Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements

This paper proposes two optimization models for the periodic inspection of a system with “hard-type” and “soft-type” components. Given that the failures of hard-type components are self-announcing, the component is instantly repaired or replaced, but the failures of soft-type components can only be detected at inspections. A system can operate with a soft failure, but its performance may be reduced. Although a system may be periodically inspected, a hard failure creates an opportunity for additional inspection (opportunistic inspection) of all soft-type components. Two optimization models are discussed in the paper. In the first, soft-type components undergo both periodic and opportunistic inspections to detect possible failures. In the second, hard-type components undergo periodic inspections and are preventively replaced depending on their condition at inspection. Soft-type and hard-type components are either minimally repaired or replaced when they fail. Minimal repair or replacement depends on the state of a component at failure; this, in turn, depends on its age. The paper formulates objective functions for the two models and derives recursive equations for their required expected values. It develops a simulation algorithm to calculate these expected values for a complex model. Several examples are used to illustrate the models and the calculations. The data used in the examples are adapted from a real case study of a hospital’s maintenance data for a general infusion pump.     

A number-dependent replacement policy for a system with continuous preventive maintenance and random lead times

This paper considers a number-dependent replacement policy for a system with two failure types that is replaced at the nth type I (minor) failure or the first type II (catastrophic) failure, whichever occurs first. Repair or replacement times are instantaneous but spare/replacement unit delivery lead times are random. Type I failures are repaired at zero cost since preventive maintenance is performed continuously. Type II failures, however, require costly system replacement. A model is developed for the average cost per unit time based on the stochastic behavior of the system and replacement, storage, and downtime costs. The cost-minimizing policy is derived and discussed. We show that the optimal number of type I failures triggering replacement is unique under certain conditions. A numerical example is presented and a sensitivity analysis is performed.     

A multi-objective approach for solving a replacement policy problem for equipment subject to imperfect repairs

This paper proposes a multi-objective approach to model a replacement policy problem applicable to equipment with a predetermined period of use (a planning horizon), which may undergo critical and non-critical failures. Corrective replacements and imperfect repairs are taken to restore the system to operation respectively when critical and non-critical failures occur. Generalized Renewal Process (GRP) is used to model imperfect repairs. The proposed model supports decisions on preventive replacement intervals and the number of spare parts purchased at the beginning of the planning horizon. A Multi-Objective Genetic Algorithm (MOGA) coupled with discrete event simulation (DES) is proposed to provide a set of solutions (Pareto-optimum set) committed to the different objectives of a maintenance manager in the face of a replacement policy problem, that is, maintenance cost, rate of occurrence of failures, unavailability, and investment on spare parts. The proposed MOGA is validated by an application example against the results obtained via the exhaustive approach. Moreover, examples are presented to evaluate the behavior of objective functions on Pareto set (trade-off analysis) and the impact of the repair effectiveness on the decision making.     

Optimal maintenance scheduling for a complex manufacturing system subject to deterioration

We address the problem of determining inspection strategy and replacement policy for a deteriorating complex multi-component manufacturing system whose state is partially observable. We develop inspection and replacement scheduling models and other simple maintenance scheduling models via employing an imperfect repair model coupled with a damage process induced by operational conditions. The system state in performance of the imperfectly repaired system is modelled using a proportional intensity model incorporating a damage process and a virtual age process caused by repair. The system is monitored at periodic times and maintenance actions are carried out in response to the observed system state. Decisions to perform imperfect repair and replacement are based on the system state and crossing of a replacement threshold. The model proposed here aims at joint determination of a cost-optimal inspection and replacement policy along with an optimal level of maintenance which result in low maintenance cost and high operational performance and reliability of the system. To demonstrate the use of the model in practical applications a numerical example is provided. Solutions to optimal system parameters are obtained and the response of the model to these parameters is examined. Finally some features of the model are demonstrated. The approach presented provides a framework so that different scenario can be explored.     

Reliability-based measures for a retrial system with mixed standby components

In this paper, we consider a retrial and repairable multi-component system with mixed warm and cold standby components. It is assumed that the failure times of primary (operating) and warm standby components follow exponential distributions. When a component fails, it is sent to a service station with a single server (repairman) and no waiting space. The failed component is repaired if the server is idle and it has to enter an orbit if the server is busy. The failed component in the orbit will try to get the repair service again after an exponentially distributed random time period. The repair time also has an exponential distribution. The mean time-to-failure, MTTF, and the steady-state availability, A_T(∞), are derived in this retrial and repairable system. Using a numerical example, we compare the systems with and without retrials in terms of the cost/benefit ratios. Sensitivity analysis for the mean time-to-failure and the steady-state availability are investigated as well.     

Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures

An n-unit system provisioned with a single warm standby is investigated. The individual units are subject to repairable failures, while the entire system is subject to a nonrepairable failure at some finite but random time in the future. System performance measures for systems observed over a time interval of random duration are introduced. Two models to compute these system performance measures, one employing a policy of block replacement, and the other without a block replacement policy, are developed. Distributional assumptions involving distributions of phase type introduce matrix Laplace transformations into the calculations of the performance measures. It is shown that these measures are easily carried out on a laptop computer using Microsoft Excel. A simple economic model is used to illustrate how the performance measures may be used to determine optimal economic design specifications for the warm standby.     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

A redundant repairable system with imperfect coverage and fuzzy parameters

This paper proposes a procedure to construct the membership functions of the system characteristics of a redundant repairable system with two primary units and one standby in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow fuzzified exponential distributions. The α-cut approach is used to extract from the fuzzy repairable system a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by management, and because the redundant system is extended to the fuzzy environment, general repairable systems are represented more accurately and the analytic results are more useful for designers and practitioners.     

Extended optimal inspection policies for a system in storage

A system such as missiles and spare parts of aircraft has to perform a normal operation in a severe environment at any time when it is used. However, the system is in storage for a long time from the delivery to the usage and its reliability goes down with time. Thus, a system in storage should be inspected and maintained at periodic times to hold a higher reliability than is prespecified.The following inspection model is considered: A system has three types of units, where unit 1 is maintained, unit 21 is not maintained but is replaced and unit 22 is neither maintained nor replaced. The system is overhauled if its reliability becomes lower than a prespecified probability. The number of replacements and time until overhaul are derived. Using these results, the average cost is obtained and both an optimal inspection time and an optimal replacement time to minimize it are numerically discussed.     

The impact of inspection errors,imperfect maintenance and minimal repairs on an imperfect production system

This paper develops an integrated model of production lot-sizing, maintenance and quality for considering the possibilities of inspection errors, preventive maintenance (PM) errors and minimal repairs for an imperfect production system with increasing hazard rates. In this study, a PM activity is imperfect in that a production system cannot be recovered as good as new and might cause the production system to shift to the out-of-control state with a certain probability. Numerical analyses are used to simulate the effect of changes in various parameters on the optimal solution for which the time that the process remains in the in-control state is assumed to follow a Weibull distribution. In addition, we investigate the effects of inspection errors and PM errors on the minimum total cost of the optimal inspection interval, inspection frequency and production quantity.     

Modelling of a deteriorating system with repair satisfying general distribution

In this paper, we model a deteriorating system that cannot be repaired “as good as new” after failures, the model comes from [19, Applied Mathematics and Computation, 217(2011), 4980-4989]. Suppose that the system has one repairman who can have multiple vacations, and if the system fails when the repairman is on vacation, it will wait for repair until the repairman is available. Herein the repair time is taken into account and supposes that the repair satisfies the general distribution. Under these assumptions, by means of the geometric process and the supplementary variable techniques, we derive a complete model of the partial differential equations, which will correct an error of mathematical model in [19]. Moreover, we deduce some important reliability indices of the system such as the availability of system, the probability of the repairman working and the rate of occurrence of failures. In particular, we prove that the rate of occurrence of failures m_f is not equal to zero.     

Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment

In this paper, we study reliability based measures and prognostic problems of a K-out-of-N system in which the failure process of each component depends not only on its intrinsic characteristic but also on its operating environment conditions. The system reliability and the expected remaining useful lifetime are calculated. Under the periodic inspection policy, the system asymptotic availability is derived. We aim at providing explicit expressions for these quantities. The model allows us to incorporate the observation information of the environment in the evaluation of the system performances. Numerical examples show the efficiency and accuracy of our method by comparing with the Monte-Carlo simulations. It is pointed out that the environment condition has significant effect on the system reliability based measures and the system prognostic analysis.     

Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure

A new method for predicting failures of a partially observable system is presented. System deterioration is modeled as a hidden, 3-state continuous time homogeneous Markov process. States 0 and 1, which are not observable, represent good and warning conditions, respectively. Only the failure state 2 is assumed to be observable. The system is subject to condition monitoring at equidistant, discrete time epochs. The vector observation process is stochastically related to the system state. The objective is to develop a method for optimally predicting impending system failures. Model parameters are estimated using EM algorithm and a cost-optimal Bayesian fault prediction scheme is proposed. The method is illustrated using real data obtained from spectrometric analysis of oil samples collected at regular time epochs from transmission units of heavy hauler trucks used in mining industry. A comparison with other methods is given, which illustrates effectiveness of our approach.     

A random review replacement model for a system subject to compound poisson shocks

We present a transform–free analysis of the following model. The state of the system is initially 0 and thereafter increases jumpwise due to compound Poisson shocks. Each shock increases the state by a random amount. The system is inspected at random points in time. If the state is above a threshold at an inspection, the system is replaced, otherwise no action is taken. Each replacement instantaneously brings the state back to 0. (Existing models assume either exponential interinspection times or discrete shock magnitudes.) This model can be applied to reliability, inventory, and queueing problems.Interpretations are given throughout to make the results easier to understand and to apply     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.