Approximate methods for optimal replacement, maintenance, and inspection policies

It might be difficult sometimes to derive theoretical and numerical solutions for analytical maintenance modelings due to the computational complexity. This paper takes up several approximate models in maintenance theory, by using the cumulative hazard function H(t) and the newly proposed asymptotic MTTF (Mean Time to Failure) skilfully. We firstly denote by t"x the time when the expected number of failures is x. Using H(t"x)=x, we estimate failure times, model age and periodic replacements, and sequential imperfect maintenance. Motivated by the asymptotic method of computation of MTTF, we secondly model the expected cost rate for a parallel system when replacement is made at system failure, and give approximate computations for the sequential inspection policy. Optimizations of each model are obtained approximately in an easier way. When failure times have a Weibull distribution, it is shown from numerical examples that the obtained approximate optimal solutions have good approximations of the exact ones.