Optimal replacement in a shock model: discrete time

1987 ◽  
Vol 24 (01) ◽  
pp. 281-287 ◽  
Author(s):  
Terje Aven ◽  
Simen Gaarder
Keyword(s):  
Discrete Time ◽  
Average Cost ◽  
Shock Model ◽  
Optimal Replacement ◽  
Long Run ◽  
History Of ◽  
Total Damage ◽  
Special Case ◽  
Random Amount ◽  
Replacement Rule

A system is subject to a sequence of shocks occurring randomly at timesn= 1, 2, ···; each shock causes a random amount of damage. The system might fail at any point in timen, and the probability of a failure depends on the history of the system. Upon failure the system is replaced by a new and identical system and a cost is incurred. If the system is replaced before failure a smaller cost is incurred. We study the problem of specifying a replacement rule which minimizes the long-run (expected) average cost per unit time. A special case, in which the system fails when the total damage first exceeds a fixed threshold, is analysed in detail.

Optimal replacement in a shock model: discrete time

1987 ◽  
Vol 24 (1) ◽  
pp. 281-287 ◽  
Author(s):  
Terje Aven ◽  
Simen Gaarder
Keyword(s):  
Discrete Time ◽  
Average Cost ◽  
Shock Model ◽  
Optimal Replacement ◽  
Long Run ◽  
History Of ◽  
Total Damage ◽  
Special Case ◽  
Random Amount ◽  
Replacement Rule

A system is subject to a sequence of shocks occurring randomly at times n = 1, 2, ···; each shock causes a random amount of damage. The system might fail at any point in time n, and the probability of a failure depends on the history of the system. Upon failure the system is replaced by a new and identical system and a cost is incurred. If the system is replaced before failure a smaller cost is incurred. We study the problem of specifying a replacement rule which minimizes the long-run (expected) average cost per unit time. A special case, in which the system fails when the total damage first exceeds a fixed threshold, is analysed in detail.

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 Parametric analysis of the Bass model

2016 ◽  
Vol 12 (1) ◽  
pp. 29-40
Author(s):  
Yair Orbach
Keyword(s):  
Euclidean Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Parametric Analysis ◽  
Inflection Point ◽  
Bass Model ◽  
Long Run ◽  
The Common ◽  
Special Case ◽  
Q Values

In this research, the authors explore the influence of the Bass model p, q parameters values on diffusion patterns and map p, q Euclidean space regions accordingly. The boundaries of four different sub-regions are classified and defined, in the region where both p, q are positive, according to the number of inflection point and peak of the non-cumulative sales curve. The researchers extend the p, q range beyond the common positive value restriction to regions where either p or q is negative. The case of negative p, which represents barriers to initial adoption, leads us to redefine the motivation for seeding, where seeding is essential to start the market rather than just for accelerating the diffusion. The case of negative q, caused by a declining motivation to adopt as the number of adopters increases, leads us to cases where the saturation of the market is at partial coverage rather than the usual full coverage at the long run. The authors develop a solution to the special case of p + q = 0, where the Bass solution cannot be used. Some differences are highlighted between the discrete time and continuous time flavors of the Bass model and the implication on the mapping. The distortion is presented, caused by the transition between continuous and discrete time forms, as a function of p, q values in the various regions

Cataloging of Unit Replacement Based on Long Run Repair Average Cost Rate (ACR) Based on Weibull Distribution Model

2021 ◽  
pp. 149-152
Author(s):  
K. Uma Maheswari ◽  
K. Subrahmanyam ◽  
A. Mallikarjuna Reddy
Keyword(s):  
Weibull Distribution ◽  
Average Cost ◽  
Replacement Policy ◽  
Weibull Analysis ◽  
Distribution Method ◽  
Major Repair ◽  
Optimal Replacement ◽  
Long Run ◽  
Wide Range ◽  
Optimal Replacement Policy

Large amounts of money are lost each year in the real-estate industry because of poor schedule and cost control, In Industry the investigated failure and repair pattern, reliabilities of generators, compressors, turbines, using simple statistical tools and simulation techniques. The repair duration is divided into the 1) Major repair 2) Minor repair, In major repair having (repair hour greater than a threshold valve) and Minor repair having (repair hour less than (or)equal to threshold valve). This approach is mainly for Weibull distribution method. In Weibull analysis is a common method for failure analysis and reliability engineering used in a wide range of applications. In this paper, the applicability of Weibull analysis for evaluating and comparing the reliability of the schedule performance of multiple projects is presented, while the successive performance of multiple projects is presented, while the successive repair times are increasing and are exposing to Weibull distribution, under these assumptions, an optimal replacement policy ‘T’ in which we replace the system, when the repair time reaches T. It can be determined that an optimal repair replacement policy T* such that long run average cost and the corresponding optimal replacement policy T* can be determined analytically.

Optimal Replacement in a Discrete time Shock Model

OPSEARCH ◽  
1998 ◽  
Vol 35 (4) ◽  
pp. 338-345 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Discrete Time ◽  
Shock Model ◽  
Optimal Replacement

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∗.

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.

The Idea of a Modern Orthodoxy

1911 ◽  
Vol 4 (4) ◽  
pp. 477-488
Author(s):  
Douglas C. Macintosh
Keyword(s):  
Human Life ◽  
Systematic Theology ◽  
Large Measure ◽  
Human Welfare ◽  
Christian Doctrine ◽  
Life And Death ◽  
Long Run ◽  
Modern Mind ◽  
History Of ◽  
Special Case

Systematic theology is, and of right ought to be, primarily practical. In the first place, true religion is both one of the ends of an ideal human life and, in the long run, an indispensable means to the morality which is most essential to human welfare, inner and outer. In the second place, theology is necessary as an instrument for the proper control of the development and expression of religion—a special case of the function of ideas in the control of life. It follows, therefore, that a sound theology is a human necessity. The purpose of the theologian, whatever else it may or must include, must be to find those religious truths which are essential to the vitality and efficiency of the best type of human religion.That this has really been the aim of theologians in the great formative periods of the history of Christian doctrine may readily be shown. The prevailing impression with regard to orthodoxy and excluded heresies is that the distinction between them is arbitrary and external. This is indeed to the modern mind true in large measure of the distinction between the old orthodoxy and heresy; but in their own day this distinction was neither arbitrary nor external. Then it was organically related to the most pressing of problems; it was supremely vital, for the issues involved were nothing short of spiritual life and death.

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