In the July 1989 issue of Quality Progress, William J. McCabe discusses using a p chart to

Question:

In the July 1989 issue of Quality Progress, William J. McCabe discusses using a p chart to study the percentage of errors made by 21 buyers processing purchase requisitions. The p chart presented by McCabe is shown in Figure 17.26. In his explanation of this chart, McCabe says,
The causes of the errors . . . could include out-of-date procedures, unreliable office equip¬ment, or the perceived level of management concern with errors. These causes are all associated with the system and are all under management control.
Focusing on the 21 buyers, weekly error rates were calculated for a 30-week period (the data existed, but weren't being used). A p-chart was set up for the weekly department error rate. It showed a 5.2 percent average rate for the department. In week 31, the manager called the buyers together and made two statements: "I care about errors because they affect our costs and delivery schedules," and "I am going to start to count errors by individual buyers so I can understand the causes." The p-chart .. . shows an almost immediate drop from 5.2 percent to 3.1 percent.
The explanation is that the common cause system (supervision, in this case) had changed; the improvement resulted from eliminating buyer sloppiness in the execution of orders. The p-chart indicates that buyer errors are now stable at 3.1 percent. The error rate will stay there until the common cause system is changed again.
FIGURE 17.26
p Chart for the Weekly Department Error Rate for 21 Buyers Processing Purchase Requisitions

a. The p chart in Figure 17.26 shows that = .052 for weeks l through 30. Noting that the subgroup size for this chart is n = 400, calculate the control limits UCL and LCL for the p chart during weeks 1 through 30.
b. The p chart in Figure 17.26 shows that after week 30 the value of is reduced to .031. Assuming that the process has been permanently changed after week 30, calculate new control limits based on = .031. If we use these new control limits after week 30, is the improved process in statistical control? Explain.