This article proposes an integrated approach for reliability modeling and maintenance scheduling of repairable parallel systems subject to hidden failures. The system consists of heterogeneous redundant subsystems whose failures are detected only by inspections. Inspections at periodic times reveal the components state, and repair actions are decided by the excursion of a basic state process describing the total number of failed components (deterioration level) in each subsystem. Using the standard renewal arguments, this article aims at minimizing the average cost rate by the joint determination of the optimal inspection interval $\tau$ and maintenance parameters $\kappa$ (partial repair threshold) and $\ell$ (preventive replacement threshold). We illustrate the procedure for the case as the components’ lifetimes conform to the Weibull distribution. The proposed model and the response of the optimal solutions to the model’s parameters are illustrated through numerical examples. The approach outlined here allows exploring different scenarios and further extensions.

Maintenance policies are developed for decision-making about repair and maintenance of deteriorating parallel systems consisting identical components whose failures are detected only by inspections. Inspections at periodic times reveal the true state of components and preventive and corrective maintenance actions are carried out in response to the observed components state. The decision process is driven by the excursion of a state process regulated through an age reduction model. The modelling approach allows a wide class of models to be considered. Assuming a threshold-type policy, the article aims at minimising the long-run average maintenance cost per unit time by determining appropriate inspection intervals and a maintenance threshold. Using the renewal-reward theorem, the expected cost per cycle and expected cycle length emerge as solutions of equations, and a recursive scheme is devised to solve them. We illustrate the procedure for the case when the components’ lifetime conforms to the Weibull distribution. Furthermore, a sensitivity analysis is performed to examine the effect of model’s parameters. The unified structure developed allows different scenarios to be explored.

Given a reward structure, this paper addresses an optimal replacement problem for complex multi-component systems. To maintain revenue stream resulting from system, the system is inspected according to a homogeneous Poisson process and certain actions are carried out in response to the system state. Decisions are based on a performance measure described by a Squared Bessel process. Given some assumption, we explore the inherent relation between the Squared Bessel process and an extended Gamma (EG) process. Since there are some flow of income and increasing costs due to inspections, the problem is to optimally stop processing the system and carrying out a renewal to maximize the reward functional. To this end, using the local characteristics of the EG process as a stopping criterion and the expected total discounted reward as a measure of policy, this paper aims at determining an optimal operating (stopping) time which truly balances both income and cost and so maximizes the expected discounted reward over a cycle. In support of the model a numerical example is provided to show feasibility of this programme in real application. Attention is restricted to perfect repair and inspection, but the paper provides the structure so that different scenarios can be explored.

Given a general cost-reward structure, this paper proposes an integrated maintenance scheduling model for deteriorating multi-state production systems. The paper develops extensions of the existing modelling techniques from non-repairable systems to repairable production systems. The development includes estimation of a value function and so the behaviour prediction of revenue resulting from the system. The estimated value function allows the optimization of system performance by exploiting controllable variables. Two types of repair actions are considered: (i) unplanned minimal repairs and (ii) planned minor and partial repairs at scheduled times to respectively retain the system or restore it to an acceptable level of performance. Planned repair actions incur costs associated with the post-planned repair state and the level of repair. Under minor repair model and two variants of the partial repair models, a system of Laplace transforms of expected net reward (profit), given the initial process state, is established from a system of integral equations. The aforementioned technique recursively provides a solution to the expected net reward. In the two-state model, explicit formulas for expected net reward are given when the initial state is |$X_{0}=1,2$|⁠. With respect to the estimated value function, an optimal solution to the operating time of the system is obtained. Results are developed to give insight into applicability of the devised model to a four-state problem. Sensitivity analysis along with a comparative study of explored repair models are given in support of the proposed model.