MGT 3900-008 SPC Variable and Discrete Control Chart Assignment (2 Separate Problems) All UCL, LCL and Cp equation calculations and analyses with formulas and formula values MUST be provided to receive ANY points. This assignment is to be completed individually and is due on Monday 3-13-23 in hard copy hand written form by 12:20 pm and is worth 15 points. #1. AirExpress, an overnight mail service, is concerned about the operating efficiency of the package-sorting department at its Pittsburgh, PA, terminal. The company would like to monitor the time it takes for packages to be put in outgoing delivery bins from the time they are received which should be between 30 and 37 minutes per package. The sorting department operates 8 hours per day, from 4:00 pm to midnight. The company randomly sampled 24 packages during each hour of operation. The time for each package to move through the system, in minutes is given in the table below. Construct a X-bar chart (std dev = 3.85) and a R chart (std dev = 1.76) from these data. Is the process operating at a state of statistical control? Explain why. Is the process capable of meeting the time specifications? Explain why. (10 points) Hourly Sample 1 2 3 4 5 6 7 8 28.2 29.2 24.1 33.9 36.5 34.1 25.9 28.2 28.1 29.1 24.3 33.2 36.7 34.7 25.3 28.1 33.3 30.3 31.1 26.3 34.1 34.1 31.9 29.3 34.6 39.6 29.4 31.4 37.7 37.1 29.9 39.1 29.4 27.4 29.7 36.5 33.3 36.3 28.7 27.6 33.7 32.7 32.9 40.1 29.7 32.7 33.9 33.1 31.7 30.7 36.9 26.8 34.6 35.9 35.9 32.0 27.4 28.4 24.1 29.6 30.9 31.9 24.9 28.4 36.5 30.5 35.5 36.1 27.4 27.4 34.5 30.5 28.8 27.8 29.6 29.0 34.1 34.9 29.6 27.1 35.1 34.1 30.1 35.9 28.8 27.8 30.9 33.0 27.5 25.5 26.3 34.8 30.1 32.8 27.3 25.9 27.6 24.6 29.9 31.8 37.9 37.1 29.1 25.6 31.6 30.6 36.3 40.2 30.8 33.8 37.5 30.9 29.7 29.7 33.2 34.9 27.6 26.6 24.9 29.7 26.1 24.1 26.8 32.7 29.7 30.9 27.2 24.9 27.4 29.4 31.6 35.2 27.6 28.6 31.6 29.1 35.1 31.1 33.0 29.6 35.2 35.9 33.4 31.6 26.9 27.9 29.9 35.1 25.1 25.9 31.8 27.9 33.6 36.6 32.4 28.7 27.9 26.9 32.7 34.6 31.9 33.9 27.1 26.2 35.1 36.1 27.6 33.1 31.2 33.2 41.2 30.7 31.6 30.6 41.2 33.2 Observations 28.7 26.7 35.2 39.7 31.5 31.5 35.1 27.7

32.5 30.5 36.8 27.9 28.6 29.6 36.2 30.0 #2. The data processing department of the PNC Bank has five data entry clerks. Each working day their supervisor verifies the accuracy of a random sample of 350 records. A record containing one or more errors is considered defective and must be redone. The results of the last 30 samples are shown in the table. (5 points) Sample # of Defective Records Sample # of Defective Records 1 7 16 18 2 5 17 12 3 19 18 8 4 15 19 6 5 11 20 11 6 8 21 17 7 12 22 12 8 9 23 6 9 8 24 17 10 13 25 13 11 18 26 10 12 15 27 14 13 16 28 8 14 8 29 11 15 11 30 9 a. Based on these historical data, set up a p-chart and determine if the process in a state of statistical control. Is the process operating at a state of statistical control? Explain why. b. After establishing the control limits, samples for the next four days showed the following: (use the control limits in part a to complete part b) Sample # of Defective Records Tuesday 19 Wednesday 13 Thursday 26 Friday 29 What is the supervisors assessment of the data entry process likely to be now?