Solved: The following X chart depicts the last 50 samples taken from the output of a

Chapter 10, Problem 3

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The thickness, in mm, of metal washers is measured on samples of size 5. The following table presents the means, ranges, and standard deviations for 20 consecutive samples.

The means are \(\overline {\overline X}=2.505\), \(\overline{R}=0.1395\), and \(\overline{s}=0.057\).

a. Calculate the \(3\sigma\)        control limits for the  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 , 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{X}

overline{overline X}=2.505

overline{R}=0.1395

overline{s}=0.057

3sigma

overline{overline X}

overline{R}

3sigma

overline{X}

3sigma

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