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Exam 10: Quality Control

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Question 71

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Which of the following relationships must always be incorrect?

A) Tolerances > process variability > control limits
B) Process variability > tolerances > control limits
C) Tolerances > control limits > process variability
D) Process variability > control limits > tolerances
E) Process variability < tolerances < control limits

F) B) and C)
G) A) and C)

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Question 72

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Tolerances represent the control limits we use on the charts.

A) True
B) False

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Question 73

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A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $\begin{array} {r } { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } & \\\hline \# 1 & 17 & 15 & 15 & 17 \\\# 2 & 16 & 25 & 18 & 25 \\\# 3 & 23 & 24 & 23 & 22\end{array}\end{array}$ What is the estimate of the process mean for whenever it is under control?

Given the following process control data for a normally distributed quality variable (three samples of size four each): $\begin{array} { r} { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } &\\\hline \# 1 & 15 & 14 & 15 & 12 \\\# 2 & 18 & 16 & 20 & 16 \\\# 3 & 16 & 17 & 16 & 17\end{array}\end{array}$ If the process is known to have a mean of 15 and a standard deviation of 3, what are the three-sigma upper and lower control limits for an x-bar chart?

Control limits used on process control charts are specifications established by design or customers.

An x-bar control chart can only be valid if the underlying population it measures is a normal distribution.

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $\begin{array} {r } { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } & \\\hline \# 1 & 17 & 15 & 15 & 17 \\\# 2 & 16 & 25 & 18 & 25 \\\# 3 & 23 & 24 & 23 & 22\end{array}\end{array}$ For upper and lower control limits of 23.29 and 16.71, which machine(s) , if any, appear(s) to have an out-of-control process mean?

Given the following process control data for a quality attribute (three samples of size 400 each): $\begin{array} { l r } \text { Sample } & \text { Defectives } \\\hline \# 1 & 36 \\\# 2 & 32 \\\# 3 & 52\end{array}$ If the process proportion of defectives is unknown, what is the alpha risk (probability of Type I error) for upper and lower control limits of .115 and .085 respectively? .13 and .07? .145 and .055?

A plot below the lower control limit on the range chart: (I) should be ignored since lower variation is desirable. (II) may be an indication that process variation has decreased. (III) should be investigated for assignable cause.

The purpose of control charts is to:

The Taguchi loss function suggests that the capability ratio can be improved by extending the spread between LCL and UCL.

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $\begin{array} {r } { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } & \\\hline \# 1 & 17 & 15 & 15 & 17 \\\# 2 & 16 & 25 & 18 & 25 \\\# 3 & 23 & 24 & 23 & 22\end{array}\end{array}$ What are the x-bar chart three-sigma upper and lower control limits?

Given the following process control data for a normally distributed quality variable (three samples of size four each): $\begin{array} { r} { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } &\\\hline \# 1 & 15 & 14 & 15 & 12 \\\# 2 & 18 & 16 & 20 & 16 \\\# 3 & 16 & 17 & 16 & 17\end{array}\end{array}$ If the process is known to have a mean of 15 and a standard deviation of 3, using three-sigma control limits, do any of the sample means indicate an out-of-control process mean?

A time-ordered plot of sample statistics is called a(n) ______ chart.

Construct the appropriate two-sigma control chart for the sample observations listed below. $\begin{array} { l l l l l l l l l l r r } \text { Observation } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\\hline \text { Num. defects per unit } & 9 & 4 & 3 & 5 & 6 & 3 & 4 & 2 & 3 & 2 & 3\end{array}$

Given the following process control data for a quality attribute (three samples of size 400 each): $\begin{array} { l r } \text { Sample } & \text { Defectives } \\\hline \# 1 & 36 \\\# 2 & 32 \\\# 3 & 52\end{array}$ If the process is known to produce 11 percent defectives on average, using three-sigma control limits, do any of the sample proportions indicate an out-of-control process proportion of defectives?

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $\begin{array} {r } { \text { Measurements } } \\\begin{array} { l l l l l } \text { Machine } & \\\hline \# 1 & 17 & 15 & 15 & 17 \\\# 2 & 16 & 25 & 18 & 25 \\\# 3 & 23 & 24 & 23 & 22\end{array}\end{array}$ What is the estimate of the sample average range based upon this limited sample?

A process that exhibits random variability would be judged to be out of control.

A control chart used to monitor the process mean is the:

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $\begin{array} { r } { \text { Service Life (hours) } }\\\begin{array} { l l l l l } \text { Sample } & \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}\end{array}$ If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error) ?