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Q-3) Samples of cight 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 $X?=9.9892,R?=0.2628$ and $s?=0.0880$ a) Calculate the $3?$ control limits for the $R$ chart. Sketch $R$ Control chart. Is the variance under control? If not, delete the samples that are out of control and re-compute $X?$ and $R?$. Sketch the new chart. b) Based on the sample range $R$, ealculate the $3?$ control limits for the $X?$ chart. Sketch the chart. Based on the $3?$ 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? d) Repeat above parts a, b, and c, using the $S$ chart in place of the $R$ chart. $(25=5+5+2.5+12.5)$

a) To calculate the control limits for the R chart, we use the following formulas:UCLR = D4R = 0.2877LCLR = D3R = 0.1783Where D4 = 3.267 and D3 = 0 fo