An Empirical Bayes Approach to a Variables Sampling Plan Problem.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Consider the following variables sampling plan problem. One is given a lot of size mn items. Each items 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 mn, 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
- Statistics and Probability