Optimal State-Dependent Replacement Policy for Deteriorating Systems

1997 ◽  
Vol 04 (04) ◽  
pp. 349-356 ◽  
Author(s):  
Ruey Huei Yeh
Keyword(s):  
Optimal Policy ◽  
Operating Cost ◽  
Sufficient Conditions ◽  
Optimization Criterion ◽  
Replacement Policy ◽  
Cost Rate ◽  
Optimal State ◽  
State Dependent ◽  
Long Run ◽  
Deteriorating Systems

This paper investigates the optimal state-dependent replacement policy for semi-Markovian deteriorating systems. It is assumed that the replacement time, replacement cost, operating cost rate and sojourn time distributions are all state-dependent. The optimization criterion is to minimize the expected long-run cost per unit time. Under some sufficient conditions on the cost and time parameters, we show that the optimal policy is of control limit type and has monotonic properties which facilitate the derivation of the optimal policy. Finally, a numerical example is given to illustrate the structure of the optimal policy.

Comparison of sequential and continuous inspection strategies for deteriorating systems

1994 ◽  
Vol 26 (2) ◽  
pp. 423-435 ◽  
Author(s):  
C. Teresa Lam ◽  
R. H. Yeh
Keyword(s):  
Continuous Time ◽  
Iterative Algorithms ◽  
Optimal Cost ◽  
Cost Rate ◽  
State Dependent ◽  
Long Run ◽  
Inspection Strategy ◽  
Optimal Policies ◽  
Finite State ◽  
Deteriorating Systems

This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.

Comparison of sequential and continuous inspection strategies for deteriorating systems

1994 ◽  
Vol 26 (02) ◽  
pp. 423-435 ◽  
Author(s):  
C. Teresa Lam ◽  
R. H. Yeh
Keyword(s):  
Continuous Time ◽  
Iterative Algorithms ◽  
Optimal Cost ◽  
Cost Rate ◽  
State Dependent ◽  
Long Run ◽  
Inspection Strategy ◽  
Optimal Policies ◽  
Finite State ◽  
Deteriorating Systems

This paper investigates inspection strategies for a finite-state continuous-time Markovian deteriorating system. Two inspection strategies are considered: sequential inspection and continuous inspection. Unlike many previous efforts, the inspection times for the sequential inspection strategy are assumed to be non-negligible. The replacement times and costs for both strategies are non-negligible and state dependent. Our objective here is to minimize the expected long-run cost rate. Iterative algorithms are provided to derive the optimal policies for both strategies. The structures of these optimal policies and their corresponding optimal cost rates are discussed and compared.

A hybrid preventive maintenance model for systems with partially observable degradation

2020 ◽  
Vol 31 (3) ◽  
pp. 345-365 ◽  
Author(s):  
Maxim Finkelstein ◽  
Ji Hwan Cha ◽  
Gregory Levitin
Keyword(s):  
Preventive Maintenance ◽  
Replacement Policy ◽  
Hybrid Strategy ◽  
Cost Rate ◽  
Shot Noise Process ◽  
Shock Process ◽  
Long Run ◽  
Age Replacement ◽  
Partially Observable ◽  
Maintenance Model

Abstract A new model of hybrid preventive maintenance of systems with partially observable degradation is developed. This model combines condition-based maintenance with age replacement maintenance in the proposed, specific way. A system, subject to a shock process, is replaced on failure or at some time ${T}_S$ if the number of shocks experienced by this time is greater than or equal to m or at time $T>{T}_S$ otherwise, whichever occurs first. Each shock increases the failure rate of the system at the random time of its occurrence, thus forming a corresponding shot-noise process. The real deterioration of the system is partially observed via observation of the shock process at time ${T}_S$. The corresponding optimization problem is solved and a detailed numerical example demonstrates that the long-run cost rate for the proposed optimal hybrid strategy is smaller than that for the standard optimal age replacement policy.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (01) ◽  
pp. 20-37 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Optimal Policy ◽  
Queueing System ◽  
Sufficient Conditions ◽  
System Capacity ◽  
Average Reward ◽  
Finite Capacity ◽  
Long Run ◽  
Optimal Policies ◽  
Service Rates ◽  
Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

AN OPPORTUNITY-BASED AGE REPLACEMENT POLICY CONSIDERING WARRANTY

1999 ◽  
Vol 06 (03) ◽  
pp. 229-236 ◽  
Author(s):  
BERMAWI P. ISKANDAR ◽  
HIROAKI SANDOH
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Failure Time Distribution ◽  
Warranty Period ◽  
Preventive Replacement ◽  
Long Run ◽  
Age Replacement

This study discusses an opportunity-based age replacement policy for a system which has a warranty period (0, S]. When the system fails at its age x≤S, a minimal repair is performed. If an opportunity occurs to the system at its age x for S<x<T, we take the opportunity with probability p to preventively replace the system, while we conduct a corrective replacement when it fails on (S, T). Finally if its age reaches T, we execute a preventive replacement. Under this replacement policy, the design variable is T. For the case where opportunities occur according to a Poisson process, a long-run average cost of this policy is formulated under a general failure time distribution. It is, then, shown that one of the sufficient conditions where a unique finite optimal T* exists is that the failure time distribution is IFR (Increasing Failure Rate). Numerical examples are also presented for the Weibull failure time distribution.

An optimal inspection and replacement policy for a deteriorating system

1986 ◽  
Vol 23 (04) ◽  
pp. 973-988 ◽  
Author(s):  
Masamitsu Ohnishi ◽  
Hajime Kawai ◽  
Hisashi Mine
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Continuous Time ◽  
Average Cost ◽  
Control Limit ◽  
Replacement Policy ◽  
Optimal Time ◽  
Time Interval ◽  
Long Run ◽  
Monotonic Properties

This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (1) ◽  
pp. 20-37 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Optimal Policy ◽  
Queueing System ◽  
Sufficient Conditions ◽  
System Capacity ◽  
Average Reward ◽  
Finite Capacity ◽  
Long Run ◽  
Optimal Policies ◽  
Service Rates ◽  
Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

A bivariate replacement policy for an imperfect repair system based on geometric processes

2018 ◽  
Vol 233 (4) ◽  
pp. 670-681
Author(s):  
Qinglai Dong ◽  
Lirong Cui ◽  
Hongda Gao
Keyword(s):  
Optimal Solution ◽  
Working Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Repair System ◽  
Cost Rate ◽  
Delayed Repair ◽  
Long Run ◽  
Average Cost Rate ◽  
Geometric Processes

A repair replacement model for a deteriorating system with delayed repair is studied, in which the successive working times after repair and the consecutive repair times of the system are described by geometric processes. The instantaneous availability is studied in the case of general distributions for the working time, repair time and delayed repair time. A bivariate replacement policy is considered, that is, the system is replaced whenever the working age of the system reaches T or at the first hitting time of the working time after repair with respect to the working time threshold τ, whichever occurs first. The explicit expression of the long-run average cost rate under the replacement policies is derived. The corresponding optimal replacement policy can be determined numerically, and numerical examples are presented to demonstrate the application of the developed model and approach. It is shown that the optimal solution and optimal value are sensitive to the tiny change in the ratios of the Geometric processes and the expectation of the delayed repair time.

A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy

2019 ◽  
Vol 234 (1) ◽  
pp. 138-150
Author(s):  
Yi Jiang
Keyword(s):  
Operating Time ◽  
Replacement Policy ◽  
Sensitivity Analyses ◽  
Optimal Order ◽  
Shock Model ◽  
Cost Rate ◽  
Long Run ◽  
Average Operating ◽  
Average Operating Time ◽  
Average Cost Rate

In this article, a generalized δ-shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N – 1)th repair and the aging system is replaced at the Nth failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C( N) and the stationary availability A( N) are derived analytically. Some convergence properties of A( N) and C( N) are also investigated. The optimal order-replacement policy N* can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

Collaborative Optimization of Replacement and Spare Ordering of a Deteriorating System with Two Failure Types

2012 ◽  
Vol 220-223 ◽  
pp. 210-214 ◽  
Author(s):  
Guo Qing Cheng ◽  
Ling Li
Keyword(s):  
Average Cost ◽  
Life Time ◽  
Collaborative Optimization ◽  
Replacement Policy ◽  
Cost Rate ◽  
Ordering Policy ◽  
Long Run ◽  
Proposed Model ◽  
Average Cost Rate ◽  
Optimal Ordering

This paper proposes a model to find optimal ordering and replacement policies for a deteriorating system. Assume that the life time of system has a normal distribution, and it has two failures types, typeⅠfailure is repairable, whereas typeⅡfailure is catastrophic which leads to replacement. A replacement policy N is adopted by which the system will be replaced by an identical new one if available at the time following the Nth typeⅠfailure or the 1st typeⅡfailure whichever occurs first. Furthermore, it considers an ordering policy M in which a spare unit is ordered at the time of the Mth typeⅠfailure or 1st typeⅡfailure, whichever occurs first. The objective is to derive the long-run average cost rate and then find the optimal policy (N,M) such that the average cost rate is minimized. Finally, a numerical example is provided to illustrate the proposed model.

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