scholarly journals Testing and preventive maintenance scheduling optimization for aging systems modeled by generalized renewal process

2009 ◽  
Vol 29 (3) ◽  
pp. 563-576 ◽  
Author(s):  
Vinícius Correa Damaso ◽  
Pauli Adriano de Almada Garcia
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Point Processes ◽  
Water System ◽  
Actual State ◽  
Feed Water ◽  
Repairable Systems ◽  
Homogeneous Poisson Process ◽  
Availability Analysis ◽  
Non Homogeneous Poisson Process

The use of stochastic point processes to model the reliability of repairable systems has been a regular approach to establish survival measures in failure versus repair scenarios. However, the traditional processes do not consider the actual state in which an item returns to operational condition. The traditional renewal process considers an "as-good-as-new" philosophy, while a non-homogeneous Poisson process is based on the minimal repair concept. In this work, an approach based on the concept of Generalized Renewal Process (GRP) is presented, which is a generalization of the renewal process and the non-homogeneous Poisson process. A stochastic modeling is presented for systems availability analysis, including testing and/or preventive maintenances scheduling. To validate the proposed approach, it was performed a case study of a hypothetical auxiliary feed-water system of a nuclear power plant, using genetic algorithm as optimization tool.

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.

An optimal parking problem

1982 ◽  
Vol 19 (4) ◽  
pp. 803-814 ◽  
Author(s):  
Mitsushi Tamari
Keyword(s):  
Poisson Process ◽  
Decision Maker ◽  
Optimal Stopping ◽  
Renewal Process ◽  
A Priori ◽  
Expected Loss ◽  
Homogeneous Poisson Process ◽  
Optimal Stopping Rule ◽  
Non Homogeneous Poisson Process ◽  
Parking Place

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.

Order statistics, Poisson processes and repairable systems

1976 ◽  
Vol 13 (3) ◽  
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.

Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes

1985 ◽  
Vol 22 (04) ◽  
pp. 828-835 ◽  
Author(s):  
J. Chandramohan ◽  
Lung-Kuang Liang
Keyword(s):  
Markov Chain ◽  
Poisson Process ◽  
Renewal Process ◽  
Point Processes ◽  
Renewal Processes ◽  
Single Pair ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Non Homogeneous Poisson Process ◽  
Dependent Point

We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes

1985 ◽  
Vol 22 (4) ◽  
pp. 828-835 ◽  
Author(s):  
J. Chandramohan ◽  
Lung-Kuang Liang
Keyword(s):  
Markov Chain ◽  
Poisson Process ◽  
Renewal Process ◽  
Point Processes ◽  
Renewal Processes ◽  
Single Pair ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Non Homogeneous Poisson Process ◽  
Dependent Point

We show that Bernoulli thinning of arbitrarily delayed renewal processes produces uncorrelated thinned processes if and only if the renewal process is Poisson. Multinomial thinning of point processes is studied. We show that if an arbitrarily delayed renewal process or a doubly stochastic Poisson process is subjected to multinomial thinning, the existence of a single pair of uncorrelated thinned processes is sufficient to ensure that the renewal process is Poisson and the double stochastic Poisson process is at most a non-homogeneous Poisson process. We also show that a two-state Markov chain thinning of an arbitrarily delayed renewal process produces, under certain conditions, uncorrelated thinned processes if and only if the renewal process is Poisson and the Markov chain is a Bernoulli process. Finally, we identify conditions under which dependent point processes superpose to form a renewal process.

Reliability analysis of underground rock bolters using the renewal process, the non-homogeneous Poisson process and the Bayesian approach

2019 ◽  
Vol 37 (2) ◽  
pp. 223-242
Author(s):  
Nicolas La Roche-Carrier ◽  
Guyh Dituba Ngoma ◽  
Yasar Kocaefe ◽  
Fouad Erchiqui
Keyword(s):  
Poisson Process ◽  
Reliability Analysis ◽  
Bayesian Approach ◽  
Renewal Process ◽  
Parameters Estimation ◽  
Homogeneous Poisson Process ◽  
Content Type ◽  
Failure Times ◽  
Non Homogeneous Poisson Process ◽  
The Bayesian Approach

Purpose Reliability plays an important role in the execution of the maintenance improvement and the understanding of its concepts is essential to predict the type of maintenance according to the equipment state. Thereby, a computational tool was developed and programming with VBA in Excel® for reliability and failure analysis in a mining context. The paper aims to discuss these issues. Design/methodology/approach The developed approach use the modeling of stochastic processes, such as the renewal process, the non-homogeneous Poisson process and less conventional method as the Bayesian approach, by considering Jeffreys non-informative prior. The resolution gives the best associated model, the parameters estimation, the mean time between failure and the reliability estimate. This approach is validated with the reliability analysis of inter-failure times from underground rock bolters subsystems, over a two-year period. Findings Results show that Weibull and lognormal probability distribution fit to the most subsystems inter-failure times. The study revealed that the bolting head, the rock drill, the screen handler, the electric/electronic system, the hydraulic system, the drilling feeder and the structural consume the most repair frequency. The hydraulic and electric/electronic subsystems represent the lowest reliability after 50 operation hours. Originality/value For the first time, this case study defines practical failures and reliability information for rock bolter subsystems based on real operation data. This paper is useful to the comparative evaluation of rock bolter by detecting the weakest elements and understanding failure patterns in the individual observation subsystems on the overall machine performance.

An optimal parking problem

1982 ◽  
Vol 19 (04) ◽  
pp. 803-814 ◽  
Author(s):  
Mitsushi Tamari
Keyword(s):  
Poisson Process ◽  
Decision Maker ◽  
Optimal Stopping ◽  
Renewal Process ◽  
A Priori ◽  
Expected Loss ◽  
Homogeneous Poisson Process ◽  
Optimal Stopping Rule ◽  
Non Homogeneous Poisson Process ◽  
Parking Place

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.

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