A delay-time-based inspection model for parallel systems

Abstract

The delay-time concept has been extensively applied in the field of maintenance, especially for determining the optimal inspection or maintenance interval. It defines a two-stage system failure process: the time from new to an initial defect, known as the normal stage, and the time from this defective point to failure, known as the delay-time stage. Previous works using the delay-time concept have mainly focused on single-component systems and multi-component systems with a series configuration. However, parallel systems also exist in reality, but most existing models for parallel systems use either a single-stage time-to-failure process or a Markov chain to describe the failure mechanism. In this article, we propose a new delay-time-based inspection model for a n-component parallel system and study the optimal inspection interval that minimizes the long-term expected cost per unit time. Two maintenance policies are considered, depending on whether the defective/failed components identified are replaced immediately or not. Numerical examples are presented to show the applicability of the model.

A Joint Reliability and Imperfect Opportunistic Maintenance Optimization for a Multi‐State Weighted k‐out‐of‐n System Considering Economic Dependence and Periodic Inspection

“…In these cases, data are usually collected intermittently based on system inspection, and thus, the inspections must be conducted based on optimized inspection intervals. Liu et al 25 proposed a delay-time-based inspection model for a parallel system and studied the optimal inspection interval that minimizes the long-term expected cost per unit time.…”

A novel data-driven approach to optimizing replacement policy

“…Maintenance optimization models based on the periodic inspection policy is vast (e.g. see [8,9,17,18,25,28,29]). For example, Lienhardt [17] study both the corrective maintenance and a periodic inspection policy for a repairable system subject to non-self announcing failures.…”

“…Given the basic assumption that, soft-type components failure is non-self announced, their model aims at optimizing the periodic inspection interval. Recently, based on a periodic inspection policy, Liu et al [18] develop a delay-time-based model to determine the optimal inspection interval for parallel systems. More recently, Bjarnason and Taghipour [8] investigate periodic inspection frequency and inventory policies for a k-out-of-n system where the component's failures are hidden and conform to a non-homogeneous Poisson process.…”

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

“…Accordingly, three system states are involved in the two‐stage failure process, ie, normal, defective, and failure states. The delay time concept is firstly proposed by Christer to describe such failure process, and over the past several decades various delay time models have been developed to analyze system reliability and optimal maintenance policy, eg, Christer and Wang, Wang, Flage, Peng et al, Liu et al, and Wang et al…”

“…Accordingly, three system states are involved in the two-stage failure process, ie, normal, defective, and failure states. The delay time concept is firstly proposed by Christer to describe such failure process, 1 and over the past several decades various delay time models have been developed to analyze system reliability and optimal maintenance policy, eg, Christer and Wang, Wang, Flage, Peng et al, Liu et al, and Wang et al [2][3][4][5][6][7] It is worth noting that existing delay time models are investigated under the assumption that the durations in normal and defective stages are independent, which is restrictive in engineering practice because a variety of industrial systems are operating in dynamic environment and subject to random shocks such as extreme weathers, fluctuated voltages, and random stress. The same shock process can affect the random durations of the normal and defective stages, eg, Liu et al, Jiang et al, Dong and Cui, and Qiu et al [8][9][10][11] Due to the shared shock process, the durations of the two stages are dependent.…”