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3-sigma control chart

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A&A Enterprises ships integrated circuits to companies that assemble computers. Because computer manufacturing operations run on little inventory, parts must be available when promised. Thus, a critical element of A&A's customer satisfaction is on-time delivery performance. To ensure that their delivery process is performing as intended, a quality improvement team decided to monitor the firm's distribution and delivery process. From the A&A corporate data base, 100 monthly shipping records were randomly selected for the previous 21 months, and the number of on-time shipments was counted.

Month On Time
January 99
February 98
March 96
April 94
May 90
June 87
July 86
August 95
September 92
October 93
November 87
December 85
January 96
February 87
March 93
April 85
May 88
June 86
July 97
August 94
September 94

Develop the appropriate 3-sigma control chart(s) for monitoring this process. Does it appear that the delivery process is in control? If not, can you suggest some possible assignable causes?

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Statistics: Construct the 3-sigma x-chart and the 3-sigma R-chart for auto pistons

Auto pistons at Yongpin Zhou's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

Day Mean(mm) Range(mm)
1 156.9 4.2
2 153.2 4.6
3 153.6 4.1
4 155.5 5.0
5 156.6 4.5

Construct the 3-sigma x-chart and the 3-sigma R-shart for this dimension, using the data observed in the table above.

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