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 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.

OPTIMAL GEOMETRIC PROCESS REPLACEMENT POLICIES BASED ON NUMBER OF DOWN TIMES

2011 ◽  
Vol 18 (06) ◽  
pp. 495-513
Author(s):  
DAVID D. HANAGAL ◽  
RUPALI A. KANADE
Keyword(s):  
Replacement Policy ◽  
Geometric Process ◽  
Optimal Replacement ◽  
Long Run ◽  
Mathematical Expressions ◽  
Cold Standby ◽  
Optimal Replacement Policy ◽  
Newton Raphson ◽  
Standby System ◽  
Raphson Method

We consider two repair-replacement policies for a cold standby system consisting of two components with a single repairman. It is assumed that each component after repair is not "as good as new". With this assumption by using geometric process we developed two replacement policies based on the number of down times of the component-1. Our problem is to choose optimal replacement policy (k) such that the long run expected reward per unit time of the system maximized. The mathematical expressions for the long run expected reward per unit time are evaluated and corresponding optimal replacement policies are obtained theoretically with numerical example and by simulation study. Also we have discussed Newton–Raphson method to find optimal k.

A bivariate optimal replacement policy for a repairable system

1994 ◽  
Vol 31 (4) ◽  
pp. 1123-1127 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Explicit Expression ◽  
Average Cost ◽  
Replacement Policy ◽  
Repairable System ◽  
Optimal Replacement ◽  
Long Run ◽  
Optimal Replacement Policy ◽  
Working Age ◽  
Better Than

In this paper, a repairable system consisting of one unit and a single repairman is studied. Assume that the system after repair is not as good as new. Under this assumption, a bivariate replacement policy (T, N), where T is the working age and N is the number of failures of the system is studied. The problem is to determine the optimal replacement policy (T, N)∗such that the long-run average cost per unit time is minimized. The explicit expression of the long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, under some conditions, we show that the policy (T, N)∗ is better than policies N∗ or T∗.

scholarly journals A note on the optimal replacement problem

1988 ◽  
Vol 20 (02) ◽  
pp. 479-482 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
The Other ◽  
Replacement Policy ◽  
Survival Times ◽  
Geometric Process ◽  
System Form ◽  
Optimal Replacement ◽  
Long Run ◽  
Replacement Model ◽  
Working Age ◽  
Replacement Problem

In this note, we study a new repair replacement model for a deteriorating system, in which the successive survival times of the system form a geometric process and are stochastically non-increasing, whereas the consecutive repair times after failure also constitute a geometric process but are stochastically non-decreasing. Two kinds of replacement policy are considered, one based on the working age of the system and the other one determined by the number of failures. The explicit expressions of the long-run average costs per unit time under these two kinds of policy are calculated.

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.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (02) ◽  
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.

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