The data in Excel worksheet Q1 list processing time values for 40 samples of siz

Question

The data in Excel worksheet Q1 list processing time values for 40 samples of size 4 that were taken from Rapid Check Kiters, Inc.’s check processing firm over a 20-hour period

a.) Compute the mean and standard deviation of all 40 samples for the sample data.

b.) Calculate the control limits and construct the - and R charts, using the first 20 samples. Is the process under control at that point?

c.) Specifications for the process are 1.065 ±0.14. If the process is under control, calculate the capability indexes, Cpu, Cpl, Cp and Cpk. What do the indexes indicate?

The results of the initial 20 samples of size 4 are shown below.

Initial data

The results of the initial 20 samples of size 4 are shown below.

Sample DATA 1 1.01 1.03 1.07 1.10 2 1.15 1.05 1.08 1.01 3 1.08 1.14 1.06 1.10 4 0.98 1.08 0.97 1.04 5 1.13 1.05 1.14 1.01 6 1.06 1.10 1.16 1.02 7 1.03 1.04 1.13 1.05 8 1.08 1.11 1.14 1.07 9 1.13 1.11 1.06 1.05 10 1.16 1.06 1.07 1.02 11 1.08 1.00 0.99 1.03 12 1.11 1.07 1.05 1.05 13 1.09 1.13 1.09 1.14 14 1.05 0.95 1.15 1.08 15 1.07 1.04 1.10 1.06 16 1.05 1.07 1.06 1.04 17 1.03 1.08 1.04 1.08 18 1.01 1.08 1.05 1.04 19 1.08 1.07 1.11 1.06 20 1.09 1.08 1.02 1.15

Explanation / Answer

Sample DATA Mean (X Bar) R 1 1.01 1.03 1.07 1.1 1.05 0.09 2 1.15 1.05 1.08 1.01 1.07 0.14 3 1.08 1.14 1.06 1.1 1.10 0.08 4 0.98 1.08 0.97 1.04 1.02 0.11 5 1.13 1.05 1.14 1.01 1.08 0.13 6 1.06 1.1 1.16 1.02 1.09 0.14 7 1.03 1.04 1.13 1.05 1.06 0.1 8 1.08 1.11 1.14 1.07 1.10 0.07 9 1.13 1.11 1.06 1.05 1.09 0.08 10 1.16 1.06 1.07 1.02 1.08 0.14 11 1.08 1 0.99 1.03 1.03 0.09 12 1.11 1.07 1.05 1.05 1.07 0.06 13 1.09 1.13 1.09 1.14 1.11 0.05 14 1.05 0.95 1.15 1.08 1.06 0.2 15 1.07 1.04 1.1 1.06 1.07 0.06 16 1.05 1.07 1.06 1.04 1.06 0.03 17 1.03 1.08 1.04 1.08 1.06 0.05 18 1.01 1.08 1.05 1.04 1.05 0.07 19 1.08 1.07 1.11 1.06 1.08 0.05 20 1.09 1.08 1.02 1.15 1.09 0.13 Mean X double bar 1.07 0.09 R bar St. Dev. 0.02 X bar n 4 UCL X Double bar +A2 *R bar 1.137537 A2 0.729 LCL X Double bar - A2 *R bar 1.001214 D3 0 D4 2.282 R bar UCL D4 * R bar 0.213367 LCL D3 * R bar 0 The process is under control Specifications for the process are 1.065 ±0.14 upper specification 1.205 lower specification 0.925 mean 1.065 Cp = (upper specification - lower specification)/ 6 2.016546 Cpl(mean - lower specification)/3 0.00108 Cpu(upper specification - mean)/3) 0.00108 Cpk = min of { (mean - lower specification)/3, (upper specification - mean)/3)} 0.00108

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