CHAPTER 12 Review Exercises

Question 12.52

12.52 Enlighten management.

A manager who knows no statistics asks you, “What does it mean to say that a process is in control? Is being in control a guarantee that the quality of the product is good?” Answer these questions in plain language that the manager can understand.

Question 12.53

12.53 Pareto charts.

You manage the customer service operation for a maker of electronic equipment sold to business customers. Traditionally, the most common complaint is that equipment does not operate properly when installed, but attention to manufacturing and installation quality will reduce these complaints. You hire an outside firm to conduct a sample survey of your customers. Here are the percent of customers with each of several kinds of complaints:

Category Percent
Accuracy of invoices 25
Clarity of operating manual 8
Complete invoice 24
Complete shipment 16
Correct equipment shipped 15
Ease of obtaining invoice adjustments/credits 33
Equipment operates when installed 6
Meeting promised delivery date 11
Sales rep returns calls 4
Technical competence of sales rep 12
  1. Why do the percents not add to 100%?
  2. Make a Pareto chart. What area would you choose as a target for improvement?

12.53

(a) The customers could make 0 or many complaints, not just 1. (b) The three biggest complaints are problems with invoices, so that should be the focus.

640

Question 12.54

12.54 Purchased material.

At the present time, about five out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they are incorrect. The plant receives about 300 lots per week. As part of an effort to reduce errors in the system of placing and filling orders, you will monitor the proportion of rejected lots each week. What type of control chart will you use? What are the initial center line and control limits?

You have just installed a new system that uses an interferometer to measure the thickness of polystyrene film. To control the thickness, you plan to measure three film specimens every 10 minutes and keep and s charts. To establish control you measure 22 samples of three films each at 10-minute intervals. Table 12.11 gives and s for these samples. The units are millimeters . Exercises 12.55 through 12.57 are based on this process improvement setting.

Question 12.55

12.55 chart.

Calculate control limits for s, make an chart, and comment on control of short-term process variation.

12.55

, using and . The first sample is out of control.

film

Question 12.56

12.56 chart.

Interviews with the operators reveal that in Samples 1 and 10, mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate after removing Samples 1 and 10. Recalculate UCL for the chart and add the new UCL to your chart from the previous exercise. Control for the remaining samples is excellent. Now find the appropriate center line and control limits for an chart, make the chart, and comment on control.

Table 12.18: TABLE 12.11 and for samples of film thickness
Sample Sample
1 848 20.1 12 823 12.6
2 832 1.1 13 835 4.4
3 826 11.0 14 843 3.6
4 833 7.5 15 841 5.9
5 837 12.5 16 840 3.6
6 834 1.8 17 833 4.9
7 834 1.3 18 840 8.0
8 838 7.4 19 826 6.1
9 835 2.1 20 839 10.2
10 852 18.9 21 836 14.8
11 836 3.8 22 829 6.7

film

Question 12.57

12.57 Categorizing the output.

Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.

  1. What type of control chart discussed in this chapter might be considered for this setting, and what would be the control limits for a sample of 100 films?
  2. Explain why the chart in part (a) would have limited practical value at current quality levels.

12.57

(a) A chart would be appropriate. , so use 0. (b) The chance of an unsatisfactory film is so small that we only expect 0.3 in each sample of 100. But if a sample has 2 defects, is already over than the UCL and would signal an out-of-control process, which isn’t true.

Question 12.58

12.58 Hospital losses revisited.

Refer to Exercise 12.14 (page 614), in which you were asked to construct and charts for the hospital losses data shown in Table 12.4.

hloss

  1. Make an chart and comment on control of the process variation.
  2. Using the range estimate, make an chart and comment on control of process level.

Question 12.59

12.59 Bone density revisited.

Refer to Exercise 12.26 (page 627), in which you were asked to construct and charts for the calibration data from a Lunar bone densitometer shown in Table 12.6.

bone

  1. Make an chart and comment on control of the process variation.
  2. Based on the standard deviations, make an chart and comment on control of process level.

12.59

(a) , using and .
(b) For . The process is in control.

Question 12.60

12.60 Even more signals.

There are other out-of-control signals that are sometimes used with charts. One is “15 points in a row within the level.” That is, 15 consecutive points fall between and . This signal suggests either that the value of used for the chart is too large or that careless measurement is producing results that are suspiciously close to the target. Find the probability that the next 15 points will give this signal when the process remains in control with the given and .

Question 12.61

12.61 It's all in the wrist.

Consider the saga of a professional basketball player plagued with poor free-throw shooting performance. Here are the number of free throws he made out of 50 attempts on 20 consecutive practice days (read left to right):

fthrow

25 27 31 28 22 21 27 20 25 27
23 22 29 34 30 27 26 25 28 25
  1. Construct a chart for the data. Does the process appear to be in control?
  2. Recognizing that the player needed insight into his free-throw shooting problems, the coach hired an outside consultant to work with the player. The consultant noticed a subtle flaw in the player's technique. Namely, the player was bending back his wrist only 85 degrees when, ideally, the wrist needs to be bent back 90 degrees for proper flick motion. Part of the problem was due to the player's stiff wrist. Over the course of the next week or so, the player was given techniques to loosen his wrist. After implementing a modification to wrist movement, he got the following results on 10 new samples (again out of 50 attempts):

    641

    34 38 35 43 31 35 32 36 28 39

    Plot the new sample proportions along with the control limits determined in part (a). What are your conclusions? What should be the values of the control limits for future samples?

12.61

(a) . The process is in control. (b) The process appears out of control because the process mean has shifted. The new control limits are .

Question 12.62

12.62 Monitoring rare events.

In certain SPC applications, we are concerned with monitoring the occurrence of events that can occur at any point within a continuous interval of time, such as the number of computer operator errors per day or plant injuries per month. However, for highly capable processes, the occurrence of events is rare. As a result, the data will plot as many strings of zeros with an occasional nonzero observation. Under such circumstances, a control chart will be fairly useless. In light of this issue, SPC practitioners monitor the time between successive events—for example, the time between accidental contaminated needle sticks in a health care setting. For this exercise, consider data on the time between fatal commercial airline accidents worldwide between January 1995 and August 2013.11

afatal

  1. Construct an individuals chart for the time-between-fatalities data. If the lower control limit computes to a negative number, set it to 0 because negative data values are not possible. Report the lower and upper control limits. Identify any observations flagged as unusual.
  2. Time-between-events data tend to be non-Normal and most often are positively skewed. Construct a histogram for the fatalities data. Is that the case for these data?
  3. For time-between-events data, transforming the data by raising them to the 0.2777 power often Normalizes the data. Apply this transformation to the time-between-fatalities data, and construct a histogram for the transformed data. Is this histogram consistent with the Normal distribution?
  4. Construct an individuals chart for the transformed data. If the lower control limit computes to a negative number, set it to 0. Report the lower and upper control limits. Identify the points that are flagged as unusual. With what national tragedy are these observations associated? Are all the observations flagged in the transformed data the same as those flagged in part (a)?
  5. Remove the unusual observations found in part (d), and reestimate and report the control limits. What impressions do you have about the time-between-fatalities process when plotted with the revised limits? Is there evidence of improvement or worsening of the process over the almost 10-year time span?

Question 12.63

12.63 Monitoring budgets.

Control charts are used for a wide variety of applications in business. In the accounting area, control charts can be used to monitor budget variances. A budget variance is the difference between planned spending and actual spending for a given time period. Often, budget variances are measured in percents. For improved budget planning, it is important to identify unusual variances on both the low and high sides. The data file for this exercise includes variance percents for 40 consecutive weeks for a manufacturing work center.

budget

  1. Construct an chart for the variance percents. Report the lower and upper control limits. Identify any observations that are outside the control limits.
  2. Apply the runs rule based on nine consecutive observations being on one side of the center line. Is there an out-of-control signal based on this rule? If so, what are the associated observations?
  3. Remove all observations associated with out-of-control signals found in parts (a) and (b). Reestimate the chart control limits, and apply them to the remaining observations. Are there any more out-of-control signals? If so, identify them and remove them and reestimate limits. Continue this process until no out-of-control signals are present. Report the final control limits to be used for future monitoring.
  4. Construct an chart based on the final data of part (c). What do you conclude?

12.63

(a) . Subgroup 5 is out of control, below the LCL. (b) Subgroups 20 to 28 are all above the CL, violating the nine-in-a-row rule. (c) The process is now in control, and there are no out of control signals. . (d) The MR chart shows the process is in control.

Question 12.64

12.64 Is it really Poisson?

Certain manufacturing environments, such as semiconductor manufacturing and biotechnology, require a low level of environmental pollutants (for example, dust, airborne microbes, and aerosol particles). For such industries, manufacturing occurs in ultraclean environments known as cleanrooms. There are federal and international classifications of cleanrooms that specify the maximum number of pollutants of a particular size allowed per volume of air. Consider a manufacturer of integrated circuits. One cubic meter of air is sampled at constant intervals of time, and the number of pollutants of size 0.3 microns or larger is recorded. Here are the count data for 25 consecutive samples (read left to right):

clean

642

7 3 13 1 17 3 6 9 12 5 5 0 6
2 9 1 12 2 3 3 7 5 0 3 13
  1. Construct a chart for the data. Does the process appear to be in control?
  2. Remove any out-of-control signals found in part (a), and reestimate the chart limits. Does the process now appear to be in control?
  3. Remove all observations associated with out-of-control signals found in parts (a) and (b). Reestimate the control limits, and apply them to the remaining observations. Are there any more out-of-control signals? If so, identify them and remove them and reestimate limits. Continue this process until no out-of-control signals are present. Report the final control limits.
  4. A quality control manager took a look at the data and was suspicious of the numerous rounds of data point removal. Even the final control limits were bothersome to the manager because the variation within the limits seemed too large. The manager made the following statement, “I am not so sure the chart is applicable here. I have a hunch that the process is not influenced by only Poisson variation. I suggest we look at the estimated mean and variance of the data values.” Calculate the sample variance of the original 25 values, and compare this variance estimate with the mean estimate. Explain how such a comparison can suggest the possibility that a Poisson distribution may not fully describe the process.