Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty

Abstract

We consider the problem of scheduling time-based preventive maintenance under uncertainty in the lifetime distribution of a unit, with the understanding that every time a maintenance action is carried out, additional information on the lifetime distribution becomes available. Under such circumstances, typically either point estimates for the unknown parameters are used, or expected costs are minimized taking the uncertainty in the parameters into account. Both approaches, however, ignore that the uncertainty is reduced much faster if preventive maintenance actions are postponed. Although this initially leads to higher costs due to a higher risk of breakdowns, the obtained additional information can be exploited thereafter as it enables better maintenance decisions going forward. We assess the longterm benefits of initially postponing preventive maintenance, and perform a numerical study to identify under what circumstances these benefits are largest. This study is the first to recognize that the choice of a maintenance strategy influences the information that becomes available, and aims to initiate follow-up research in the area of maintenance planning.

A dynamic auto-adaptive predictive maintenance policy for degradation with unknown parameters

“…Here, an IG process is assumed with the proposed prior distribution of hyperparameters given in (13). The initial values of the hyperparameters are not updated.…”

“…In fact the model parameters are usually unknown and must be estimated, see, e.g., [3,15,27]. De Jonge et al [13] considered time-based preventive maintenance under uncertainty in lifetime distribution and analyzed the effect of postponing maintenance actions on cost. The case when the degradation parameters change after a change in the system degradation rate and the new parameters are unknown was considered by Fouladirad and Grall [8].…”

“…This cost can be compared with the cost in (14) which is significantly lower. Actually, the distribution of degradation parameters from (11) and (12) is less informative with the set of hyperparameters given in (15) than with the set of hyperparameters given in (13) (the variances of δ and λ are greater). It follows that the density function of (λ, δ) is more spread out.…”

“…Values of EC and their standard deviations for the SNAP policy assessed based on the hyperparameters given in(13).Here, we assume that the degradation parameters are unknown and consider policies involving Bayesian updates. First, the case with constant decision variables (the SAAP maintenance policy)…”

Preventive replacement with defaulting

“…al, 2018). In De Jonge et al (2015a, uncertainty in the input parameters of the lifetime distribution is modelled, and the notion of learning by postponement is articulated in de Jonge et al (2015b). Li et al (2016) consider advancement of the schedule due to production stops.…”