A certain manufacturing plant is having problems meeting its delivery commitments. One of the problems has been traced to purchased materials which are frequently late, received in the wrong quantities, or the vendor ships the wrong parts in error. The purchasing director has been tasked to see if errors in purchase orders are contributing to the problem. Ten purchase orders per day are selected at random over a 20-day period. Each purchase order is carefully scrutinized and the total number of errors is recorded. The aggregate total for all 10 purchase orders sampled is then computed. The results are shown below.

a. Is the process of purchase order error generation stable? What is your best estimate of the number of errors that will be on the next purchase order cut? Support your answers with control chart data.
b. The following data were collected for a 20-day period following the implementation of some improvements in the purchasing department. Using the control chart that you constructed for part a, demonstrate whether there is statistical evidence to validate the improvement

c. Construct a control chart for the process following the improvements. Is the process in control? What is your best estimate of the number of errors in the next purchase order cut?
d. Management wishes to reduce the sampling effort from 10 to 5 per day. What centerline and control limits should be placed on the control chart?

Errors in Ten Randomly Selected Purchase Orders Errors ErrorsDay Recorded Day Recorded 15 12 13 14 15 16 17 18 19 20 10 13 16 13 16 19 7 15 13 10 10 Errors in Ten Randomly Selected Purchase ErrorS Recorded Errors Recorded Day Day 32 23 24 25 26 27 28 29 30 34 35 36 37 38 39 40