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This article proposes a system design optimization for a circular k -out-of- n : G balanced system with equal load-sharing units. The system consists of n identical units whose failure times are assumed to follow an exponential distribution, and it is subject to an equally shared load among the working units. The load-sharing relationship between the amount of load and the failure rates of the working units is assumed to follow a power rule. If the system is not balanced, it can be balanced by forcing some operating units into standby or returning the standby units into operation. We arrange the system failure paths and use them in the exact reliability evaluation for systems with a small number of units (rotors). Due to the longer computation time, we use a Monte Carlo simulation to approximate the reliability of systems with a large number of units (rotors). We apply two maintenance policies, corrective maintenance, and condition-based preventive maintenance, to understand the effects of system balance conditions, load-sharing rule parameters, system configuration k , and various cost parameters on the optimal maintenance settings, using numerical examples.

This article presents a stochastic dynamic programming model for a condition-based maintenance application. The approach seeks to determine the most opportune moment to inspect and execute preventive maintenance over each component of a nonredundant system, where the number of inspections to be performed simultaneously during each period is limited due to resource constraints. The model minimizes the total maintenance cost per unit of time, considering failure, maintenance, and inspection costs. Unlike most related literature, the model proposed herein allows nonperiodic inspections; it does not require to predefine a maintenance threshold and does not necessarily connect inspections to maintenance actions. Also, the criticality of each component is not static through time, or defined beforehand, but dynamically determined according to the available resources and the risk of failure. A numerical example illustrates the performance of the proposed model in comparison to three traditional maintenance models, namely corrective maintenance, age-based maintenance, and condition-based maintenance with periodic inspections. Results suggest that the proposed model yields the best solution among the studied policies and is more efficient, with a significant reduction of 90% in inspection resources.

This paper integrates preventive maintenance with tactical production planning in multi-state systems. The proposed model coordinates the production with the maintenance decisions, so that the total expected cost is minimized. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance, and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs, and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-states, and s-independent components. A method is proposed to evaluate the times and the costs of preventive maintenance and minimal repair, and the average production system capacity in each period. We show how the formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. For large-size problems, a genetic algorithm is developed to deal with the preventive maintenance selection task in the integrated planning model.

In this paper, the coverage modeling of an automated restoration mechanism with two components is studied, and optimal maintenance frequencies are determined. Failures and repairs are exponentially distributed for the two components, while the failures of the automated mechanism follow a Weibull distribution. A corrective maintenance policy is considered for each component whereas, for the automated restoration mechanism, an additional preventive maintenance is taken into account. The system is modeled with a continuous time Markov chain and two performability indicators: one performability indicator modeling the downtime, and a second one modeling the overall operational cost. Consequently, two optimal maintenance frequencies are derived: first by minimizing the downtime, and second by minimizing the overall operational cost. A numerical example is used to evaluate the applicability of the proposed method.

Condition based maintenance (CBM) aims to balance two extreme sides (i.e., corrective maintenance (CM), and preventive maintenance (PM)) by observing and forecasting the real time health of machines. Recent developments in CBM revealed promising technologies for advanced fault detection, and forecasting. Traditional maintenance scheduling in CBM is based on the threshold setting on forecasted failure probability, or remaining useful life (RUL) for individual components. However, this approach may not give the best result for the system, because individual components are inter-related, and mutually dependent. It is not uncommon in systems that turning off a machine due to failure or maintenance causes other machinery or components to be turned off. Designing a comprehensive tool that optimizes availability & cost of the whole system incorporating prognostics information is crucial to fully benefit from CBM. The goal of this paper is to emphasize this need by demonstrating scenarios in CM, PM, and CBM; and to present a solution that optimizes system availability, and cost with system-maintenance constraints using genetic algorithms. The proposed tool acquires the forecasted failure probability of individual components from the prognostics module, and their reliability expectations after maintenance. The tradeoff between maintenance & failure is quantified in risk as the objective function to be minimized. The risk is minimized utilizing genetic algorithms for the whole system rather than individual components. The results of the proposed tool are compared with PM, CM, and CBM in which prognostics information of components are analyzed individually.

A joint preventive maintenance and spare parts provisioning strategy is suggested for a failure prone system. Replacements are carried-out at failure, if spare parts are available, and at spare parts replenishment delivery instants. Spare parts are provisioned according to an (s, Q) control policy. The ordering parameters, and preventive maintenance interval are derived from a mathematical model which aims at maximizing the system's availability under a budget constraint. The model takes into account the system lifetime distribution, the preventive and corrective maintenance costs and durations, as well as the total spare parts inventory management cost. Unlike classical inventory management models, the s-expected total cost is derived using the system lifetime distribution. Because each demand for spare parts is triggered by failure, the probabilities of shortage, and surplus will be evaluated based on the system failure distribution rather than the demand distribution during the lead-time. Numerical results have been obtained for an illustrative example.

In the reliability literature, maintenance time is usually ignored during the optimization of maintenance policies. In some scenarios, costs due to system failures may vary with time, and the ignorance of maintenance time will lead to unrealistic results. This paper develops maintenance policies for such situations where the system under study operates iteratively at two successive states: up or down. The costs due to system failure at the up state consist of both business losses & maintenance costs, whereas those at the down state only include maintenance costs. We consider three models: Model A, B, and C: /spl middot/ Model A makes only corrective maintenance (CM). /spl middot/ Model B performs imperfect preventive maintenance (PM) sequentially, and CM. /spl middot/ Model C executes PM periodically, and CM; this PM can restore the system as good as the state just after the latest CM. The CM in this paper is imperfect repair. Finally, the impact of these maintenance policies is illustrated through numerical examples.

A new condition-based maintenance model for a system, subject to deterioration-failures and to Poisson-failures, is presented. After an inspection, based on the degree of deterioration, a minimal maintenance or a major maintenance is performed, or no action is taken. Deterioration failures are restored by major repair; Poisson failures are restored by minimal repair. Major maintenance or major repair restores the system to "good as new" while minimal maintenance restores the system one stage. Generalized stochastic Petri Nets are used to represent and analyze the model, which represents a condition-based maintenance strategy. Based on maximization of the system throughput, an optimal inspection policy within this strategy and optimal inter-inspection time are obtained. The effects of inspection, maintenance and repair parameters are investigated. For a given inspection parameter, a 3-region diagram identifies the effectiveness of an inspection policy based on minimal maintenance, major maintenance, and major repair parameters.

The concept of availability includes reliability as well as preventive and corrective maintenance. An availability model which includes both aspects of this problem is proposed in this paper. The model includes the following decision variables: 1. failure rates and repair rates of individual units 2. the time period for perfect-preventive maintenance for a given mission time 3. the optimal failure and repair rates as a function of design costs, corrective and preventive maintenance costs. The objective is to minimize the design and operating costs where the availability requirements are satisfied. An example is solved for a system with n subsystems in series where two units in parallel comprise each subsystem. The general approach is applicable to solving other complex availability problems.

This paper shows the span of results which can be obtained by modeling a system's behavior by stochastic processes and demonstrates practical rules for employing Markov and semi-Markov models. The introduction summarizes several methods for reliability analysis and gives the advantages and drawbacks of four methods: Markov processes, semi-Markov processes, supplementary variables, the method of stages. The remainder deals with reliability and availability modeling of a 2-unit redundant computer system. There are a) two types of maintenance: corrective (c. m.) and preventive (p. m.), and b) two system parameters: coverage, and an increased failure rate when one unit is under repair or inspection. Approximate expressions for reliability, mean time to failure, and asymptotic availability show the effects of the system parameters as well as of the shapes of the Cdf's of the times related to maintenance actions. For c.m., Markov modeling is a good approximation. For p.m., Markov modeling is a rough approximation; one can go to semi-Markov models or to the method of stages. Lastly, an approximate expression is given for the mean inspection interval which maximizes reliability and availability for p.m.

The operational Availability and Reliability (OAR) model is designed to evaluate the availability and reliability of systems with components in any combination of series, parallel, and r-out-of-n:G combinations. In terms of the OAR model, systems are composed of Optimal Replaceable Units (ORUs). Failure, corrective maintenance, and spare acquisition probabilities are calculated via random sampling of the ORU failure, corrective maintenance, and spare acquisition distributions. ORU failures are statistically independent and, to allow for versatility in describing system characteristics, ``3-parameter Weibull'' distributed. System availability and reliability are then computed by employing the system failure, corrective maintenance, and spare acquisition data.

This paper describes the approach and progress on a 1981 study of photovoltaic (PV) system reliability being conducted by Battelle-Columbus for Sandia Laboratories as part of DOE's PV Systems Definition Project. Initially, the study is concerned with the functional modeling of reliability and maintenance of a PV system. We begin with relatively general, but simple, system level reliability models that can be expanded to more detailed, lower-level forms as input data justify. Corrective maintenance is Included to permit estimates of system availability. The output of these models will be coupled with life-cycle energy cost models and applied to PV system designs.

This paper presents the mathematical development of, and a simple solution technique for, an optimal sequential maintenance scheduling problem. The model is shown to satisfy the Kuhn-Tucker conditions, the necessary and sufficient conditions for the existence of an optimal solution. Real-world systems consisting of mixtures of constant and increasing failure rate devices are considered in the model. Sequential preventive maintenance schedules are developed for groups of identical items with increasing failure rates. Provision is made for the corrective maintenance of these groups if failures occur in between the preventive maintenance schedules. Also, constant failure rate devices are accorded corrective maintenance when failures occur. Optimality is achieved by minimizing the total annual maintenance cost, subject to constraints on the system availability, number of maintenance personnel and intervals of preventive maintenance. The model is applied to a coal mine power system example.

This paper provides an overview of the reliability-centered maintenance (RCM) engineering process. RCM is a unique tool used by reliability, safety, and/or maintenance engineers for developing optimum maintenance plans which define requirements and tasks to be performed in achieving, restoring, or maintaining the operational capability of a system or equipment. Implementing the RCM process requires the application of a decision logic that enables systematic analysis of failure mode, rate, and criticality data to determine the most effective maintenance requirements for maintenance-important items. It is through this process that the scheduled maintenance burden and support costs are reduced while sustaining the necessary readiness state. The RCM process is designed to focus engineering attention to the part level in a formal and disciplined manner leading logically to the formulation of a maintenance strategy and plan. RCM benefits include: *The development of high quality maintenance plans in less time and at lower cost. *The availability of a maintenace history for each system; one is able to correlate this experience with specific parts and their failure modes and criticalities. *The assurance that all maintenance-important parts and their failure modes and criticality are considered in the development of maintenance requirements. *The increased probability that the level and content of the maintenance requirement is optimally specified. *The basis for routine, on-line information exchange among the engineering staff and management even in a widely dispersed organization.

Highly reliable systems with long mission time, that can tolerate no down time, have motivated the study of system reliability. The emergence of fault-tolerant computing systems, where small down times may be tolerable, and preventive and corrective maintenance permitted, motivates a revisit to measures like mean availability. Vendors of computer systems are being required to specify the level of availability that will be met by their systems over a finite time interval, and pay a penalty for non-compliance. Since no closed-form solution has been reported in the literature, numerical approaches have often been used to compute systems availability over a finite time, even for simple Markov models. We report a Laplace transform solution for the distribution of availability over a finite interval, for a semi-Markov model. The transform of the distribution is analytically inverted to obtain a closed-form solution for the corresponding Markov model.