W. A. Wallis1 proposed a method for constructing a two-sided variables acceptance sampling plan under the assumption that a quality characteristic of interest, X, has a normal distribution. This method has been introduced in some books, such as Schilling2, as an illustration of a two-sided variables acceptance sampling plan. George J. Resnikoff3 suggested another two-sided acceptance sampling plan based on the Uniformly Minimum-Variance Unbiased Estimator (UMVUE) of the fraction outside of specifications. The UMVUE method has long been used in U.S. Military Standards, and prescribed by the American National Standards Institute (ANSI) and the International Organization for Standardization (ISO). Hamilton and Lesperance4 proposed a method of constructing an acceptance sampling plan based on the Maximum Likelihood Estimator (MLE) of the fraction defective, in an attempt to improve on the UMVUE method;Computer facilities in the 1950's were not as powerful as today. With today's high technology, can we improve on the early methods? In this dissertation a likelihood ratio test statistic with attractive statistical properties is used as a device to develop a new variables acceptance sampling method (called here the Likelihood Ratio Test (LRT) method);The maximum thickness of an acceptance sampling plan's Operating Characteristic (OC) band is taken as a basis for comparing the acceptance sampling methods. Comparisons are made among the four methods;To implement and study the various variables acceptance sampling plans, FORTRAN programs have been written which produce acceptance regions for the different methods and any combination of sample size and producer's risk (for a specified proportion defective). After intensive computational effort, the following major conclusions have been reached. For small sample sizes, the UMVUE method is still the best choice currently available. However, an "optimized" LRT method will provide the best sampling plan for large sample sizes (say, n≥30);In a particular application, OC bands can be produced for variables acceptance sampling plans based on any of these four methods using the FORTRAN program. With these OC bands in hand, a producer or a consumer will be able to assess what is achievable through the use of variables acceptance sampling for various sample sizes, and then choose a sample size and plan with acceptable statistical properties. ftn1Wallis, W. A. (1950) "Lot Quality Measured by Proportion Defective," Acceptance Sampling - A Symposium, American Statistical Association, Washington, 117-122. 2Schilling, E. G. (1982) Acceptance Sampling in Quality Control, Marcel Dekker, New York, 232-236. 3Resnikoff, G. J. (1952) "A New Two-Sided Acceptance Region for Sampling by Variables," (Report No. 8) Stanford Technical Report Series, Stanford University, Stanford, CA. 4Hamilton, D. C., and Lesperance, M. L. (1995) "A Comparison of Methods for Univariate and Multivariate Acceptance Sampling by Variables," to appear in Technometrics, August 1995.