Stochastic Comparisons of Random Processes, with Applications in Reliability

摘要

In many applied problems, the exact calculation of quantities of interest for the stochastic process under study is a forbidding task. In such cases, the statistician may compute bounds on these parameters by comparing the given stochastic process with a simpler stochastic process. For example, in Pledger and Proschan (1971), the reliability of certain types of systems of unlike components is approximated by computing the reliability of corresponding systems of like components. It is important to note that in making such comparisons, the statistician is obtaining a bound on one or perhaps several parameters. In the present paper the authors introduce a consieerably stronger type of comparison of two stochastic processes. (Author)