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On optimal replacement of systems with failure rates described by a random jump process
Author(s) -
Cha Ji Hwan,
Finkelstein Maxim,
Levitin Gregory
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2343
Subject(s) - bivariate analysis , univariate , jump , shock (circulatory) , failure rate , preventive maintenance , poisson process , stochastic process , poisson distribution , mathematics , random effects model , statistics , computer science , reliability engineering , engineering , multivariate statistics , physics , medicine , meta analysis , quantum mechanics
Preventive maintenance (age replacement) of items operating in a random environment modeled by a Poisson shock process, resulting in random jump process in the system failure rate, is considered. The corresponding univariate and bivariate models are described. In the univariate model, an item is replaced either on failure or on the predetermined replacement time, whichever comes first. In the bivariate model, the preventive maintenance is performed also on the occurrence of the m th shock. Each shock in our stochastic model has a triple effect. On one hand, it acts directly on the failure rate of an item, increasing it by a random amount or resulting in a failure. On the other hand, each shock causes additional ‘damage’, which can be attributed, eg, to a short drop in the output of an item. The corresponding optimization problem is formulated and illustrated by detailed numerical examples.