Homework Ch 3 and 13

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Chapter 3 and Chapter 13 Homework

Problem 03-02.
The Road King Tire Company in Birmingham wants to monitor the quality of the tires it manufactures. Each day the company quality-control manager takes a sample of 100 tires, tests them, and determines the number of defective tires. The results of 20 samples have been recorded as follows:

Sample Number of Defectives Sample Number of Defectives 1 14 11 18 2 12 12 10 3 9 13 19 4 10 14 20 5 11 15 17 6 7 16 18 7 8 17 18 8 14 18 22 9 16 19 24
10 17 20 23

Construct a -chart for this process using limits and describe the variation in the process.

P-chart average = 0.178
UCL = 0.178+3*SqRt(0.178*(1-0.178/200) = 0.2591
LCL = 0.178-3*SqRt(1-0.0.178/200) = 0.0969
The process is NOT in control.

Problem 03-06.
One of the stages in the process of making denim cloth at the Southern Mills Company is to spin cotton yarn onto spindles for subsequent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some number of breaks is considered normal; however, too many breaks might mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours:

Sample Number of Breaks Sample Number of Breaks 1 3 11 3 2 2 12 4 3 4 13 6 4 1 14 7 5 5 15 8 6 3 16 6 7 2 17 5 8 4 18 7 9 0 19 8
10 2 20 6

Construct a -chart using limits for this process and indicate if the process was out of control at any time.

Yes. The process was out of control a majority of the time, including in samples 2, 4, 7, 9, 10, 13, 14, 15, 16, 18, 19 and 20.

Sample Observed Values (x) UCL LCL UCL - x X - LCL Out of control…...

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