Optimal maintenance-policies for deteriorating systems undervarious maintenance strategies

This paper presents algorithms for deriving optimal maintenance policies to minimize the mean long-run cost-rate for continuous-time Markov deteriorating systems. The degree of deterioration (except failure) of the system is known only through inspection. The time durations of inspection and replacement are nonnegligible. The costs are for inspection, replacement, operation, and downtime (idle). In particular, the replacement time, replacement cost, and operating cost-rate increase as the system deteriorates. Five maintenance strategies are considered-failure replacement, age replacement, sequential inspection, periodic inspection, and continuous inspection. Iterative algorithms are developed to derive the optimal maintenance policy and the corresponding cost rate for each strategy. Under sufficient conditions, structural optimal policies are obtained     

Age replacement of components during IFR delay time

This paper proposes two alternative policies for preventive replacement of a component, which shows sign of occurrence of a fault, and operates for some random time with degraded performance, before its final failure. The time between fault occurrence and component failure is termed as delay time. The first policy, namely age replacement during delay time policy (ARDTP), recommends replacement of a faulty component on failure or preventive replacement of the same after a fixed time during its delay time. It considers the performance degradation during delay time to develop an age replacement policy. It is also shown that the policy is a feasible proposition for a component that has positive (nonnegative) performance degradation during its CFR (IFR) delay time. The second policy, OARDTP, extends ARDTP to opportunistic age replacement policy where a faulty component is replaced at the first available randomly occurring maintenance opportunity, after a fixed time from occurrence of fault, or on failure. The time between opportunities (TBO) is considered to be exponentially distributed. This policy reduces the number of forced shutdowns, which is essential to ARDTP. It is shown that the second policy is superior to the first policy if the cost of a preventive replacement with forced shutdown is more than the preventive replacement cost during an opportunity. The policies are appropriate for complex process plants, where the tracking of the entire service life of each component is difficult. Their implementation requires tracking of components' delay time only, and estimation of mean time to occurrence of faults. The policies are relatively insensitive to estimation error in failure replacement cost. As their implementation requires immediate capturing of fault occurrence information, they are particularly attractive to organizations where operators are involved in the maintenance of machines.     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system     

Preventive replacement in systems with dependent components

A multicomponent series system includes a component which deteriorates over time, changing its operating characteristics and, consequently, increasing the failure rates of neighboring components. Preventive replacement of the deteriorating component can be beneficial. Replacement policies that include inspecting the deteriorating component at system failure instances and replacing it if the deterioration exceeds a critical level, or continuously monitoring the deteriorating component are considered. The system is modeled as a Markov chain solved by an efficient algorithm that exploits the system structure. For a two-component system, a closed-form equation gives the critical level for the minimum-average-cost failure-replacement policy. For the general case, replacement policies are evaluated by mean cost rate and by the ratio of the reduction in the number of failures to the number of preventive replacements     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Periodic replacement when minimal repair costs depend on the age and the number of minimal repair for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening component failures. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repair. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

Optimal replacement policies for systems with multiple standbycomponents

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs     

Decision support system for inspection and maintenance: a case study of oil pipelines

The existing method of pipeline health monitoring, which requires an entire pipeline to be inspected periodically, is unproductive. A risk-based decision support system (DSS) that reduces the amount of time spent on inspection has been presented. The risk-based DSS uses the analytic hierarchy process (AHP), a multiple attribute decision-making technique, to identify the factors that influence failure on specific segments and analyzes their effects by determining probability of occurrence of these risk factors. The severity of failure is determined through consequence analysis. From this, the effect of a failure caused by each risk factor can be established in terms of cost and the cumulative effect of failure is determined through probability analysis. The model optimizes the cost of pipeline operations by reducing subjectivity in selecting a specific inspection method, identifying and prioritizing the right pipeline segment for inspection and maintenance, deriving budget allocation, providing guidance to deploy the right mix labor for inspection and maintenance, planning emergency preparation, and deriving logical insurance plan. The proposed methodology also helps derive inspection and maintenance policy for the entire pipeline system, suggest design, operational philosophy, and construction methodology for new pipelines.     

Marginally monotonic maintenance policies for a multi-state deteriorating machine with probabilistic monitoring, and silent failures

We characterize the structure of optimal policies for maintenance & replacement actions over a finite horizon. The context is machine monitoring when the following are true: 1) The machine can operate in one of N states in S/spl isin/{0,1,...,N-1} where 0 is good, 1 to N-2 represent increasing levels of deterioration (i.e., the system becomes increasingly worn, but is still able to produce usable parts), and N-1 is bad (or failed). 2) Observations are related probabilistically to the state of the process. 3) The machine's state is known with certainty only immediately after a replacement. The last assumption, consistent with "silent" failures, distinguishes our results from others. We prove [using the theory & results of partially observable Markov decision processes (POMDP)] that the policy that minimizes the total expected cost of system maintenance has a "marginally monotonic" structure. The concept of "marginal monotonicity", which requires a component-wise partial ordering, and monotonicity of the expected total cost function with respect to each component of the state space, allows characterization of the policy that minimizes the total expected cost. This feature allows us to represent the optimal policy by a collection of decision rules characterized by at most N functions.     

并联电子系统级联失效可靠性分析与维护策略

与各部件失效相互独立的并联系统相比,级联失效这一因素显著降低了系统的可靠性。运用更新过程和马尔可夫理论。分析了存在级联失效关系的两同型部件并联系统的可靠性。为了有效地应对级联失效对并联电子设备系统的影响,引入了预防维护策略,并且建立了期望费用率模型．得到了使期望费用率最小的维护策略,最后给出了算例。     

Joint optimization of block-replacement and periodic-review spare-provisioning policy

This paper considers the problem of joint optimization of "preventive maintenance" and "spare-provisioning policy" for system components subject to wear-out failures. A stochastic mathematical model is developed to determine the jointly optimal "block replacement" and "periodic review spare-provisioning policy." The objective function of the model represents the s-expected total cost of system maintenance per unit time, while the preventive replacement interval and the maximal inventory level are chosen as the decision variables. The objective function of the model is in an analytic form with parameters easily obtainable from field data. The model has been tested using field data on electric locomotives in Slovenian Railways. The calculated optimal values of the model decision variables are realistic. "Sensitivity analysis of the model" shows that the model is relatively insensitive to moderate changes of the parameter values. The results of testing and of sensitivity analysis of the model prove that a trade-off exists between the replacement related cost and the inventory related cost. The jointly optimal preventive replacement interval defined by this model differs appreciably from the corresponding interval determined by the conventional model where only replacement related costs are considered. Also, the results of the sensitivity analysis show that even minor modification of the value of each model decision variable (without the appropriate adjustment of the value of the other decision variable) can lead to important increase of the s-expected total cost of system maintenance. This indicates that separate optimization of preventive maintenance policy and spare-provisioning policy does not ensure minimal total cost of system maintenance. This model can be readily applied to optimize maintenance procedures for a variety of industrial systems, and to upgrade maintenance policy in situations where block replacement preventive maintenance is already in use.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

Coverage Modeling and Optimal Maintenance Frequency of an Automated Restoration Mechanism

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.     

Replacement Policies for a Unit with Random and Wearout Failures

This paper considers three replacement models with random and wearout failures; a) the unit is replaced at failure, b) the unit undergoes minimal repair at failure, and c) the unit is replaced at failure only in a wearout failure period. Optimum replacement policies which minimize the s-expected cost rate for each model are discussed.     

R&M 2000 and Environmental Stress Screening

The United States Air Force, Army, and Navy have established the need for Environmental Stress Screening (ESS). The Air Force policy statement issued 1986 November imposed the provision that all fielded major electronic systems must deliver 2000 hours failure free. To accomplish this will require changes in design, producibility, and manufacturing attitudes. Defectives must be removed in the factory, at the most cost effective point in the production cycle. This will require assessing failures from the field, then developing a system to identify these defectives in the factory, at the lowest level of assembly. Poor reliability rooted in high component failure rates leads to premature equipment failures. Fielded systems and spares provisioning with resultant maintenance actions cost heavily during each year of life. The result is that the spares provisioning & logistic support is now exceeding 50 percent of the defense allocation (1984 and 1985 budgets). Cost increases result from poor equipment reliability. Today, systems originally contracted to deliver over 500 hours mean time-between-failures (MTBF) are delivering less than 50 hours MTBF, (Navy Maintenance Material Management ``3M' report). Excessive failure of components is a major cause of reduced life of equipment. Most maintenance actions involve the replacement of piece parts. The roots of this problem lie in the factory. Manufacturers are not removing defectives early in the product design/production cycle. Because of inadequate testing, most defectives are not detected in the factory. Failures are then precipitated in the field.     

Warranty Policies For Non-Repairable Items Under Risk Aversion

An approach is presented for analyzing full replacement and linear prorated warranty policies for items receiving renewable warranties when failure occurs during the warranty interval. The model corrects a model of Thomas and then extends the methodology by describing how sellers' risk aversity influences the policy. For constant failure intensities, linear replacement policies are more attractive to risk averse sellers than shorter term full replacement policies that result in the same average cost.     

Maintenance strategy optimization using a continuous-state partially observable semi-Markov decision process

Due to the limitation of current condition monitoring technologies, the estimates of asset health states may contain some uncertainties. A maintenance strategy ignoring this uncertainty of asset health state can cause additional costs or downtime. The partially observable Markov decision process (POMDP) is a commonly used approach to derive optimal maintenance strategies when asset health inspections are imperfect. However, existing applications of the POMDP to maintenance decision-making largely adopt the discrete time and state assumptions. The discrete-time assumption requires the health state transitions and maintenance activities only happen at discrete epochs, which cannot model the failure time accurately and is not cost-effective. The discrete health state assumption, on the other hand, may not be elaborate enough to improve the effectiveness of maintenance. To address these limitations, this paper proposes a continuous state partially observable semi-Markov decision process (POSMDP). An algorithm that combines the Monte Carlo-based density projection method and the policy iteration is developed to solve the POSMDP. Different types of maintenance activities (i.e., inspections, replacement, and imperfect maintenance) are considered in this paper. The next maintenance action and the corresponding waiting durations are optimized jointly to minimize the long-run expected cost per unit time and availability. The result of simulation studies shows that the proposed maintenance optimization approach is more cost-effective than maintenance strategies derived by another two approximate methods, when regular inspection intervals are adopted. The simulation study also shows that the maintenance cost can be further reduced by developing maintenance strategies with state-dependent maintenance intervals using the POSMDP. In addition, during the simulation studies the proposed POSMDP shows the ability to adopt a cost-effective strategy structure when multiple types of maintenance activities are involved.     

Evaluation of Maintenance Policies using Markov Chains and Fault Tree Analysis

Reliability analyses of multi-component systems can often be refined by combining Markov-chain models for detailed component characterizations with fault-tree evaluation techniques for describing over-all system behavior. A difficulty encountered in the application of this combined approach is that component maintenance policies can induce statistical dependence among component failures. Thereby, straightforward evaluation of overall system characteristics based upon the assumption of statistically independent component failures can lead to erroneous conclusions. This paper examines the effect of dependent component failures, as induced by the component maintenance policies, on system performance; and it demonstrates that for certain types of maintenance policies (when component maintenance is independent of the condition of the other system components), meaningful results can be obtained by assuming the independence of component failures. The feasibility of the proposed approach is illustrated through a maintenance scheduling problem in nuclear engineering practice.     

Maintenance strategies following the expiration of warranty

The authors study two types of replacement policies, following the expiration of warranty, for a unit with an IFR failure-time distribution: (1) the user applies minimal repair for a fixed length of time and replaces the unit by a new one at the end of this period; and (2) the unit is replaced by the user at first failure following the minimal repair period. In addition to stationary strategies that minimize the long-run mean cost to the user, the authors also consider nonstationary strategies that arise following the expiration of a nonrenewing warranty. Following renewing warranties, they prove that the cost rate function is pseudo-convex under a fixed maintenance period policy. The same result holds under nonrenewing repair warranties, and nonrenewing replacement warranties when the optimal maintenance period of each cycle is determined as a function of the age of the item in use at the end of the warranty period