δ -shock model based on Polya process and its optimal replacement policy

2017 ◽  
Vol 263 (2) ◽  
pp. 690-697 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Replacement Policy ◽  
Shock Model ◽  
Model Based ◽  
Optimal Replacement ◽  
Optimal Replacement Policy ◽  
Polya Process ◽  
Pólya Process

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.

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∗.

Burn-in procedures for a generalized model

2001 ◽  
Vol 38 (02) ◽  
pp. 542-553 ◽  
Author(s):  
Ji Hwan Cha
Keyword(s):  
The Other ◽  
Replacement Policy ◽  
Type I ◽  
Type Ii ◽  
Failure Model ◽  
Minimal Repair ◽  
Optimal Replacement ◽  
Complete Repair ◽  
Optimal Replacement Policy ◽  
Type Of Failure

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.

scholarly journals A Robust Bayesian Approach to an Optimal Replacement Policy for Gas Pipelines

Entropy ◽  
2015 ◽  
Vol 17 (6) ◽  
pp. 3656-3678 ◽  
Author(s):  
José Arias-Nicolás ◽  
Jacinto Martín ◽  
Fabrizio Ruggeri ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Bayesian Approach ◽  
Replacement Policy ◽  
Gas Pipelines ◽  
Optimal Replacement ◽  
Optimal Replacement Policy
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