Effect of Measurement Error on Shewhart Control Charts

Abstract

Significant measurement error often exists in quality control applications. Measurement error is known to result in reduced power to detect a given change in the mean or variance of a quality characteristic. There are often several available measurement techniques, among which one yields the greatest power per measurement to detect process shifts. The effect of measurement error on the performance of X̄ and S2 charts using a linear covariate is investigated. One of the effects of measurement error is a loss of power in detecting parameter shifts in the underlying process variable. In the presence of measurement error, it may be desirable to take multiple measurements for each of the items in a subgroup. Conditions under which multiple measurements are desirable are identified, and a cost model is suggested for selection of an optimal sampling plan. A model involving measurement error variance that is a linearly increasing function of the process mean is also investigated.

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