Accession Number : AD0729068

Title :   An Empirical Bayes Approach to a Variables Sampling Plan Problem.

Descriptive Note : Technical rept.,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Craig,James A. , Jr

Report Date : 28 FEB 1971

Pagination or Media Count : 64

Abstract : Consider the following variables sampling plan problem. One is given a lot of size m+n items. Each item's quality is characterized by some continuous random variable x. If this random variable, X, for a given item is within some specification limits, say (a,b), the item is considered acceptable. On the basis of a random sample of size n, it is desired to accept or reject the remaining m items. The random variable, X, is known to be normally distributed with some unknown mean mu and unknown variance sigma squared. The random variable, X, for any other item in the lot. Furthermore, it is known that mu and sigma squared are random variables with some unknown prior distribution G. If one knew the prior distribution G, one could determine a Bayesian decision rule based on the sample mean x and sample variance s squared that would minimize the average expected loss. It is shown in this research that in certain cases, if one has data from past lost of size m+n, it is possible to estimate the Bayesian decision rule empirically. That is, one has an empirical Bayes decision rule, and, consequently, one has an empirical Bayes approach to a variables sampling plan problem. (Author)

Descriptors :   (*SAMPLING, DECISION THEORY), QUALITY CONTROL, ANALYSIS OF VARIANCE, MONTE CARLO METHOD, RANDOM VARIABLES, STATISTICAL DISTRIBUTIONS, SIMULATION, THESES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE