Samples of eight bolts are taken periodically, and their diameters (in mm) are measured

Chapter 10, Problem 8

(choose chapter or problem)

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 \(\overline {\overline X}=9.9892\), \(\overline R=0.2628\) and \(\overline s=0.0880\).

a. Calculate the \(3\sigma\) control limits for the R chart. Is the variance under control? If not, delete the samples that are out of control and recompute \(\overline {\overline X}\) and \(\overline R\).

b. Based on the sample range R, calculate the \(3\sigma\) control limits for the \(\overline X\) chart. Based on the \(3\sigma\) 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?

Equation Transcription:

Text Transcription:

overline{overline X}=9.9892

overline{R}=0.2628

overline{s}=0.0880

3{sigma}

overline{overline X}

overline{R}

3{sigma}

overline{X}

3{sigma}