Condition-based maintenance has been proven effective in reducing unexpected failures with minimum operational costs. This study considers an optimal condition-based replacement policy with optimal inspection interval when the degradation conforms to an inverse Gaussian process with random...

We consider time-changed Poisson processes, and derive the governing difference–differential equations (DDEs) for these processes. In particular, we consider the time-changed Poisson processes where the time-change is inverse Gaussian, or its hitting time process, and discuss the governing...

Abstract We analyze a data set containing rental revenues, maintenance costs, and sale prices of five different types of rental machines to econometrically estimate key relationships needed to implement a dynamic programming model of the optimal timing of replacement of rental equipment owned by...

A system (e.g., a car) must operate for the next t time units. A certain component (e.g., a battery) must be replaced whenever it fails, as it is essential for the operation of the system. There are several types of components differing only in price and life distribution. The problem of...

Conditions for the dairy industry in northern Victoria over the past decade have been tough. High prices for feed inputs, especially when combined with low farmgate milk prices, have seen situations where dairy farmers are losing money feeding cows. In this environment, it is natural to consider...

This paper studies the optimal replacement policy of an item that experiences stochastic geometric growth in maintenance costs. The model integrates corporate taxes, tax credits, depreciation, and salvage value. We extend this traditional application to cover the cost of replacement with the...

The US Air Force is asking when to replace its aging aircraft. We develop a framework to identify economically optimal replacement strategies that recognizes cost trade-offs and incorporates age effects. We also preview a stochastic methodology. We use the framework to identify an optimal...

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Lévy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive...

A system with a single activated unit subject to Markovian deterioration is considered. It is shown by a numerical example that the optimality of control limit rules is not sufficient for the validity of two assertions of the paper by P. Kolesar (Kolesar, P. 1966. Minimum cost replacement under...

Many practical problems involve making optimal decisions for systems with state characterized by many components. These problems lead to dynamic programming problems with a very large number of state variables. Thus, an exact derivation of the optimal policy for such problems is not feasible to...