Quality and Quality Control

For each of the following cases, fi nd the CL, UCL, and LCL for an x chart based on the given information.

(a) n = 9, x = 26.7, R = 5.3. (b) n = 17, x = 138.6, R = 15.1. (c) n = 4, x = 84.2, R = 9.6. (d) n = 22, x = 8.1, R = 7.4

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Altoona Tire Company sells its ATC-50 tires with a 50,000-mile tread-life warranty. Lorrie Ackerman, a quality control engineer with the company, runs simulated road tests to monitor the life of the output from the ATC-50 production process. From each of the last 12 batches of 1,000 tires, she has tested 5 tires and recorded the following results, with x and R measured in thousands of miles:

Batch 1 2 3 4 5 6 7 8 9 10 11 12 x 50.5 49.7 50.0 50.7 50.7 50.6 49.8 51.1 50.2 50.4 50.6 50.7 R 1.1 1.6 1.8 0.1 0.9 2.1 0.3 0.8 2.3 1.3 2.0 2.1 (a) Use the data above to help Lorrie construct an x chart. (b) Is the production process in-control? Explain.

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For each of the following cases, find the CL, UCL, and LCL for an x chart based on the given information.

(a) n = 12, x = 16.4, x σ = 1.2. (b) n = 12, x = 16.4, R = 7.6. (c) n = 8, x = 4.1, R = 1.3. (d) n =15, x = 141.7, R = 18.6

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The Wilson Piston Company manufactures pistons for LawnGuy mowers, and the diameter of each piston must be carefully monitored. Jeff Wilson, the quality control engineer, has sampled 8 pistons from each of the last 15 batches of 500 pistons and has recorded the following results, with x and R measured in centimeters:

Batch123456789101112131415
x15.8515.9515.8615.8415.9115.8115.8615.8415.8315.8315.7215.9615.8815.8415.89
R0.150.170.180.160.140.210.130.220.190.210.280.120.190.220.24
    Use the data above to help Jeff construct an x chart.
  1. Is the production process in-control? Explain

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Dick Burney is director of 911 emergency medical services in Ann Arbor, Michigan. He is concerned about response time, the amount of time that elapses between the receipt of a call at the 911 switchboard and the arrival of a municipal rescue squad crew at the calling location. For the last 3 weeks, he has randomly sampled response times for 9 calls each day to get the following results, with x ̅ and R measured in minutes:

Batch123456789101112131415
x15.8515.9515.8615.8415.9115.8115.8615.8415.8315.8315.7215.9615.8815.8415.89
R0.150.170.180.160.140.210.130.220.190.210.280.120.190.220.24
    Use the data above to help Jeff construct an x chart.
  1. Is the production process in-control? Explain

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