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.

Replacement Policy for Cold Standby Repairable System with Priority in Use by Using Arithmetico-Geometric Process

2019 ◽  
Vol 27 (03) ◽  
pp. 2050009
Author(s):  
Raosaheb V. Latpate ◽  
Babasaheb K. Thorve
Keyword(s):  
Working Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Repairable System ◽  
Policy System ◽  
Geometric Process ◽  
Long Run ◽  
Cold Standby ◽  
Study Component ◽  
Renewal Cycle

In this paper, we consider the arithmetico-geometric process (AGP) repair model. Here, the system has two nonidentical component cold standby repairable system with one repairman. Under this study, component 1 has given priority in use. It is assumed that component 2 after repair is as good as new, whereas the component 1 follows AGP. Under these assumptions, by using AGP repair model, we present a replacement policy based on number of failures, [Formula: see text], of component 1 such that long-run expected reward per unit time is maximized. For this policy, system can be replaced when number of failure of the component 1 reaches to [Formula: see text]. Working time of the component 1 is AGP and it is stochastically decreasing whereas repair time of the component 1 is AGP which is stochastically increasing. The expression for long-run expected reward per unit time for a renewal cycle is derived and illustrated proposed policy with numerical examples by assuming Weibull distributed working time and repair time of the component 1. Also, proposed AGP repair model is compared with the geometric process repair model.

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.

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.

An optimal inspection–repair–replacement policy for standby systems

1995 ◽  
Vol 32 (1) ◽  
pp. 212-223 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Geometric Model ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Replacement Policy ◽  
System State ◽  
Expected Cost ◽  
Long Run ◽  
Optimal Maintenance ◽  
Maintenance Model

In this paper, an optimal maintenance model for standby systems is studied. An inspection–repair–replacement policy is employed. Assume that the state of the system can only be determined through an inspection which may incorrectly identify the system state. After each inspection, if the system is identified as in the down state, a repair action will be taken. It will be replaced some time later by a new and identical one. The problem is to determine an optimal policy so that the availability of the system is high enough at any time and the long-run expected cost per unit time is minimized. An explicit expression for the long-run expected cost per unit time is derived. For a geometric model, a simple algorithm for the determination of an optimal solution is suggested.

scholarly journals Determining Optimal Replacement Policy with an Availability Constraint via Genetic Algorithms

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shengliang Zong ◽  
Guorong Chai ◽  
Yana Su
Keyword(s):  
Genetic Algorithm ◽  
Average Cost ◽  
Operating Time ◽  
Threshold Value ◽  
Replacement Policy ◽  
Time Interval ◽  
Cost Rate ◽  
Optimal Replacement ◽  
Optimal Replacement Policy ◽  
Average Cost Rate

We develop a model and a genetic algorithm for determining an optimal replacement policy for power equipment subject to Poisson shocks. If the time interval of two consecutive shocks is less than a threshold value, the failed equipment can be repaired. We assume that the operating time after repair is stochastically nonincreasing and the repair time is exponentially distributed with a geometric increasing mean. Our objective is to minimize the expected average cost under an availability requirement. Based on this average cost function, we propose the genetic algorithm to locate the optimal replacement policyNto minimize the average cost rate. The results show that the GA is effective and efficient in finding the optimal solutions. The availability of equipment has significance effect on the optimal replacement policy. Many practical systems fit the model developed in this paper.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (2) ◽  
pp. 296-311 ◽  
Author(s):  
Jie Mi
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Average Amount ◽  
Failure Time Distribution ◽  
Long Run ◽  
Random Failure ◽  
Age Replacement ◽  
Work Size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

Geometric process repair model for an unreliable production system with an intermediate buffer

2016 ◽  
Vol 231 (4) ◽  
pp. 747-759 ◽  
Author(s):  
Guoqing Cheng ◽  
Binghai Zhou ◽  
Ling Li
Keyword(s):  
Production System ◽  
Buffer Stock ◽  
Sensitivity Analyses ◽  
Cost Rate ◽  
Long Run ◽  
Proposed Model ◽  
Joint Policy ◽  
Traditional Assumption ◽  
Average Cost Rate ◽  
Continuous Demand

In this paper, we consider an unreliable production system consisting of two machines (M1 and M2) in which M1 produces a single product type to satisfy a constant and continuous demand of M2 and it is subjected to random failures. In order to palliate perturbations caused by failures, a buffer stock is built up to satisfy the demand during the production unavailability of M1. A traditional assumption made in the previous research is that repairs can restore the failed machines to as good as new state. To develop a more realistic mathematical model of the system, we relax this assumption by assuming that the working times of M1 after repairs are geometrically decreasing, which means M1 cannot be repaired as good as new. Undergoing a specified number of repairs, M1 will be replaced by an identical new one. A bivariate policy [Formula: see text] is considered, where S is the buffer stock level and N is the number of failures at which M1 is replaced. We derive the long-run average cost rate [Formula: see text] used as the basis for optimal determination of the bivariate policy. The optimal policies [Formula: see text] and [Formula: see text] are derived, respectively. Then, an algorithm is presented to find the optimal joint policy [Formula: see text]. Finally, an illustrative example is given to validate the proposed model. Sensitivity analyses are also carried out to illustrate the effectiveness and robustness of the proposed methodology.

scholarly journals A Stochastic Failure Model with Dependent Competing Risks and its Applications to Condition-Based Maintenance

2015 ◽  
Vol 52 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Ji Hwan Cha ◽  
Inma T. Castro
Keyword(s):  
Competing Risks ◽  
Common Source ◽  
Maintenance Strategy ◽  
Failure Model ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Long Run ◽  
Degradation Failure ◽  
Average Cost Rate ◽  
Optimal Maintenance Policy

In this paper a stochastic failure model for a system with stochastically dependent competing failures is analyzed. The system is subject to two types of failure: degradation failure and catastrophic failure. Both types of failure share an initial common source: an external shock process. This implies that they are stochastically dependent. In our developments of the model, the type of dependency between the two kinds of failure will be characterized. Conditional properties of the two competing risks are also investigated. These properties are the fundamental basis for the development of the maintenance strategy studied in this paper. Considering this maintenance strategy, the long-run average cost rate is derived and the optimal maintenance policy is discussed.

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