Let us reconsider Example 13.2a under the new supposition that the process is just beginning and so

Question:

Let us reconsider Example 13.2a under the new supposition that the process is just beginning and so μ and σ are unknown. Also suppose that the sample standard deviations were as follows:

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Since all the X i fall within these limits, we suppose that the process is in control with μ = 3.067 and σ = S/c(4) = .1324.
Suppose now that the values of the items produced are supposed to fall within the specifications 3 ± .1. Assuming that the process remains in control and that the foregoing are accurate estimates of the true mean and standard deviation, what proportion of the items will meet the desired specifications?

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