Dynamic maintenance policy for systems with repairable components subject to mutually dependent competing failure processes

Abstract

In this paper, a repairable multi-component system is studied where all the components can be repaired individually within the system. The whole system is inspected at inspection intervals and the failed components are detected and replaced with a new one, while the other components continue functioning. Replacing components individually within the system makes their initial age to be different at each inspection time. Different initial age of all the components have affect on the system reliability and probability of failure and consequently the optimal inspection time, which is for the whole system not individual components. A dynamic maintenance policy is proposed to find the next inspection time based on the initial age of all the components. Two competing failure processes of degradation and a shock process are considered for each component. In our paper, there is a mutual dependency between the degradation process and shock process. Each incoming shock adds additional abrupt damages on the cumulative degradation path of all the components, and the shock arrival process is affected by the system degradation process.A realistic numerical example is presented to illustrate the proposed reliability and maintenance model.

A Dynamic Failure Time Degradation-Based Model

“…where B(T, w, λ, µ) = α(T) exp − λ 2µ 2 w (w − µα(T)) 2 for any T > 0. Whenever T has survival function (12) in the case where…”

“…If the random lifetime T has survival function (12), so that W(t) ∼ IG(µα(t), λα 2 (t)), the hazard rate is derived as…”

“…The methods developed in the context of degradation-based modelling have been considered as indispensable and operative procedures to make inference on the lifetimes of different sorts of deteriorating systems (see, e.g., Kharoufeh and Cox [1], Park and Padgett [2], Gebraeel and Pan [3], Si et al [4], Jiang et al [5], Rafiee et al [6], Ye and Xie [7], Chen et al [8], Zhai and Ye [9], Zhang et al [10], Huang et al [11], Yousefi et al [12], Dong et al [13], and Balali et al [14]). The lifetime of deteriorating items which exhibit an observable degradation can be generally modeled using a stochastic process and, specifically, by a nonhomogeneous gamma process or nonhomogeneous inverse Gaussian process.…”

A Combined Maintenance Strategy Considering Spares, Buffer, and Quality

“…3 Grall et al 4 proposed a CBM model by determining the replacement threshold and inspection time for a stochastically and continuously deteriorating single-unit system. Yousefi et al 5,6 developed CBM models for multi-component systems experiencing degradation and shocks, with repairable and nonrepairable components. de Jonge 7 studied continuous-state deterioration processes and illustrated the application of CBM.…”

Modeling multi-state system reliability analysis in a power station under fatal and nonfatal shocks: a simulation approach

“…In such situations, through applying degradation data, the reliability of the product can be analyzed, provided that some quality characteristics exist, which correlate with reliability. In order to model the degradation process, several methods can be used including general degradation path models, continuous-time stochastic processes and the Markov models (Yousefi et al , 2020). As a regression model, the general degradation path model has random or fixed coefficients fitted to the degradation observations.…”