1. ¹Durham University, Durham, UK
2. ²University of Bath, Bath, UK

Correspondence: SC Shaw, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. E-mail: s.c.shaw@maths.bath.ac.uk

^†Dedicated to the memory of Pauline Coolen-Schrijner, who died on 23 April 2008.

Received October 2007; Accepted July 2008; Published online 8 October 2008.

Abstract

In this paper age replacement (AR) and opportunity-based age replacement (OAR) for a unit are considered, based on a one-cycle criterion, both for a known and unknown lifetime distribution. In the literature, AR and OAR strategies are mostly based on a renewal criterion, but in particular when the lifetime distribution is not known and data of the process are used to update the lifetime distribution, the renewal criterion is less appropriate and the one-cycle criterion becomes an attractive alternative. Conditions are determined for the existence of an optimal replacement age T^* in an AR model and optimal threshold age T_opp^* in an OAR model, using a one-cycle criterion and a known lifetime distribution. In the optimal threshold age T_opp^*, the corresponding minimal expected costs per unit time are equal to the expected costs per unit time in an AR model. It is also shown that for a lifetime distribution with increasing hazard rate, the optimal threshold age is smaller than the optimal replacement age. For unknown lifetime distribution, AR and OAR strategies are considered within a nonparametric predictive inferential (NPI) framework. The relationship between the NPI-based expected costs per unit time in an OAR model and those in an AR model is investigated. A small simulation study is presented to illustrate this NPI approach.