Effect of Measurement Error and Instrument Bias on Operating Characteristics for Variables Sampling Plans

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Abstract
The effect of measurement error on the operating characteristics of one-sided (normal distribution) variables sampling plans is discussed. A table showing the effect on the operating characteristic curves for the proportion nonconforming is given in terms of the ratio of the standard deviation of the measuring device (including the effect of the operator of the device) to the standard deviation of the item being measured, for a properly calibrated measuring instrument. This effect is salutory for the consumer, but unfair to the producer. A similar table is given for the case of a biased instrument which has no measurement error. Here the effect can be either in the consumer's favor or the producer's favor, depending on the direction of the bias. An alternative analysis gives the effect of measurement error and instrument bias on the consumer's and producer's risks for a specified plan. The results of the alternative analysis change from plan to plan, while the first analysis is independent of the plan and the resulting tables apply universally to variables sampling plans based on the normal distribution.

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