scholarly journals A note on the optimal replacement problem

1988 ◽  
Vol 20 (2) ◽  
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.

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.

scholarly journals A repair replacement model

1990 ◽  
Vol 22 (02) ◽  
pp. 494-497 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Average Cost ◽  
Replacement Policy ◽  
Average Reward ◽  
Survival Times ◽  
System Form ◽  
Optimal Replacement ◽  
Long Run ◽  
Replacement Model ◽  
Optimal Replacement Policy ◽  
Long Run Average Reward

In this paper, we study a similar replacement model in which the successive survival times of the system form a process with non-increasing means, whereas the consecutive repair times after failure constitute a process with non-decreasing means. The system is replaced at the time of the Nth failure since the installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policy N∗ and the maximum of the long-run average reward explicitly. Under additional conditions, the policy N∗ is even optimal among all replacement policies.

scholarly journals A repair replacement model

1990 ◽  
Vol 22 (2) ◽  
pp. 494-497 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Average Cost ◽  
Replacement Policy ◽  
Average Reward ◽  
Survival Times ◽  
System Form ◽  
Optimal Replacement ◽  
Long Run ◽  
Replacement Model ◽  
Optimal Replacement Policy ◽  
Long Run Average Reward

In this paper, we study a similar replacement model in which the successive survival times of the system form a process with non-increasing means, whereas the consecutive repair times after failure constitute a process with non-decreasing means. The system is replaced at the time of the Nth failure since the installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policy N∗ and the maximum of the long-run average reward explicitly. Under additional conditions, the policy N∗ is even optimal among all replacement policies.

scholarly journals Optimal replacement policies for a deteriorating system with imperfect maintenance

1989 ◽  
Vol 21 (4) ◽  
pp. 949-951 ◽  
Author(s):  
A. Rangan ◽  
R. Esther Grace
Keyword(s):  
Imperfect Maintenance ◽  
Survival Times ◽  
Expected Cost ◽  
Geometric Process ◽  
Imperfect Repair ◽  
Optimal Replacement ◽  
Long Run ◽  
Working Age ◽  
Imperfect Repairs ◽  
Explicit Expressions

A system is repaired on failure. With probability p, it is returned to the ‘good as new' state (perfect repair) and with probability 1 – p, it is returned to the functioning state, but is only as good as a system of age equal to its age at failure (imperfect repair). In this article, we develop replacement policies for a deteriorating system with imperfect maintenance. The successive survival times and consecutive repair times form a geometric process which is stochastically non-increasing or non-decreasing respectively. Explicit expressions are obtained for the long-run expected cost under two kinds of replacement policies based on the working age of the system and the number of imperfect repairs before a replacement.

scholarly journals Optimal replacement policies for a deteriorating system with imperfect maintenance

1989 ◽  
Vol 21 (04) ◽  
pp. 949-951 ◽  
Author(s):  
A. Rangan ◽  
R. Esther Grace
Keyword(s):  
Imperfect Maintenance ◽  
Survival Times ◽  
Expected Cost ◽  
Geometric Process ◽  
Imperfect Repair ◽  
Optimal Replacement ◽  
Long Run ◽  
Working Age ◽  
Imperfect Repairs ◽  
Explicit Expressions

A system is repaired on failure. With probabilityp,it is returned to the ‘good as new' state (perfect repair) and with probability 1 –p, it is returned to the functioning state, but is only as good as a system of age equal to its age at failure (imperfect repair). In this article, we develop replacement policies for a deteriorating system with imperfect maintenance. The successive survival times and consecutive repair times form a geometric process which is stochastically non-increasing or non-decreasing respectively. Explicit expressions are obtained for the long-run expected cost under two kinds of replacement policies based on the working age of the system and the number of imperfect repairs before a replacement.

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 Monotone Process Maintenance Model for a Multistate System

2005 ◽  
Vol 42 (01) ◽  
pp. 1-14 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Average Cost ◽  
Process Model ◽  
Replacement Policy ◽  
Geometric Process ◽  
Optimal Replacement ◽  
Multistate System ◽  
Long Run ◽  
Optimal Replacement Policy ◽  
Monotone Process ◽  
Maintenance Model

In this paper, we study a monotone process maintenance model for a multistate system with k working states and ℓ failure states. By making different assumptions, we can apply the model to a multistate deteriorating system as well as to a multistate improving system. We show that the monotone process model for a multistate system is equivalent to a geometric process model for a two-state system. Then, for both the deteriorating and the improving system, we analytically determine an optimal replacement policy for minimizing the long-run average cost per unit time.

A bivariate optimal replacement policy for a repairable system

1994 ◽  
Vol 31 (04) ◽  
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∗.

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.

scholarly journals A Monotone Process Maintenance Model for a Multistate System

2005 ◽  
Vol 42 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Average Cost ◽  
Process Model ◽  
Replacement Policy ◽  
Geometric Process ◽  
Optimal Replacement ◽  
Multistate System ◽  
Long Run ◽  
Optimal Replacement Policy ◽  
Monotone Process ◽  
Maintenance Model

In this paper, we study a monotone process maintenance model for a multistate system with k working states and ℓ failure states. By making different assumptions, we can apply the model to a multistate deteriorating system as well as to a multistate improving system. We show that the monotone process model for a multistate system is equivalent to a geometric process model for a two-state system. Then, for both the deteriorating and the improving system, we analytically determine an optimal replacement policy for minimizing the long-run average cost per unit time.

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