On preventive maintenance of systems with lifetimes dependent on a random shock process

Self Cite

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 mth 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.

Section: The Failure Model and Supplementary Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On optimal replacement of systems with failure rates described by a random jump process

Hwan

Finkelstein

Levitin

2018

Self Cite

“…The third term is the joint probability density function for the arrival times of n shocks and the number of shocks by time n. From Cha et al, 18 we can obtain that f S 1 ;…;S n ;N x;t…”

Section: Proof Of Theoremmentioning

confidence: 97%

“…For these systems, Lemoine and Wenocur firstly investigated the dynamic dependency between system intrinsic characteristics and eternal environmental conditions within the framework of shot‐noise process. Utilizing the shot‐noise process, Cha and Mi utilized the process to study the system reliability performance, which assumed that system failure rate is increased at the occurrence of a shock; Cha and Finkelstein investigated the optimal preventive replacement policy for systems with lifetime dependent on shocks; Levitin and Finkelstein investigated the optimal mission abort policy for systems operating in a random environment with variable shock rate; Qiu et al optimized the maintenance policy for systems subject to complex failure behavior operating under periodic preventive maintenance; Qiu et al presented formulas on system availability considering the dependence between soft and hard failures.…”

Section: Introductionmentioning

confidence: 99%

Reliability evaluation and opportunistic maintenance policy based on a novel delay time model

Zhang

2018

The delay time concept is widely adopted in literature to model the two‐stage failure process of most industrial systems which can be divided into normal stage (from new to an initial point of a defect) and defective stage (from defect arrival point to failure). Most existing delay time models assume that the normal and defective stages are independent. A generalized delay time model is proposed in this paper by considering the dependence between the normal and defective stages which is reflected in the fact that they share the same external shock process. According to the definition of shot‐noise process, external shocks will incur random hazard rate increments in the two stages. The failure state is self‐announcing, whereas the defective state can only be detected by block‐based inspection or opportunistic inspection offered by unexpected shutdown due to unavoidable external factors. The system is correctively replaced upon the occurrence of a system failure or preventively replaced at the detection of a defective state. Based on the stochastic failure model and maintenance policy, this paper evaluates system reliability performance and average long‐run cost rate via a Markov‐chain based approach. Finally, a case study on a steel convertor plant is given to demonstrate the applicability of the proposed model.

“…On this basis, Cha and Mi utilized the process to test the system reliability performance, which assumed that system failure rate is increased by a fixed amount at the occurrence of a shock. Cha and Mi extended the work in by assuming that each shock can cause immediate failure with some probability or increases the system failure rate by a random amount. Cha et al developed a bivariate preventive maintenance model for systems operating in a dynamic environment modeled by a Poisson process of shocks.…”

Section: Introductionmentioning

confidence: 99%

Preventive maintenance policy of single‐unit systems based on shot‐noise process

Qiu

Cui

Dong

2018

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system.