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

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.

Comparison of two replacement policies

1986 ◽  
Vol 23 (03) ◽  
pp. 759-769 ◽  
Author(s):  
Antonín Lešanovský
Keyword(s):  
Finite Number ◽  
Discrete Time ◽  
Optimal Replacement

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.

On the reliability and optimal maintenance of systems under a generalized mixed δ-shock model

2021 ◽  
pp. 1748006X2110023
Author(s):  
Majid Bohlooli-Zefreh ◽  
Majid Asadi ◽  
Afshin Parvardeh
Keyword(s):  
Survival Function ◽  
Replacement Policy ◽  
Critical Threshold ◽  
Shock Model ◽  
Failure Model ◽  
Optimal Replacement ◽  
Reliability Characteristics ◽  
Optimal Replacement Policy ◽  
Optimal Maintenance ◽  
Theoretical Results

This article is a study on the reliability characteristics of a system under a failure model called the generalized mixed [Formula: see text]-shock model. We assume that the system is subject to shocks according to a stochastic process. Each shock may cause some damage to the system. The system fails either the magnitude of the damage caused by a shock exceeds a threshold [Formula: see text] or the time between two consecutive shocks is less than a pre-specified threshold [Formula: see text] and simultaneously magnitude of the damage is bigger than a pre-specified critical threshold [Formula: see text] ([Formula: see text]). The survival function and other characteristics of the system lifetime are investigated. By imposing a cost function, we arrive at an optimal replacement policy for the system based on the proposed failure model. Several examples are provided under which we illustrate the theoretical results numerically and graphically.

Reliability analysis of an extended shock model

2021 ◽  
pp. 1748006X2098779
Author(s):  
Mohammad Hossein Poursaeed
Keyword(s):  
Discrete Time ◽  
Probability Generating Function ◽  
Reliability Function ◽  
Time Interval ◽  
Shock Model ◽  
Critical Levels ◽  
Shock Models ◽  
The Mean ◽  
First Time ◽  
Mean Time

Suppose that a system is subject to a sequence of shocks which occur with probability p in any period of time [Formula: see text], and suppose that [Formula: see text] and [Formula: see text] are two critical levels ([Formula: see text]). The system fails when the time interval between two consecutive shocks is less than [Formula: see text], and the time interval bigger than [Formula: see text] has no effect on the system activity. In addition, the system fails with a probability of, say, [Formula: see text], when the time interval varies between [Formula: see text] and [Formula: see text]. Therefore, this model can be regarded as an extension of discrete time version of [Formula: see text]-shock model, and such an idea can be also applied in the extension of other shock models. The present study obtains the reliability function and the probability generating function of the system’s lifetime under this model. The present study offers some properties of the system and refers to a generalization of the new model. In addition, the mean time of the system’s failure is obtained under reduced efficiency which is created when the time between two consecutive shocks varies between [Formula: see text] and [Formula: see text] for the first time.

Comparison of two replacement policies

1986 ◽  
Vol 23 (3) ◽  
pp. 759-769 ◽  
Author(s):  
Antonín Lešanovský
Keyword(s):  
Finite Number ◽  
Discrete Time ◽  
Optimal Replacement

Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.

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