Question 1

Which of the following statements are not true?

Accepted Answer

A)  One standard method for designing a double-sampling plan involves specifying values $p _ { 1 } \text { and } p _ { 2 }$
Along with corresponding acceptance probabilities $1 - \alpha \text { and } \beta$
Then find a plan that satisfies these conditions. 
B)  The average outgoing quality (AOQ) is the short-run proportion of defective items among those sent on before the sampling plan is employed. 
C)  Because the average outgoing quality AOQ = 0 when either p = 0 or p = 1, it follows that there is a value of p between 0 and 1 for which AOQ is a maximum. 
D)  The maximum value of the average outgoing quality (AOQ) is called the average outgoing quality limit (AOQL). 
E)  It is common practice to select a sampling plan that has a specified average outgoing quality limit (AOQL) and, in addition, minimum average total number inspected (ATI) at a particular quality level p. 
A)  One standard method for designing a double-sampling plan involves specifying values $p _ { 1 } \text { and } p _ { 2 }$
Along with corresponding acceptance probabilities $1 - \alpha \text { and } \beta$
Then find a plan that satisfies these conditions. 
B)  The average outgoing quality (AOQ) is the short-run proportion of defective items among those sent on before the sampling plan is employed. 
C)  Because the average outgoing quality AOQ = 0 when either p = 0 or p = 1, it follows that there is a value of p between 0 and 1 for which AOQ is a maximum. 
D)  The maximum value of the average outgoing quality (AOQ) is called the average outgoing quality limit (AOQL). 
E)  It is common practice to select a sampling plan that has a specified average outgoing quality limit (AOQL) and, in addition, minimum average total number inspected (ATI) at a particular quality level p. B

Question 2

Which of the following statements are not true?

Accepted Answer

A)  If we let $\Delta$
Denote the size of a shift in a process mean $\mu$
That is to be quickly detected using a CUSUM procedure, then it is common practice to let $k = 2 \Delta$
Where k denotes the slope of the lower arm of the V-mask. 
B)  A quality control practitioner may specify a desired value of an ARL (average run length) when the process is in control $\left( \mu = \mu _ { 0 } \right)$ 
C)  A quality control practitioner may specify a desire value of an ARL (average run length) when the process is out of control because the mean has shifted by $\Delta \left( \mu = \mu _ { 0 } + \Delta \text { or } \mu = \mu _ { 0 } - \Delta \right)$ 
D)  All of the above statements are true. 
E)  None of the above statements are true. 
A)  If we let $\Delta$
Denote the size of a shift in a process mean $\mu$
That is to be quickly detected using a CUSUM procedure, then it is common practice to let $k = 2 \Delta$
Where k denotes the slope of the lower arm of the V-mask. 
B)  A quality control practitioner may specify a desired value of an ARL (average run length) when the process is in control $\left( \mu = \mu _ { 0 } \right)$ 
C)  A quality control practitioner may specify a desire value of an ARL (average run length) when the process is out of control because the mean has shifted by $\Delta \left( \mu = \mu _ { 0 } + \Delta \text { or } \mu = \mu _ { 0 } - \Delta \right)$ 
D)  All of the above statements are true. 
E)  None of the above statements are true. A

Question 3

Which of the following statements are true?

Accepted Answer

A)  A defect on the traditional $\bar { X }$
Chart is its inability to detect a relatively small change in a process mean. 
B)  Whether a process is judged out of control at a particular time depends only on the sample at that time, and not on the past history of the process. 
C)  The computational version of a cumulative sum (CUSUM) procedure is used almost exclusively in practice, but the logic behind the procedure is most easily grasped by first considering the graphical form. 
D)  All of the above statements are true. 
E)  None of the above statements are true. 
A)  A defect on the traditional $\bar { X }$
Chart is its inability to detect a relatively small change in a process mean. 
B)  Whether a process is judged out of control at a particular time depends only on the sample at that time, and not on the past history of the process. 
C)  The computational version of a cumulative sum (CUSUM) procedure is used almost exclusively in practice, but the logic behind the procedure is most easily grasped by first considering the graphical form. 
D)  All of the above statements are true. 
E)  None of the above statements are true. D

Question 4

Which of the following statements are not true?

Accepted Answer

A)  Control charts and acceptance sampling plans were first developed in the 1960's and 1970's. 
B)  Statisticians and engineers have recently introduced many statistical methods for identifying types and levels of production inputs that will ensure high-quality output. 
C)  There is a large body of material known as "Taguchi methods", named after Japanese engineer/statistician G. Taguchi. 
D)  All of the above statements are true. 
E)  None of the above statements are true. 
A)  Control charts and acceptance sampling plans were first developed in the 1960's and 1970's. 
B)  Statisticians and engineers have recently introduced many statistical methods for identifying types and levels of production inputs that will ensure high-quality output. 
C)  There is a large body of material known as "Taguchi methods", named after Japanese engineer/statistician G. Taguchi. 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 5

The p control chart for the fraction of defective items produced is based on the __________ probability distribution.

Accepted Answer

The answer of The p control chart for the fraction...

Question 6

If $Y _ { 1 } , Y _ { 2 } , \ldots Y _ { n }$ are independent Poisson variables with common parameter $\theta$ then $\sum _ { i = 1 } ^ { n } Y _ { i }$ has also a Poisson distribution with parameter $\lambda$ = __________, where $\lambda$ denotes the expected number of defects per unit.

Accepted Answer

The answer of If \(Y _ { 1 } ,...

Question 7

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

Accepted Answer

The answer of Suppose there are 24 samples obtained at...

Question 8

Suppose a control chart is constructed so that the probability of a point falling outside the control limits when the process is actually in control is .005.
a. What is the probability that ten successive points (based on independently selected samples) will be within the control limits?
b. What is the probability that 25 successive points will all lie within the control limits?
c. What is the smallest number of successive points plotted for which the probability of observing at least one outside the control limits exceeds .10?

Accepted Answer

a. P (10 successive points inside the li

Question 9

An $\bar { x }$ control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard deviation control limits are LCL = __________ and UCL =__________.

Accepted Answer

The answer of An $\bar { x }$ control chart...

Question 10

If the size of a shift in a process mean $\mu$ is .40, then the customarily value of the slope of the lower arm of the V-mask is __________.

Accepted Answer

The answer of If the size of a shift in...

Question 11

The use of 3-sigma control limits is presumed to result in P(statistic <LCL $\approx$ __________, when the process is in control.

Accepted Answer

The answer of The use of 3-sigma control limits is...

Question 12

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

Accepted Answer

For a standard normal random v

Question 13

Suppose that at each of the time points 1,2,3,….., a sample of size n is selected at random from a normal distribution with known mean $\mu$ and standard deviation $\sigma$ In order to construct a 3-sigma $\bar { X }$ chart, we need to

Accepted Answer

A)  determine $\bar { x } _ { 1 } , \bar { x } _ { 2 } , \bar { x } _ { 3 } , \ldots \ldots$
Calculated values of the corresponding sample means. 
B)  plot $\bar { x } _ { 2 } ^ { \prime } s$
Over time; that is, plot the points $\left( 1 , \bar { x } _ { 1 } \right) , \left( 1 , \bar { x } _ { 2 } \right) , \left( 1 , \bar { x } _ { 3 } \right) , \ldots \ldots$
And so on. 
C)  Draw horizontal lines across the plot as $\mu \pm 3\sigma / \sqrt { n }$
) 
D)  All of the above are needed. 
E)  Only A and B are needed. 
A)  determine $\bar { x } _ { 1 } , \bar { x } _ { 2 } , \bar { x } _ { 3 } , \ldots \ldots$
Calculated values of the corresponding sample means. 
B)  plot $\bar { x } _ { 2 } ^ { \prime } s$
Over time; that is, plot the points $\left( 1 , \bar { x } _ { 1 } \right) , \left( 1 , \bar { x } _ { 2 } \right) , \left( 1 , \bar { x } _ { 3 } \right) , \ldots \ldots$
And so on. 
C)  Draw horizontal lines across the plot as $\mu \pm 3\sigma / \sqrt { n }$
) 
D)  All of the above are needed. 
E)  Only A and B are needed.

Question 14

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

Accepted Answer

The answer of An $\bar { x }$ control chart...

Question 15

Which of the following statements are not true?

Accepted Answer

A)  To construct an $\bar { X }$
Chart, there are two different commonly used methods for estimating the unknown process standard deviation $\sigma$
; one based on the k sample standard deviations and the other on the k sample ranges. 
B)  In the case of a normal population distribution, the estimator of the unknown process standard deviation $\sigma$
Based on sample standard deviations S is more efficient than that based on the sample range. 
C)  The sample standard deviation S is an unbiased estimator of the population standard deviation $\sigma$
; that is, E(S)= $\sigma$
) 
D)  All of the above statements are true. 
E)  None of the above statements are true. 
A)  To construct an $\bar { X }$
Chart, there are two different commonly used methods for estimating the unknown process standard deviation $\sigma$
; one based on the k sample standard deviations and the other on the k sample ranges. 
B)  In the case of a normal population distribution, the estimator of the unknown process standard deviation $\sigma$
Based on sample standard deviations S is more efficient than that based on the sample range. 
C)  The sample standard deviation S is an unbiased estimator of the population standard deviation $\sigma$
; that is, E(S)= $\sigma$
) 
D)  All of the above statements are true. 
E)  None of the above statements are true.

Question 16

Suppose that 25 samples, each of size 100, were selected from what is believed to be an in-control process, and that $\sum \hat { p } _ { i} = 1.8$ where $\hat { p } _ { i }$ is the fraction of defective items in sample i. The p chart for the fraction of defective items has its center line at height equals to __________.

Accepted Answer

The answer of Suppose that 25 samples, each of size...

Question 17

Which of the following statements are true?

Accepted Answer

A)  We might think of "natural random variation" as uncontrollable background noise. 
B)  Control charts provide a mechanism for recognizing situations where assignable causes may be adversely affecting product quality. 
C)  Once a control chart indicates an out-of-control situation, an investigation can be launched to identify causes and take corrective action. 
D)  A basic element of control charting is that samples have been selected from the process of interest at a sequence of time points. 
E)  All of the above statements are true. 
A)  We might think of "natural random variation" as uncontrollable background noise. 
B)  Control charts provide a mechanism for recognizing situations where assignable causes may be adversely affecting product quality. 
C)  Once a control chart indicates an out-of-control situation, an investigation can be launched to identify causes and take corrective action. 
D)  A basic element of control charting is that samples have been selected from the process of interest at a sequence of time points. 
E)  All of the above statements are true.

Question 18

The two control limits for 3=sigma $\bar { x }$ chart have been calculated. If the variable of interest is normally distributed, and 3 is replaced by 2.5 in the control limits formulas, then probability of Type I error $( \alpha )$ __________, but for fixed n and $\sigma$ , probability of Type II error $( \beta )$ will __________.

Accepted Answer

The answer of The two control limits for 3=sigma \(\bar...

Question 19

Let p denote the proportion of defective items in the lot, and P(A) denote the probability that the lot is accepted. Let us designate two different values of p, one for which P(A) is a specified value close to 1 and the other for which P(A) is a specified value near 0. These tow values of $p - \operatorname { say } p _ { 1 } \text { and } p _ { 2 } -$ are often called the __________, denoted AQL, and the __________, denoted by LTPD.

Accepted Answer

acceptance quality l

Question 20

Under curtailment in a double-sampling plan, it can be shown that the expected number of items inspected in a __________ is smaller than the number of items examined in a __________ when the operating characteristic (OC) curves of the two plans are close to be identical.

Accepted Answer

double-sam

Which of the following statements are not true?

Which of the following statements are not true?

Which of the following statements are true?

Which of the following statements are not true?

The p control chart for the fraction of defective items produced is based on the __________ probability distribution.

If $Y _ { 1 } , Y _ { 2 } , \ldots Y _ { n }$ are independent Poisson variables with common parameter $\theta$ then $\sum _ { i = 1 } ^ { n } Y _ { i }$ has also a Poisson distribution with parameter $\lambda$ = __________, where $\lambda$ denotes the expected number of defects per unit.

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

An $\bar { x }$ control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard deviation control limits are LCL = and UCL =.

If the size of a shift in a process mean $\mu$ is .40, then the customarily value of the slope of the lower arm of the V-mask is __________.

The use of 3-sigma control limits is presumed to result in P(statistic <LCL $\approx$ __________, when the process is in control.

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

Suppose that at each of the time points 1,2,3,….., a sample of size n is selected at random from a normal distribution with known mean $\mu$ and standard deviation $\sigma$ In order to construct a 3-sigma $\bar { X }$ chart, we need to

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

Which of the following statements are not true?

Which of the following statements are true?

Under curtailment in a double-sampling plan, it can be shown that the expected number of items inspected in a is smaller than the number of items examined in a when the operating characteristic (OC) curves of the two plans are close to be identical.

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Tests of Hypotheses Based on a Single Sample

Inferences Based on Two Samples

The Analysis of Variance

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Filters

Exam 16: Quality Control Methods

Which of the following statements are not true?

Which of the following statements are not true?

Which of the following statements are true?

Which of the following statements are not true?

The p control chart for the fraction of defective items produced is based on the __________ probability distribution.

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

If the size of a shift in a process mean μ\muμ is .40, then the customarily value of the slope of the lower arm of the V-mask is __________.

The use of 3-sigma control limits is presumed to result in P(statistic <LCL ≈\approx≈ __________, when the process is in control.

In the case of known μ and σ,\mu \text { and } \sigma ,μ and σ, what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

Suppose that at each of the time points 1,2,3,….., a sample of size n is selected at random from a normal distribution with known mean μ\muμ and standard deviation σ\sigmaσ In order to construct a 3-sigma Xˉ\bar { X }Xˉ chart, we need to

An xˉ\bar { x }xˉ control chart is based on control limits μ0±2.88σ/n\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }μ0​±2.88σ/n​ When the process is in control, then the average run length (ARL) is __________.

Which of the following statements are not true?

Which of the following statements are true?

Under curtailment in a double-sampling plan, it can be shown that the expected number of items inspected in a __________ is smaller than the number of items examined in a __________ when the operating characteristic (OC) curves of the two plans are close to be identical.

Overview and Descriptive Statistics

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Joint Probability Distributions and Random Samples

Point Estimation

Statistical Intervals Based on a Single Sample

Tests of Hypotheses Based on a Single Sample

Inferences Based on Two Samples

The Analysis of Variance

Multifactor Analysis of Variance

Simple Linear Regression and Correlation

Nonlinear and Multiple Regression

Goodness-Of-Fit Tests and Categorical Data Analysis

Distribution-Free Procedures

Filters

If the size of a shift in a process mean $\mu$ is .40, then the customarily value of the slope of the lower arm of the V-mask is __________.

The use of 3-sigma control limits is presumed to result in P(statistic <LCL $\approx$ __________, when the process is in control.

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

Suppose that at each of the time points 1,2,3,….., a sample of size n is selected at random from a normal distribution with known mean $\mu$ and standard deviation $\sigma$ In order to construct a 3-sigma $\bar { X }$ chart, we need to

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

Under curtailment in a double-sampling plan, it can be shown that the expected number of items inspected in a is smaller than the number of items examined in a when the operating characteristic (OC) curves of the two plans are close to be identical.