An Empirical Bayes Approach to a Variables Sampling Plan Problem.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 28, 1971
- Accession Number
- AD0729068
Entities
People
- James A. Craig Jr
Organizations
- Southern Methodist University