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Exam 10: Quality Control

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Question 41

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A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each: $\begin{array} { r } { \text { Weight (ounces) } }\\\begin{array} { l l l l l } \text { Day } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\text { Tuesday } & 23 & 21 & 19 & 21 \\\text { Wednesday } & 20 & 19 & 20 & 21 \\\text { Thursday } & 18 & 19 & 20 & 19 \\\text { Friday } & 18 & 20 & 22 & 20\end{array}\end{array}$ What is the mean of the sampling distribution of sample means when this process is under control?

A) 18 ounces
B) 19 ounces
C) 20 ounces
D) 21 ounces
E) 22 ounces

F) B) and D)
G) A) and B)

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Question 42

Multiple Choice

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The following data occurs chronologically from left to right: $\begin{array} { l l l l l l } 15.2 & 19.7 & 16.0 & 11.1 & 14.8 & 14.5\end{array}$ The number of runs with respect to the sample median is:

A) 2.
B) 3.
C) 4.
D) 5.
E) none of these.

F) A) and B)
G) B) and E)

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Question 43

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Run tests give managers an alternative to control charts; they are quicker and cost less.

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 is the alpha risk (probability of Type I error) for upper and lower control limits of 16.5 and 13.5 respectively? 18 and 12? 19.5 and 10.5?

The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are under control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: $\begin{array} { l c } \text { Instructor } & \text { Number of Failures } \\\hline \text { Prof. A } & 13 \\\text { Prof. B } & 0 \\\text { Prof. C } & 11 \\\text { Prof. D } & 16\end{array}$ Using .95 control limits (5 percent risk of Type I error) , which instructor(s) , if any, should he conclude is (are) out of control?

Studies on a machine that molds plastic water pipe indicate that when it is injecting 1-inch-diameter pipe, the process standard deviation is 0.05 inches. The 1-inch pipe has a specification of 1 inch plus or minus 0.10 inch. What is the process capability index (C_pk) if the long-run process mean is 1 inch?

The best way to assure quality is to use extensive inspection and control charts.

Control limits are based on multiples of the process standard deviation.

The sampling distribution can be assumed to be approximately normal even when the underlying process distribution is not normally distributed.

Given the following process control data for a quality attribute (three samples of size 400 each): $\begin{array} { l r } \text { Sample } & \text { Defectives } \\\hline \# 1 & 36 \\\# 2 & 32 \\\# 3 & 52\end{array}$ What is the sample proportion of defectives for sample #1? #2? #3?

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, what are the upper and lower control limits for an alpha risk of .10? .05? .01?

The following chart depicts 16 sample means that were taken at periodic intervals and plotted on a control chart. Does the output appear to be random?

Processes that are in control eliminate variations.

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: $\begin{array} { r } { \text { Service Life (hours) } }\\\begin{array} { l l l l l } \text { Sample } & \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}\end{array}$ What is the sample mean service life for sample 2?

The number of defective parts in a sample is an example of variable data because it will "vary" from one sample to another.

The amount of inspection needed is governed by the costs of inspection and the expected costs of passing defective items.

_______ variation is a variation whose cause can be identified.

Low-cost, high-volume items often require more intensive inspection than other types of items.

A control chart used to monitor the number of defects per unit is the:

The specification limit for a product is 8 cm and 10 cm. A process that produces the product has a mean of 9.5 cm and a standard deviation of 0.2 cm. What is the process capability, C_pk?