Abstract
I have studied maintenance theory for about half a century and published three books(1)~(3), that summarize my research results up to 2010. It is necessary to study stochastic processes to understand reliability theory. My fourth book(4) was rewritten as an elementary textbook on stochastic processes in which all the examples are based on reliability models. Recently, systems have been randomized as they have become increasingly complex and large-scale. My fifth book(5) shows how to form stochastic random models, to analyze them theoretically, and to derive a variety of optimal maintenance policies. Classic maintenance theory was established by the book(6) written by Barlow and Proschan fifty years ago. In this report, replacement problems are roughly divided into three periods: the past, present, and future: In the past period, I introduce the standard replacement policy in Barlow and prosvhan's book and its modifications and extensions, in the present period, I discuss some parts of my fifth book, and in the future period, I propose new reliability problems and replacement policies that are currently being studied, and explain simply them as an examples of cumulative damage models. I use the word ‘replacement' in this report, which may be used interchangeably with ‘preventive maintenance's.
