1. You are helping to manage a Performance Based Logistics contract which has a target of 48 hour delivery for parts to customers in the continental USA. You are monitoring variability in the contract via a control chart (a P-Chart).

Each week, your office examines a random selection of 100 transactions to test for the level of variability in performance. You have found that on average (across many samples, while the process is in control) there are 5 late deliveries per week, which you count as defects for the purpose of the P-Chart.

Each time the weekly sample indicates that the number of defects (late deliveries) has exceeded the upper control limit on the control chart, the program office will notify the vendor, and conduct a formal review of that weeks performance to see if the delivery process has gone out of control.

1. What is P-bar on the P-Chart?
2. Using the standard formula given in the slide, with 3 for the multiplier on the standard deviation, what is the UCL?
3. The office has decided they want to conduct a review unnecessarily (producers risk) no more than 1% of the time, and they have asked you to adjust the P-Chart (the Upper Control Limit) appropriately to match this risk appetite. What should be the new UCL? (Hint: for the purpose of this question you may assume the defect percentage is normally distributed).