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

It is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub‐shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Nonzero repair times dependent on the failure hazard

Arnold

Chukova

Hayakawa

et al. 2019

“…Then, we focus on the derivation of R Y (t, x) in Equation 20. Using the law of total probability, R Y (t, x) can be derived by conditioning on the number of shocks occurring in [x, t) as follows:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…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.

“…21 Maintenance actions involve preventive maintenance (PM) and corrective maintenance (CM) carried out to restore a system to an acceptable operating condition according to the implementation time of repair before or after system failures. 22,23 Replacement, which serves as an effective policy in maintenance theory, is typically classified into three fundamental categories, that is, age replacement, periodic replacement, and inspection replacement. 24 Age replacement policy implies that a system is preventively replaced at a specified age T (0 < T ≤ ∞) or correctively replaced at failure, whichever occurs first, whereas periodic replacement means that a system is always replaced at periodic times kT (k = 1,2,Á Á Á) independent of its age.…”

Section: Introductionmentioning

confidence: 99%

Time‐based replacement policies for a fault tolerant system subject to degradation and two types of shocks

Dong

Cao

Bae

2020

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed-form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time-based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long-run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.