A Combined Control Chart to Monitor the Process Mean in a Two‐Stage Sampling

Abstract

This paper proposes a new combined control chart for monitoring the mean of a process. A sample of size n is split into two sub‐samples of sizes n1 and n2 = n ‐ n1, determined by an optimization search. The units of the first sub‐sample are evaluated by attributes and plotted on an npx control chart. If this chart signals an out‐of‐control condition, then values of the quality characteristic of interest are collected from the units of the second sub‐sample, and the sample mean is calculated and plotted on an control chart. If both control charts signal, then the process is halted for adjustment. The possibility that all n items will not be inspected may lead to a reduction in both the cost and time spent on examining the sampled items. The performance of the proposed procedure is compared to that of two separate and npx control charts. The proposed procedure exhibits superior performance to the control chart for a variety of sample sizes, n, and shifts, δ, of the target mean. The average time to signal (ATS) for the combined control chart was lower than that calculated for a single or npx control chart, indicating that the combined control chart is an efficient tool for monitoring the process mean. Copyright © 2013 John Wiley & Sons, Ltd.

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