Samples of eight bolts are taken periodically, and their diameters (in mm) are measured. The following table presents the means, ranges, and standard deviations for 25 consecutive samples.

The means are X̅ = 9.9892, R = 0.2628, and s̅ = 0.0880.

a. Calculate the 3σ control limits for the R̅ chart. Is the variance under control? If not, delete the samples that are out of control and recompute X̅ and R.

b. Based on the sample range R̅, calculate the 3σ control limits for the X̅ chart. Based on the 3σ limits, is the process mean in control? If not, when is it first detected to be out of control?

c. Based on the Western Electric rules, is the process mean in control? If not, when is it first detected to be out of control?

Transcribed Image Text:

Sample X R S 1 0.09 9.99 10.02 0.28 2 0.43 0.13 3 10.10 0.16 0.05 4 9.90 0.26 0.09 5 9.92 0.22 0.40 0.08 0.07 6 10.05 9.97 0.15 7 0.03 9.93 0.48 0.15 9 10.01 0.25 0.09 10 9.87 0.29 0.10 11 9.90 0.39 0.14 9.97 0.27 12 13 0.08 0.07 10.02 0.20 14 9.99 0.37 0.13 0.06 15 9.99 0.20 0.26 0.09 0.07 0.12 16 10.04 17 10.07 0.23 18 10.04 0.35 19 0.09 9.95 9.98 0.25 20 0.15 0.06 21 9.98 0.30 0.10 22 10.02 0.14 0.06 23 9.94 0.24 0.07 24 10.04 0.13 0.04 25 10.04 0.24 0.07