Question 1

A manufacturing company has a production process that has a target percentage of nonconformance as 4 percent which was developed based on numerous samples of 200 observations each. They want to develop control charts using 3 standard deviation limits.
a.What is the center line for the p-chart?
b.What is the upper control limit for a p-chart?
c.What is the lower control limit for a p-chart?

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Question 2

Define statistical process control (SPC), and differentiate between common cause and special (or assignable) cause variation.

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Question 3

Flaws are counted on a standard steel plate (sheet). Each sheet has the exact same dimensions. Ten sheets are selected at random and the number of flaws per sheet is as follows:
 $$\begin{array} { | c | c | } 
\hline \text { Sheet } & \text { Number of Flaws } \
\hline 1 & 3 \
\hline 2 & 1 \
\hline 3 & 3 \
\hline 4 & 0 \
\hline 5 & 2 \
\hline 6 & 2 \
\hline 7 & 0 \
\hline 8 & 1 \
\hline 9 & 1 \
\hline 10 & 2 \
\hline
\end{array}$$ Determine the lower and upper control limits for a c-chart.

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Question 4

Over several days, 25 samples of 100 items each were tested for electrical resistance. A total of 60 items failed. Determine the control limits for a p-chart.

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Question 5

Discuss the three basic quality control practices used in manufacturing.

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Question 6

Discuss the difference between a continuous metric and a discrete metric, give examples of each, and list the common control charts associated with each.

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Question 7

Define quality at the source.

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Question 8

A company is measuring the time it takes to complete an order. Twenty-five samples of size 6 resulted in an average time of 80 minutes with an average range of 20 minutes. Find control limits for the appropriate control chart(s) that would be used to monitor this process.

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Question 9

A production process is sampled 24 times with a sample size of 6 yields, an overall mean of 25.2, and an average range of 0.8. Determine the control limits for the x-bar and R-charts.

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Question 10

Describe the steps required to develop and use control charts.

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Question 11

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of eight was used. $$\begin{array} { | c | c | c | } 
\hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
\hline 2 & 16.10 & 0.38 \
\hline 3 & 16.02 & 0.08 \
\hline 4 & 15.95 & 0.15 \
\hline 5 & 16.12 & 0.42 \
\hline 6 & 16.18 & 0.23 \
\hline 7 & 15.87 & 0.36 \
\hline 8 & 16.20 & 0.40 \
\hline
\end{array}$$ 
a.Compute the limits for both an R-chart and x-bar chart. Compare the sample results to the limits of the charts.
b.Briefly explain what the quality control charts tell you. What actions, if any, would you take?

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Question 12

An operator has determined the percentage of defectives for a machine which she operates. Based on several samples of 75 observations, she found the p-bar to be 10 percent. She wants to set up a control chart using 3 standard deviation control limits.
a.What is the upper control limit for a p-chart?
b.What is the lower control limit for a p-chart?

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Question 13

Alico Steel manufactures steel tubes that are used in gas grills for residential customers. The tube's overall length is crucial to assure a proper fit, and this dimension has been targeted as an important dimension to be stabilized for the steel tube manufacturing process. Gas grill performance and customer safety are key objectives and highlight the importance of producing high quality steel tubes. Tubes are cut from rolls of steel tubing using a punch press. The tubes are measured using an operationally defined method, and Table 1 below summarizes the results. Appendix B with all factors for control charts will be given as a separate class handout.Table 1 Tube Length (in centimeters)
Sample Observations 1 to 6
$\text { Number Average x-bar Average range (R) }$
$\begin{array}{lll}
\hline 1 & 12.90 & 0.35 \
2 & 13.30 & 0.50 \
3 & 12.87 & 0.32 \
4 & 10.93 & 0.44 \
5 & 11.43 & 0.91 \
6 & 11.93 & 0.42 \
7 & 12.90 & 0.29 \
8 & 13.03 & 0.58 \
9 & 13.70 & 0.21 \
10 & 13.70 & 0.11 \
\hline
\end{array}$
Total 126.69 4.13
(a) 	The center line for the trial R-chart is _____.
The center line for the trial X-chart is _____.
The trial UCL for the R-chart is _____.
The trial LCL for the R-chart is _____.

(b)	Assuming that special causes for out-of-control situations in (a) are investigated and corrected using the seven tools of quality management, find the "final set of revised control limits" (i.e., take out any special cause sample(s) from your trial charts and recompute the following). (6 points)

The center line for the final revised R-chart is _____. 
The center line for the final revised X-chart is _____.
The final revised UCL for the R-chart is _____.
The final revised LCL for the R-chart is _____.
The final revised UCL for the x-bar chart is _____. 
The final revised LCL for the x-bar chart is _____.
(c)Plot the X-chart below and make sure you label the chart correctly.

(d) Is the process in statistical process control (SPC)? Justify and explain using facts. What action would you take given your "management by fact" data analysis?

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Question 14

An airline found that on average, 0.62 percent of the luggage they received from passengers at LAX (Los Angeles Airport) is lost or damaged. On a typical day, 1000 pieces of luggage pass through this airport. What are the control limits for a p-chart for monitoring the daily fraction nonconforming?

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Question 15

Find the control limits for a c-chart with c-bar= 7.

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Question 16

Explain and give the significance of the 1:10:100 Rule.

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Question 17

In general, discuss how to interpret control charts.

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Question 18

Fifteen samples of size 5 have been taken from a production process. The sum of the sample averages was found to be 92.54 cm, while the sum of the ranges was 115.36. Find the values of the center lines for the x-bar and R-charts.

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Question 19

Define and give an example of the three components of any control system.

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Question 20

A manufacturer inspected 40 circuit boards and found a total of 640 defects. If the company wants to use statistical process control (SPC) to control the manufacturing process by monitoring the number of defects per circuit board, what type of chart should they use and what should be the control limits?

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Quiz 16: Quality Control and Spc