SECTION 12.3 Exercises

For Exercises 12.41 and 12.42, see page 636; and for 12.43 and 12.44, see page 638.

Question 12.45

12.45 Aircraft rivets.

After completion of an aircraft wing assembly, inspectors count the number of missing or deformed rivets. There are hundreds of rivets in each wing, but the total number varies depending on the aircraft type. Recent data for wings with a total of 34,700 rivets show 208 missing or deformed. The next wing contains 1070 rivets. What are the appropriate center line and control limits for plotting the from this wing on a chart?

12.45

, so use 0.

Question 12.46

12.46 Call center.

A large nationwide retail chain keeps track of a variety of statistics on its service call center. One of those statistics is the length of time a customer has to wait before talking to a representative. Based on call center research and general experience, the retail chain has determined that it is unacceptable for any customer to be on hold for more than 90 seconds. To monitor the performance of the call center, a random sample of 200 calls per shift (three shifts per day) is obtained. Here are the number of unacceptable calls in each sample for 15 consecutive shifts over the course of one business week:

callc

Shift Shift 1 Shift 2 Shift 3 Shift 1 Shift 2 Shift 3
Unacceptable 6 17 6 9 16 10
Shift Shift 1 Shift 2 Shift 3 Shift 1 Shift 2 Shift 3
Unacceptable 8 14 5 6 16 6
Shift Shift 1 Shift 2 Shift 3
Unacceptable 9 14 7
  1. What is for the call center process?
  2. What are the center line and control limits for a chart for plotting proportions of unacceptable calls?
  3. Label the data points on the chart by the shift. What do you observe that the chart limits failed to pick up?

Question 12.47

12.47 School absenteeism.

Here are data from an urban school district on the number of eighth-grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth-graders changes a bit from month to month, these totals are also given for each month.

school

Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June
Students 911 947 939 942 918 920 931 925 902 883
Absent 291 349 364 335 301 322 344 324 303 344

639

  1. Find . Because the number of students varies from month to month, also find , the average per month.
  2. Make a chart using control limits based on students each month. Comment on control.
  3. The exact control limits are different each month because the number of students is different each month. This situation is common in using charts. What are the exact limits for October and June, the months with the largest and smallest ? Add these limits to your chart, using short lines spanning a single month. Do exact limits affect your conclusions?

12.47

(a) .
(b) . The process is in control.
(c) For October, .
For June, . Exact limits do not affect the conclusions.

Question 12.48

12.48 charts and high-quality processes.

A manufacturer of consumer electronic equipment makes full use not only of statistical process control but of automated testing equipment that efficiently tests all completed products. Data from the testing equipment show that finished products have only 3.5 defects per million opportunities.

  1. What is for the manufacturing process? If the process turns out 5000 pieces per day, how many defects do you expect to see at this rate? In a typical month of 24 working days, how many defects do you expect to see?
  2. What are the center line and control limits for a chart for plotting daily defect proportions?
  3. Explain why a chart is of no use at such high levels of quality.

Question 12.49

12.49 Monitoring lead time demand.

Refer to the lead time demand process discussed in Exercise 5.83 (page 285). Assuming the Poisson distribution given in the exercise, what would be the appropriate control chart limits for monitoring lead time demand?

12.49

.

Question 12.50

12.50 Purchase order errors.

Purchase orders are checked for two primary mistakes: incorrect charge account number and missing required information. Each day, 10 purchase orders are randomly selected, and the number of mistakes in the sample is recorded. Here are the numbers of mistakes observed for 20 consecutive days (read left to right):

poerr

6 4 11 6 3 7 3 10 14 6
3 5 6 7 5 7 7 4 3 7
  1. What is for the purchase order process? How many mistakes would you expect to see in 50 randomly selected purchase orders?
  2. What are the center line and control limits for a chart for plotting counts of purchase order mistakes per 10 orders? Are there any indications of out-of-control behavior?
  3. Remove any out-of-control observation(s) from the data count series and recompute the chart control limits. Comment on control of the remaining counts.

Question 12.51

12.51 Implications of out-of-control signal.

For attribute control charts, explain the difference in implications for a process and in actions to be taken when the plotted statistic falls beyond the upper control limit versus beyond the lower control limit.

12.51

Usually with attribute control charts, we are keeping track of count data that have a negative aspect, such as the number of mistakes. So, if we get an out-of-control point above the UCL, we want to find the source of special cause and try to correct it. However, if we get an out-of-control point below the LCL, we want to find the source of the special cause and mimic it in the future to potentially change (reduce) the level of the process.