Some Multiple Decision and Related Problems with Special Reference to Restricted Families of Distributions and Applications to Reliability Theory.

摘要

The paper deals with procedures for selecting a subset from k given populations so as to include the best with a specified guaranteed minimum probability. Some general results relating to subset selection and specific procedures for important classes of distributions are reviewed with special emphasis on restricted families of probability distributions. Such families are defined through partial order relations and are extensively considered in reliability theory. A selection problem for tail-ordered family of distributions is considered and tables are provided for constants needed to implement the procedure. A general partial order relation is defined through a class of real valued functions and a related selection problem is discussed. These results provide a unified view of earlier known results. The rest of the paper gives a brief survey of some important results pertaining to restricted families of distributions such as the star-ordered and convex-ordered distributions. These results relate to life test sampling plans,inequalities for linear combinations of order statistics,estimation of failure rate function and some tests of hypotheses. (Author)