SQC Sample Problems

 

Note for Ch15_data: Go through hyperlink to data file Ch15_data. Save the file as "html" to your floppy disc. Open the file in Excel 97. Save the file as an Excel 97 file. Copy the data for each problem into Minitab and calculate the answers.

 

1. The mean of the sample means and pooled standard deviation of 40 samples of size 9 taken from a production process under control are shown below. Compute the centerline, control limits, and zone boundaries for the x-bar chart.

x-bar-bar = 181.1

S = 11.0

Answers: 170.1, 181.1, 192.1

2. Twenty-five samples of size 4 were taken from a production process. The sample means are listed in file Ch15_data. The mean of the sample means and the pooled standard deviation are:

x-bar-bar = 13.3

S = 3.8

  1. Find the centerline and control limits for the x-bar chart
  2. Plot the sample means on he x-bar chart
  3. Is the process under control? Explain?

Answers: a) 7.6, 13.3, 19.0, c) out of control at samples 8, 9, 21, 22, 25

3. Thirty samples of size 4 were drawn from a production process. The data were stored in file Ch15_data.

  1. Construct an S chart
  2. Construct an x-bar chart
  3. Do the charts allow you to conclude that the process is under control?
  4. If the process went out of control, which of the following is the likely cause: level shift, instability, trend, or cycle. Explain your answer.

Answers: c) The process is out of control at samples 29 and 30 of x-bar chart, d) level shift

4. The fence of a saw is set so that it automatically cuts 2 by 4’s into 96-inch lengths needed to produce prefabricated homes. To ensure that the lumber is cut properly, 3 pieces of wood are measured after each 100 cuts are made. The measurements in inches for the last 40 samples are stored in file Ch15_data.

  1. Do these data indicate that the process is out of control?
  2. If so, when did it go out of control?
  3. What was the likely cause: level shift, instability, trend or cycle? Explain your answer.
  4. Speculate how the problem could be corrected.

Answers: a,b) The process is out of control at sample 1, c) trend, d) clean out the sawdust more frequently

5. Twenty-five samples of size n = 4 were drawn. For each sample, the mean and range were computed as shown in file Ch15_data.

  1. Draw the R-chart
  2. Draw the x-bar chart
  3. Does it appear that the process is under control? Explain your answer.

Answers: a) 0, 11.68, 26.65, b) 10.25, 18.76, 27.27, c) The process is out of control at sample 13 of the x-bar chart

6. Refer to problem 4.

  1. Draw the R-chart
  2. Draw the x-bar chart (using the sample ranges to estimate he process standard deviation.)
  3. Is the process under control? Explain your answer.

Answers: a) 0, .1358, .3496, b) 95.78, 95.92, 96.06, c) The process is out of control at sample 1 of the x-bar chart

7. Random samples of 200 trucks were taken on an assembly line every hour for the past 25 hours. The number of defective trucks is stored in file Ch15_data.

  1. Are there any points beyond the control limits?
  2. If so, what do they tell you about the production process?

Answers: The process is out of control at sample 25

8. The Woodsworth Publishing Company produces millions of books containing hundreds of millions of pages each year. To ensure the quality of the printed page, Woodworth uses statistical process control. In each production run, 1000 pages are randomly inspected. The examiners look for print clarity and whether the material is properly centered on the page. The number of defective pages in the last 40 production runs is listed in file Ch15_data.

  1. Draw the p chart
  2. Using the pattern tests, can we conclude that the production process is under control? Explain your answer.

Answers: The process is out of control at samples 37-40

9. Optical scanners are used in all supermarkets to speed the checkout process. Whenever the scanner fails to read the bar code on the product, the cashier is required to manually punch the code into the register. Obviously, unreadable bar codes slow the checkout process. SPC is used to determine whether the scanner is working properly. Once a day at each checkout counter, a sample of 500 scans is taken and the number of times the scanner is unable to read the bar code is determined. (The sampling process is performed automatically by the cash register.) The results for one checkout counter for the past 25 days are stored in file Ch15_data.

  1. Draw the appropriate control charts.
  2. Does it appear that the process went out of control?
  3. If so, identify when this happened and suggest several possible explanations for the cause.

Answers: The process is out of control at sample 24 of the x-bar chart

10. Almost all computer hardware and software producers offer a toll-free telephone number to solve problems associated with their product. The ability to work quickly to resolve difficulties is critical. One software maker’s policy is that all calls must be answered by a software consultant within 120 seconds. (All calls are initially answered by computer and the caller is put on hold until a consultant attends to the caller.) To help maintain the quality of service, four calls per day are monitored. The amount of time before the consultant responds to the caller is recorded. The record of the last 30 days is stored in file Ch15_data.

  1. Draw the appropriate control chart(s).
  2. Does it appear that the process went out of control?
  3. If so, when did this happen?
  4. What are the likely causes and remedies?

Answers: The process is out of control at sample 25