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One-sided variables acceptance sampling plans such as the one presented in Schilling (1982) assume that a quality characteristic of interest, X, has a normal distribution and that measurements are exact. However, when measurements contzun error and standard plans are used, the probability of accepting a lot for a fixed population proportion non­ conforming varies widely depending on the population and measurement error parzmieter 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 Walsh (1959) suggested a one-sided variables ac­ ceptance 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 on the estimated proportion nonconforming. With great improvements in the speed of computers, other more computationally inten­ sive plans can be compared with the earlier methods. This dissertation develops two other variables acceptance sampling plans (LRTl and LRT2) where the accept/reject decision is bcised 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. xi The major findiDgs are that the LRT2 method generally yields smaller maximum consumer risks than the other three methods. (In some special Ccises, the David method yields smadler 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 com­ pared 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 vari­ ance. It is not clear which method is more useful because neither method out-performs the other in all situations.

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