A comparison of one-sided variables acceptance sampling methods when measurements are subject to error

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Morse, Peter
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Stephen B. Vardeman
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One-sided variables acceptance sampling plans such as the one presented in Schilling1 assume that a quality characteristic of interest, X, has a normal distribution and that measurements are exact. However, when measurements contain error and standard plans are used, the probability of accepting a lot for a fixed population proportion nonconforming varies widely depending on the population and measurement error parameter values. In this dissertation we consider methods for variables acceptance sampling in the presence of measurement error and evaluate their performance under lower bound constraints on the population variance;In the late 1950's, David, Fay and Walsh2 suggested a one-sided variables acceptance sampling method (David) for problems where the measurement error variance is known. A competitor to this plan (MLE) is one based on plugging maximum likelihood estimates for the parameters of the population into the normal cumulative distribution function and determining lot disposal based the on estimated proportion nonconforming. With great improvements in the speed of computers, other more computationally intensive plans can be compared with the earlier methods. This dissertation develops two other variables acceptance sampling plans (LRT1 and LRT2) where the accept/reject decision is based on the value of a likelihood ratio statistic;For a fixed sample size, each of the four plans is developed to guarantee a maximum producer's risk no larger than a pre-specified upper bound under the restriction that the ratio of population to measurement error variance is bounded below. The best plan gives the smallest maximum consumer's risk;The major findings are that the LRT2 method generally yields smaller maximum consumer risks than the other three methods. (In some special cases, the David method yields smaller values.) This result is true across a variety of different combinations of plan parameters;Additionally, variations on the David and MLE methods are developed and compared for the situation where the measurement error variance is unknown, but can be estimated. Plans are developed for two different approaches to estimating the error variance. It is not clear which method is more useful because neither method out-performs the other in all situations. ftn1Schilling, Edward G. (1982) Acceptance Sampling in Quality Control, Marcel Dekker, Inc., New York. 2David, H. T., E. A. Fay and J. E. Walsh. (1959) Acceptance Inspection by Variables when Measurements are Subject to Error. Annals of the Institute of Statistical Mathematics, 10: 107-129.

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