A Bayesian expert judgement model to determine lifetime distributions for maintenance optimisation

Abstract

Preventive maintenance of mechanical equipment subject to random failures requires a lifetime distribution to establish an optimal maintenance interval. Typically, the optimal maintenance interval under an age replacement regimen is obtained by minimising the long term average cost of the maintenance activity. Only when the cost of maintaining the equipment preventively is less than the cost of failure of the equipment, can preventive maintenance be worthwhile. In practical contexts with an effective preventive maintenance policy, the estimation of such a lifetime distribution is complicated due to a lack of failure time data despite an abundance of right censored data, i.e. survival data of the component up to the time it was preventively maintained. Herein, we shall present a model for eliciting lifetime distributions via a histogram technique reminiscent of the method proposed by Van Noortwijk et al. (Van Noortwijk, J.A., et al., 1992. On the use of expert opinion for maintenance optimization. IEEE Transactions in Reliability, 41, 427–432). The elicited discrete distribution is used to estimate the prior parameters of a Dirichlet Process (DP). This DP is next updated using the failure time and maintenance data in a Bayesian fashion. The resulting lifetime distribution follows the posterior estimate of the DP process. Utilising the posterior lifetime distribution estimate, a maintenance interval can be established graphically by plotting the long term average cost as a function of the preventive maintenance frequency. An illustrative calculation example is presented.