scholarly journals A study on stochastic modelling of the repairable system

2021 ◽  
Vol 5 (2) ◽  
pp. 76-82
Author(s):  
Syed Tahir Hussainy ◽  
Shabeer B
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Stochastic Modelling ◽  
Time Factors ◽  
Repairable Systems ◽  
Reliability Models ◽  
Decision Making Processes ◽  
Excellent Method ◽  
Time Required ◽  
Reliability Systems

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible.When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

scholarly journals Stochastic Modelling Of The Repairable System

2015 ◽  
Vol 35 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Karol Andrzejczak
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Stochastic Modelling ◽  
Time Factors ◽  
Repairable Systems ◽  
Reliability Models ◽  
Decision Making Processes ◽  
Excellent Method ◽  
Time Required ◽  
Reliability Systems

Abstract All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

scholarly journals Extended and conditional versions of the PASTA property

1990 ◽  
Vol 22 (2) ◽  
pp. 510-512 ◽  
Author(s):  
Dieter König ◽  
Volker Schmidt
Keyword(s):  
Stochastic Processes ◽  
Point Processes ◽  
Long Run ◽  
Run Time

Two types of conditions are discussed ensuring the equality between long-run time fractions and long-run event fractions of stochastic processes with embedded point processes. Modifications of this equality statement are considered.

Reliability Analysis of Repairable Systems Subject to System Modifications

1998 ◽  
Author(s):  
Z. H. Jiang ◽  
L. H. Shu ◽  
B. Benhabib
Keyword(s):  
Life Cycle ◽  
Steady State ◽  
Cost Estimation ◽  
Life Cycle Cost ◽  
Repairable Systems ◽  
Environmentally Conscious ◽  
Reliability Indices ◽  
Reliability Models ◽  
System Reconfiguration ◽  
Environmentally Conscious Design

Abstract This paper approaches environmentally conscious design by further developing a reliability model that facilitates design for reuse. Many reliability models are not suitable for describing systems that undergo repairs performed during remanufacture and maintenance because the models do not allow the possibility of system reconfiguration. In this paper, expressions of reliability indices of a model that allows system reconfiguration are developed to enable life-cycle cost estimation for repairable systems. These reliability indices of a population of repairable systems are proven theoretically to reach steady state. The expressions of these indices at steady state are obtained to gain insight into the model behavior, and to facilitate life-cycle cost estimation.

Unification of Software Reliability Models by Self-Exciting Point Processes

1997 ◽  
Vol 29 (2) ◽  
pp. 337-352 ◽  
Author(s):  
Yiping Chen ◽  
Nozer D. Singpurwalla
Keyword(s):  
Software Reliability ◽  
Point Processes ◽  
Computer Software ◽  
Probability Models ◽  
Reliability Models ◽  
Common Structure ◽  
Software Reliability Models ◽  
Special Cases ◽  
Active Debate ◽  
The Subject

Assessing the reliability of computer software has been an active area of research in computer science for the past twenty years. To date, well over a hundred probability models for software reliability have been proposed. These models have been motivated by seemingly unrelated arguments and have been the subject of active debate and discussion. In the meantime, the search for an ideal model continues to be pursued. The purpose of this paper is to point out that practically all the proposed models for software reliability are special cases of self-exciting point processes. This perspective unifies the very diverse approaches to modeling reliability growth and provides a common structure under which problems of software reliability can be discussed.

Optimal Reliability and Cost of Non-Repairable Systems Subject to Two Failure Modes Considering Correlated Failures

2018 ◽  
Vol 25 (05) ◽  
pp. 1850024
Author(s):  
Anusha Krishna Murthy ◽  
Saikath Bhattacharya ◽  
Lance Fiondella
Keyword(s):  
Failure Mode ◽  
System Reliability ◽  
Failure Modes ◽  
Optimal Number ◽  
Optimal Designs ◽  
Repairable Systems ◽  
Independent Manner ◽  
Reliability Models ◽  
Correlated Failures ◽  
The Impact

Most reliability models assume that components and systems experience one failure mode. Several systems such as hardware, however, are prone to more than one mode of failure. Past two-failure mode research derives equations to maximize reliability or minimize cost by identifying the optimal number of components. However, many if not all of these equations are derived from models that make the simplifying assumption that components fail in a statistically independent manner. In this paper, models to assess the impact of correlation on two-failure mode system reliability and cost are developed and corresponding expressions for reliability and cost optimal designs derived. Our illustrations demonstrate that, despite correlation, the approach identifies reliability and cost optimal designs.

Order statistics, Poisson processes and repairable systems

1976 ◽  
Vol 13 (03) ◽  
pp. 519-529 ◽  
Author(s):  
Douglas R. Miller
Keyword(s):  
Order Statistics ◽  
Point Processes ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Renewal Processes ◽  
Repairable Systems ◽  
Homogeneous Poisson Process ◽  
Necessary And Sufficient ◽  
Non Homogeneous Poisson Process ◽  
Weibull Process

Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.

Stochastic comparison of repairable systems by coupling

1998 ◽  
Vol 35 (2) ◽  
pp. 348-370 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Point Processes ◽  
Stochastic Comparison ◽  
Repairable Systems ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Comparison Results ◽  
Special Cases ◽  
Repair Models

Stochastic comparison results for replacement policies are shown in this paper using the formalism of point processes theory. At each failure moment a repair is allowed. It is performed with a random degree of repair including (as special cases) perfect, minimal and imperfect repair models. Results for such repairable systems with schemes of planned replacements are also shown. The results are obtained by coupling methods for point processes.

A class of interacting marked point processes: rate of convergence to equilibrium

2002 ◽  
Vol 39 (1) ◽  
pp. 137-160 ◽  
Author(s):  
G. L. Torrisi
Keyword(s):  
Stochastic Processes ◽  
Rate Of Convergence ◽  
Point Processes ◽  
Marked Point ◽  
Marked Point Processes ◽  
Convergence To Equilibrium ◽  
Birth And Death Processes ◽  
Loss Networks

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results of Brémaud, Nappo and Torrisi. The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth and death processes.

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