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     

A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

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.     

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     

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.     

Reliability analysis of a Markovian deteriorating system

The reliability of a complex system passes through a gradual deterioration until at some critical level, the system fails completely. The study of such a system failure requires the application of Markov processes to obtain reliability measures such as mean time of system failure. The Laplace transform of reliability of the system starting from each operating state is employed for solving such a complex system of differential equations. A four-state deteriorating system is considered and various particular cases of the arbitrary repair times distribution are discussed.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

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     

An Age-Based Inspection and Replacement Policy for Heterogeneous Components

This paper considers a hybrid maintenance policy for a single component from a heterogeneous population. The component is placed in a socket, and the component and socket together comprise the system. The $s$-population of components consists of two sub-populations with different failure characteristics. By supposing that a component may be in a defective but operating state, so that there exists a delay time between defect arrival and component failure, we consider a novel maintenance policy that is a hybrid of inspection and replacement policies. There are similarities in this approach with the concept of “burn-in” maintenance. The policies are investigated in the context of traction motor bearing failures. Under certain circumstances, particularly when the mixture parameter is large, and the distribution of lifetimes for the two component types are well separated, the hybrid policy has significant cost savings over the standard age-based replacement policy, and over the pure inspection policy. In addition to the cost metric, the mean time between operational failures of the system under the hybrid policy can be used to guide decision-making. This maintenance policy metric is calculated using simulation, and using an approximation which assumes that operational failures occur according to a Poisson process with a rate that can be calculated in a straightforward way. The simulation results show good agreement with the approximation.      

A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.     

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

A policy of periodic replacement with minimal repair at failure is considered for a multi-unit system which has a specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed for any intervening component failure. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repairs. 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. The necessary and sufficient conditions for the existence of an optimal replacement interval are found.     

A Component-Testing Procedure For A Parallel System With Type II Censoring

We consider the problem of acceptance testing for a parallel (1-out-of-n:G) system of n different components with constant failure rates. The components are individually tested and the tests are terminated as soon as a preassigned number of each component fails. This paper provides a criterion for accepting or rejecting the system based on the product of the total times on test for each component. The critical level for the test statistic is chosen so as to guarantee that the specified levels of consumer and producer risks on the system reliability are not exceeded. If the testing costs depend on the number of each component tested, aminimum-cost procedure can be found from the feasible set of plans.     

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.     

Reliability analysis of a container spreader

The concepts of system reliability are applied to optimum replacement policies for a container spreader subsystem. Actual failure data of the spreader components are analyzed; and the probability distributions of these failures are determined. Models for optimum replacement policies for the spreader components are presented.     

Analysis of a two unit deteriorating standby system with repair

This paper deals with the reliability analysis of a two unit standby system with repairs for common cause failure and critical human error. The deteriorating effect of the standby unit on the system is studied. Various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Optimal periodic preventive repair and replacement policy assuming geometric process repair

In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate replacement policy such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined numerically. An example is given where the operating time of the system is given by a Weibull distribution.     

A type-II censored, log test time based, component-testingprocedure for a parallel system

The authors consider the problem of acceptance testing for a parallel (1-out-of-n:G) system of different components with constant failure rates. The components are individually tested and the tests are terminated as soon as a preassigned number of each component fails. The authors provide a criterion for accepting or rejecting the system based on the sum of the logarithms of the total times on test for each component. The critical level for the test statistic is chosen so as to guarantee that the specified consumer and producer risks on the system reliability are not exceeded. The use of this statistic makes the computation of these critical values much simpler as compared with that of a previously used statistic based on the product of the total times on test for each component. Several approximate procedures are considered for deriving these critical values. The authors also formulate the optimization problem for deriving the minimum-cost component-testing plans when a type-II censored component-test procedure is used for a parallel system     

(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     

Optimal replacement policy for induced draft fans

This paper derives the optimal block replacement policies for four different operating configurations of induced draft fans. Under the usual assumption of higher cost of repair or replacement on failure compared to preventive replacement, the optimal preventive replacement interval is found by minimising the total relevant cost per unit time. Specifically, this paper finds optimal preventive maintenance strategies for the following two situations.

1. (i)|Both the time to failure and time to carry out minimal repair or replacement are exponentially distributed.

2. (ii)|The time to failure follows the Weibull distribution and there is no possibility of on-line repair or replacement.

For both situations closed form expressions are derived whose solutions give optimum preventive maintenance intervals.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.