99 the P value may be read from the table. However the tables of t-distribution are typically only presented to ten tail areas, so the P values when using the t tables may be presented as?
Bounded
The equation Y=f(x) is referred to in Lean Six Sigma terms as?
Breakthrough Equation
When a control chart indicates an out-of-control performance, an Out-of-Control Action Plan (OCAP) must accompany the control chart. Which one of the following is not one of the charts typically used as part of the OCAP?
Bubble Chart
The Exponentially Weighted Moving Average control chart has a performance in detecting small shifts approximately equivalent to what?
CSUM
Two very effective alternatives to Shewhart control charts may be used when small process shifts are of interest are?
CSUM & EWMA
What does the mean of a probability distribution represent?
Central Tendancy
A designed experiment is a test or series of tests in which changes are made to the input variables in order to observe what?
Changes in the Output Response
The distributions shown below for selected values of n (degrees of freedom) are slightly skewed. What type of distributions are these?
Chi-square Distribution
If x1, x2,..., xn are normally and independently distributed random variables, with zero means and variance one, then what distribution does the random variable y have where y = x12 + x22 +, ..., xn2 ?
Chi-square distribution
Which of the following is not one of the primary analytic tools used in Quality Improvement?
Circuit Design
The CSUM control chart is very effective in detecting small shifts however not as effective as the Shewhart chart in detecting large shifts. An approach to improving the ability of the CSUM control chart to detect large process shifts is to use what?
Combined CSUM & Shewhart
The magnificent seven major SPC problem solving tools do not include?
Common Cause Diagram
Chance cause is usually due to natural variation in the process, also know as what?
Common cause variation
A two-factor factorial design is considered to be what kind of design?
Completely Randomized
What is the range of values called that's likely to include a population value with a certain degree of confidence and often expressed as a percentage?
Confidence Interval
As part of your business, you collect confidential customer information. Your supplier has indicated that they could improve the quality of their product if you would only share your customers confidential information with them. What element of the code of ethics might be in violation here?
Confidentiality
A supplier is attempting to win more business from your organization, and they recognize you as a key stakeholder who can speak up regarding the quality of their product. They offer you expensive tickets to a football game where your favorite team happens to be playing in. What element of the code of ethics might be in violation here?
Conflict of Interest
When a value being measured can be expressed on a continuous scale.., what is the probability distribution called?
Continuous Distribution
The sum-product of an effect column and the treatment column is called what?
Contrast
What is a primary statistical tool used in the control phase of DMAIC?
Control Charts
The Total Cost of Quality (CoQ) is defined by which choice?
Cost of Poor Quality + Prevention Costs + Appraisal Costs
In hypothesis testing, the set of values of the test statistic leading to rejection of the null hypothesis is called what?
Critical Region
What is a key characteristic important to the customers perception of quality is called?
Critical to Quality Characteristic
What is the probability that the normal random variable is less than some value?
Cumulative Normal Distribution
Six sigma is primarily aimed at reducing?
Defects
The requirements for a Lean Six-Sigma Process are defined in this phase?
Define
DMAIC stands for?
Define, Measure, Analyze, Improve, Control
The Union of Japanese Scientists and Engineers established the first prize for quality named after what prominent influencer?
Deming
The runs of the experiments listed in a tabular format is often called what?
Design Matrix
A process having many variables may be in statistical control but still has poor capability. In order to establish which variables are most important a valuable in improving process capability is what technique?
Design of Experiments
When formulating improvements using the DMAIC methodology which statistical tool can be very usefull?
Design of Experiments
Experimental design may be used in the process of Engineering Design in all of the following except which one?
Determining schedule delays
When a parameter being measured can only take on certain values, such as integers 0,1,2 ..., what is the probability distribution called?
Discrete Distribution
In the fractional design the effect if the generator is to what?
Divide into fractions
The goal of design of experiments is to what?
Draw Practical Conclusions
A successful experiment develops all of the following except what?
Efficiency values
What is a probability distribution called, that models the time to fail using a failure rate of λ and appears visually as shown?
Exponential
If w and y are two independent chi-square random variable with u and v degrees of freedom respectively, then what is the distribution of the following? random variable ~ (w/u)/(y/v)
F-Distribution
The distributions shown below with selected u and v degrees of freedom are what type of distributions?
F-Distribution
(Inference on the Variance of Two Normal Distributions) Consider the hypothesis that the variances of two independent normal distributions are equal. If we construct a test with the ratio of the two variances what distribution is used for the test statistic?
F-distribution
ANOVA works by examining the computing the value of SS Treatments and SSE and expressing this as: Mean Square for Treatments = SS Treatments / (a-1) Error Mean Square = SSE / a(n-1) The ratio of the Mean Square for Treatments / Error Mean Square has what type of distribution?
F-distribution
What distribution is typically used for test of significance in a regression model?
F-distribution
When there are several factors of interest in an experiment, what type of design should be use?
Factorial Design
You have two suppliers for an important component. One supplier has asked If they can get a copy of the receiving inspection data from their competitor. . . What element of the code of ethics might be in violation here?
Fairness
You're on the manufacturing floor investigating a non-conformance. Your production folks are a very diverse group. While interviewing one operator, he indicated that the root cause was "those foreigners over there" as he points as a group of employees. What element of the code of ethics was violated by this operator?
Fairness
Attributes charts are generally more informative than variables charts because there is more information classifying a unit as conforming or nonconforming.
False
Bar charts and histogram are the same chart?
False
In a 6-Sigma process there are only 233 defects per million opportunities.
False
Many quality-engineering authorities strongly recommend routine use of the ratios Cp and Cpk because of they capture the complete complex process.
False
The mean and variance of the Hypergeometric Distribution are the same?
False
To construct a probability plot, first order the sample points from largest to smallest, then plot the points against the observed relevant frequency. If the hypothesized distribution adequately describes the data, the points will fall approximately along a straight line.
False
When we have only samples of the product available, we can still conduct a complete process capability analysis.
False
The sample median of a distribution is also know as?
Fiftieth Percentile 2nd Quartile
The ratio of the number of nonconforming items in a population to the total number of items in that population is what?
Fraction Nonconforming
As the number of factors in a 2^k design increases, the number of runs required increases rapidly. If we can assume a principle of Sparsity of Effects where higher order interactions are negligible, then a more efficient technique using fewer than 2^k runs can be used, is known as what?
Fractional Factorial
What distribution has a shape parameter r, and a scale parameter λ and appears visually similar to this diagram?
Gamma
Who is first credited with characterizing the bell shaped curve?
Gauss
The weights of the EWMA tend to decline in what way with time?
Geometrically
Kaizen is a methodology embraced within lean six sigma and is characterized by gradual incremental improvements and using input from the workers to make improvement. What does the Japanese word Kaizen mean in English?
Good Change
"Quality means doing it right when no one is looking," this is a quote by who?
Henry Ford
Data must be divided into intervals, cells or bins to construct this graphical chart?
Histogram
You are investigating a recent non-conformance, and the data suggests that the root cause is a recent change that was made to the production line that results in nearly $1M in scrap reduction. The operations director approaches you to ask you to find a different root cause. What element of the code of ethics might be in violation here?
Honesty
If a random sample of n items is selected from a finite population without replacement, and the number of items that fall into the class of interest x is observed, then what is the distribution of x?
Hypergeometric
You are interviewing for a new job for a quality engineering position. The interviewer asks you if you're ever been involved in a validation for an automated piece of equipment. In your work experience you've had extensive experience in validating semi-automated equipment, however never a completely automated piece of equipment. You believe you have to say yes to get the job, what would you do?
I have had experience with semi-automated equipment, not fully automated, but I'm sure I can learn quickly.
What is the advantage of using the histogram to estimate process capability?
Immediate Visual Impression
At what phase of the DMAIC process is a process redesign likely to take place?
Improvement
A phase I control chart analyzes data using trial control limits to see if the limits are reliable in monitoring future production. A phase II control chart starts when the process is what?
In-Control
Experimental design is a critically important engineering tool for improving a process or in the development of a new process. Which of the following is not a result of design of experiments?
Increased variation
What type of observations are required for the sample to be considered Random?
Independent
You are validating a new piece of production equipment, and during the measurement of the product, you find a data point that is out of spec, which you believe to be a result of measurement error. The technician suggests that you re-measure the part and record the result on a new data sheet, and discard the original data point. What element of the code of ethics might be in violation here?
Integrity
In some experiments the difference in response between the levels of one factor is not the same at all levels of the other factors, which means there is what present?
Interaction Effect
In the following what is the x1 x2 term referred to? y = β0 + β1 x1 + β2 x2 + β12 x1 x2 + ϵ
Interaction Term
Regression is a useful technique in quality engineering reflected in the model: y = β0 + β1 x1 + β2 x2 + ϵ In this model what does β0 represent?
Intercept of the plane
It is important to keep in mind that experimentation is a learning process. As we move along we tentatively formulate a hypothesis, and on the basis of results formulate a new hypothesis, an so on. This suggests that experimentation is what?
Iterative Process
The exponential distribution has what property that no other distribution has?
Lack of Memory
What is a common technique used to estimate the regression coefficients in a linear regression model?
Least Squares
Data is plotted as a) Normal b) Lognormal c) Weibull and d) exponential. What distribution provides the most reasonable model for the distribution?
Lognormal
What distribution does a random variable X have when X = exp (w) and w has a normal distribution?
Lognormal Distribution
The design matrix is often coded with + or - signs, or -1 and +1 to indicate what?
Low and High
The change in the level of a factor that causes a change in the response variable is what?
Main Effect
In an exponential distribution, what is 1/λ called?
Mean Time to Failure
What DMAIC phase is critical data typically gathered for use in lean six-sigma projects?
Meaure
Which of the following is not a primary sample statistic?
Metadata
In lean six sigma, anything that does not increase value in the eye of the customer must be considered?
Muda
Control limits on the Xbar and R chart are driven by the natural variability of the process, also known as what?
Natural Tolerance Limits of the Process
In a Binomial distribution we fix the sample size (number of Bernoulli trials) and observe the number of successes, with what distribution do we fix the number of successes and observed the sample size required to achieve them?
Negative Binomial
A distribution with mean μ and variance σ2 is called what?
Normal
Suppose x is a normally distributed random variable with a mean μ and variance σ2 . If x1, x2, ... is a random sample of size n, then what is the distribution of the sample mean?
Normal
The data below is plotted on normal probability paper, what distribution model does the plot suggest?
Normal
What distribution approximates the Binomial Distribution where the number of trials n is large?
Normal
What is the most important distribution used in statistics?
Normal
In hypothesis testing the two hypothesis are?
Null and Alternate
The factorial design is a more efficient method of experiment than what?
One Factor at a Time
The Cpk is equal to what?
One sided PCR test for the spec limit
What type of curves are useful to determine how large a sample is required to detect a specified difference with a particular probability?
Operating-characteristic curves
We may describe the single factor model observations as a linear statistical model yij = μ + τij + ϵij for i = 1,2,...,a and j = 1,2,..., n What does μ represent
Overall Mean
What value is the smallest level of significance that would lead to rejection of the null hypothesis?
P -value
The main effect would be considered significant if the computed F statistic exceeds the tabular value at the appropriate level significance level, or if what is small than the significance level?
P Value
What are the two broad categories of statistical inference?
Parameter Estimation and Hypothesis Testing
In Quality Engineering we are interested in making inferences about the parameters of probability distributions where the parameters are generally unknown. If a random sample of n observations is taken and the sample mean and variance computed, these are said to be what type of estimates of the population mean and variance?
Point Estimates
Sometimes sums of Poisson random variables are used in quality engineering. Consider a random sample of size n from a Poisson distribution with parameter λ , what is the distribution of the sample sum? x = x1 + x2 + ... + xn
Poisson
What distribution having a parameter of λ = np, where p is small and n is large, approximates the Binomial Distribution?
Poisson
What is the distribution commonly used to model the number of defects or nonconformities that occur in a unit of product?
Poisson
The choice of generator selected with a positive sign will result in what?
Principal Fraction
What is a mathematical model that relates the value of the variable with the probability of occurrence?
Probability Distribution
What is a graphical method for determining if data conforms to a hypothesized distribution?
Probability Plots
The general activity of analyzing the variability relative to product requirements or specifications, and using metrics to assisting in reducing variability, is known as what?
Process Capability Analysis
Which of the following is not one of the forms of waste addressed with Lean Six Sigma?
Production
Which of the following is not one of the SPIOC process analysis?
Project
The interquartile range, or IQR, is computed as?
Q3-Q1
Deming's 14 points were often cited as transformational quality improvement approaches. Which one of the following is not one of the 14 points?
Quality is Free
For numerical variables, process variability may be monitored with a control chart for standard deviation or the more widely used what?
R Chart
If both the xbar and R charts show non-random patterns, the best strategy is to eliminate assignable cause first from where?
R Chart
We may describe the single factor model observations as a linear statistical model yij = μ + τij + ϵij for i = 1,2,...,a and j = 1,2,..., n What does ϵ represent
Random Error
What is a variable that takes on different values in a population according to some random mechanism?
Random Variable
In practical application when calculating the Cp value the Sigma of the population is unknown. To estimate Sigma for calculating CP we use what?
Rbar/d2 or s
Lean and Six Sigma are combined into a unified methodology call Lean Six-Sigma, which is focused on?
Reduce Waste and Reduce Variation
Lean production focuses on?
Reducing Waste
Regression is a useful technique in quality engineering reflected in the model: y = β0 + β1 x1 + β2 x2 + ϵ In this model what does β1 and β2 represent?
Regression Coefficients
The goal of any experimental design is to express the relationship between main effects and response as a quantitative model such as what?
Regression Model
Regression is a useful technique in quality engineering reflected in the model: y = β0 + β1 x1 + β2 x2 + ϵ In this model what does x represent?
Regressor Variables
The R^2 statistic in a regression model is the amount of reduction in the variability of y obtained by using what?
Regressor Variables
When constructing a histogram, what does the the vertical axis represent?
Relative Frequency
What is one important technique use to check the adequacy of the regression model?
Residual Plot
Regression is a useful technique in quality engineering reflected in the model: y = β0 + β1 x1 + β2 x2 + ϵ In this model what does y represent?
Response Variable
During a validation, you're having to build hundreds of samples to satisfy the requirements in the validation protocol. This requires you to constantly start and stop the automated equipment to take samples from the line. A maintenance technician suggests that you bypass the safety curtain around your equipment to speed up the process. What element of the code of ethics might be in violation here?
Responsibility
The primary techniques used in process capability analysis do not include?
Root Cause Analysis
The define phase of DMAIC often includes the following characterization.
SIPOC
A collection of measurements selected from some larger measurements is called what?
Sample
What is the square root of the sample standard variance?
Sample Standard Deviation
The probability distribution of a statistic is called what?
Sampling Distribution
What does the standard deviation reflect?
Scatter About the Average
Sometimes experiments that seek to identify a relatively few significant factors from a larger number of factors are called what?
Screening Experiments
Fractional factorial design is highly useful in experimental problems because we can run sequences of small, efficient experiments and combine information across several experiments, taking advantage of learning about the process along as we go along - this is known as what?
Sequential
Cumulative sum charts are more effective than Shewhart charts in detecting small process shifts because the combine information from what?
Several samples
When estimating the sigma level, when do we use the 1.5 x Sigma shift?
Short Term vs. Long Term Measurement
What statistic can estimate the probability of a defect?
Sigma Level
Which of the following is not part of the 5S method?
Simplify
In evaluating a product quality characteristic process capability, what spread is customarily used?
Six Sigma
The quality manager at Motorola credited with introducing the six-sigma concept was?
Smith
Assignable cause variation, that usually requires further investigation as to it's origin, is also known as what?
Special Cause Variation
The standard deviation as an indication of?
Spread
The Box plot simultaneously displays several important statistics. Which is not one of the statistics shown with the box plot?
Standard Deviation
(Inference on Population Proportion) Suppose we wish to test the hypothesis that the proportion of a population equals a standard value - say po. If n is large and p ≥ 0.1, an approximation to the binomial distribution is used to construct the confidence interval based on what distribution? p^ - Zα/2 sqrt(p(1−p)/n) ≤ p ≤ p^ + Zα/2 sqrt(p(1−p)/n)
Standard Normal
(Inference on Two Population Proportions) If we construct a confidence interval on the difference in two population proportions, what statistical distribution do we use?
Standard Normal
(Two Samples - Inference for a Difference in Means with Known Variances) Suppose we draw a random sample from population one, and draw a random sample from population two, then what distribution do we use to construct a hypothesis test and confidence interval for the difference between two means?
Standard Normal
What is a normal distribution with mean = 0 and standard deviation = 2 called?
Standard Normal
(Inference on the mean of a distribution with the variance unknown) Consider the random variable x, with unknown mean μ and known variance σ2 . Suppose that a random sample of n observations is taken, e.g. x1, x2, ... , xn and we compute x¯. Then a 100(1-α)% two sided Confidence Interval of μ is based on what distribution? x¯ = Z α/2 σ/sqrt(n) ≤ μ ≤ x¯ + Z α/2 σ/sqrt(n)
Standard Normal Distribution
Generally the first step in the guidelines for design of experiments is to what?
State the Problem
What topic is concerned with drawing conclusions about a population based on a sample?
Statistical Inference
In the design of experiments, what type of methods should be used to analyze the data so that results and conclusions are objective rather than judgemental?
Statistical Methods
What science analyzes data and draws conclusions taking into account variability in the data?
Statistics
One very useful graphical method in statistics characterized by breaking the data into two parts, one part with the leading digit and the second part with the remaining digits is called a?
Stem-and-leaf plot
The Sum of Squares Error in the ANOVA table is usually calculated by subtracting the effect Sum of Squares from what?
Sum of Squares Total
Recognizing patterns is a process of what looking for what?
Systematic or nonrandom patters
Who pioneered Lean production by characterizing 7 forms of "Muda" or waste?
Taiichi Ohno
A major disadvantage of Shewhart control charts s that they use only the information in the last observation and ignores information from what?
The entire sequence
Collectively, CSUM and EWMA Charts are sometimes called what?
Time Weighted Control Charts
Lean production innovation began at what company?
Toyota
We may describe the single factor model observations as a linear statistical model yij = μ + τij + ϵij for i = 1,2,...,a and j = 1,2,..., n What does τ represent
Treatment Effect
The ANOVA technical partitions the total variability into two component parts SST = SS Treatments + SSE What is SS Treatments
Treatment Sum of Squares
What are levels of factors sometimes called?
Treatments
A Control Chart can indicate an out-of-control condition even though no single point is outside the control limits.
True
An acceptance test procedure can be based on the hypergeometric distribution where x items are selected at random without replacement to determine the probability of finding non-conforming items.
True
Computations for ANOVA are usually summarized in a tabular form such as the one below.
True
DMAIC is a structured problem solving process associated with six sigma methodology.
True
Efficient computational formulas for ANOVA and data analysis computer routines are available to make the ANOVA computations easier.
True
Hypothesis testing sometimes seems like a very hard subject because there are so many variations and cases.
True
If the number of occurrences of an event of an event has a Poisson distribution with parameter λ, then the distribution of the interval between occurrences is an exponential with parameter λ.
True
Probability paper is designed to test hypothesized distributions and is available for normal, lognormal, Weibull, chi-square and gamma distributions.
True
Since the Normal Distribution can serve as an approximation to the Binomial Distribution, and since the Poisson Distribution can be used to approximate the Binomial Distribution, it seems logical that the Normal Distribution can be used to approximate the Poisson Distribution.
True
Statistical hypothesis testing procedures may be used to check the conformity of process parameters to their specified values, or to assist in modifying the process until the desired values are obtained.
True
The approach of approximating one distribution with another is very useful when simplifying computations by hand. However using calculators and computers has largely made using the approximations unnecessary.
True
The central limit theorem implies that the sum of independently distributed random variables is approximately normal regardless of the distribution of the individual variables.
True
The lifetime of a product that degrades over time is often modeled as a lognormal distribution.
True
The mean and variance of the Poisson Distribution is the same?
True
The sample average is equivalent to the arithmetic mean?
True
When presenting control charts to production personnel or management, the percentage conforming is often used instead of the fraction, because the percentage has more intuitive appeal.
True
While the quadratic estimator of the standard deviation is preferrable, the estimate of standard deviation based on the range can also provide some estimate where R = Max(xi) = Min (xi)
True
What type of error is it when a null hypothesis is rejected when it is true?
Type I Error
What type of error is it when the null hypothesis is not rejected, and it is false?
Type II Error
The ANOVA evaluation uses a F statistic implying what type of test?
Upper Tail, One-Tail Critical Region
Your primary supplier also does business with your biggest competitor. In error, your supplier accidentally sends you your competitors' data. What would you do? How might your reaction possibly violate certain elements of the code of ethics?
Use honesty and integrity and delete the message. Reply back telling them about their mistake and assure them you have deleted the message.
Quality is inversely proportional to what?
Variability
If the quality characteristic can be measured on a continuous scale of measurement, it is usually analyzed on what type of control chart?
Variables
Control charts used to examine quality characteristics expressed as numerical measurements are called what?
Variables Control Charts
What data is most likely to be collected in the define phase?
Voice of the Customer
Who popularized continuous quality improvement by promoting the PDCA cycle?
W. Edwards Deming
Who developed the first Control Chart?
Walter Shewhart
In addition to Control Limits, limits are sometimes added at +/- 2 Sigma known as what?
Warning Limits
What distribution has a parameter β, reduces to the Exponential distribution when β = 1, and appears as shown below?
Weibull
The zone rules developed for control charts that suggest concluding the process is out of control are also known as what?
Western Electric Rules
When evaluating numerical variables, control of the process average or mean quality is usually monitored with what chart?
Xbar Chart
What value should be used as the centerline of the xbar chart?
Xbarbar
The control chart for defect or nonconformities is?
c Chart
The X-bar charts computes control limits using an estimate of sigma based on the Range average; SigmaHat = Rbar/Constant, where the Constant varies by the number of observations and is looked up in the Appendix; that constant is what?
d2
A one half fraction of the 2^k factorial design contains how many runs?
k-1
If the Xbar chart is being used to detect moderate to large process shifts - say on the order of 2Sigma - then what sample size is reasonably effective?
n = 4, 5 or 6
To compute the sample variance divide the sum of the square deviations by?
n-1
What is the mean of a binomial distribution?
np
The control chart for number of defects or nonconformities is what?
np Chart
The control chart for the fraction nonconforming is called what?
p chart
If x is a standard normal random variable and if y is a chi-square random variable with k degrees of freedom, and x and y are independent, then what distribution does the following random variable have? random variable ~ x/sqrt(y/k)
t-Distribution
(Inference For a Difference in Means of Two Normal Distributions, Variances Unknown) Consider a test on hypothesis on the difference in means of two normal distributions, where variances are unknown, what distribution do we used to construct the hypothesis test and confidence interval?
t-distribution
The distributions shown below with selected k degrees of freedom approximate normal distributions. What type of distributions are these?
t-distribution
The hypothesis for testing the significance of any individual regression coefficient uses what distribution?
t-distribution
The CSUM chart incorporates all information in the sequence of sample values by plotting the cumulative sum of the deviations of sample values from a what?
target value
The EWMA control chart is constructed by plotting the moving average versus the sample number (or time) with the center line representing the what?
target value
A control chart for nonconformities per unit is what?
u Chart