Optimizing the Periodic Inspection Interval for a 1‐out‐of‐2 Cold Standby System Using the Delay‐Time Concept

Abstract

In this article, we deal with a 1‐out‐of‐2 system with a cold‐standby component. The failure process of these two components is statistically identical and characterized by the delay‐time concept, which divides the component's life into a two‐stage process with a normal stage from new to a defect initiation point and a following failure delay stage from this point to failure. A fixed interval periodic inspection is carried out to check whether the working component is defective or not. If a defect is identified, the working component is shut down and sent to be repaired. The repair shop capacity is limited for repairing one component only. If the repair shop is occupied by the standby component (under repair) when the working one is failed, the system is shut down. There are five scenarios of the state of the system at an inspection epoch, which are derived analytically. The expected total cost per unit time of the system consists of the expected cost caused by preventive repair, unplanned failure repair, and system downtime. In this article, these three costs are determined and the optimal inspection interval with respect to the minimum of the expected total cost per unit time is found. To incorporate a nonexponential distribution for the normal time, delay stages, and repair time of the components, the elapsed time in the normal time, delay stages, and repair time at inspection is taken into consideration. A stationary distribution of the elapsed time exists, and it is calculated by an iteration method. Copyright © 2012 John Wiley & Sons, Ltd.

Delay-time inspection model with dimensioning maintenance teams: A study of a company leasing construction equipment

“…The delay-time concept is also applied by Lu et al (2012) to optimize the time interval for periodic inspections of stand by systems with a k-out-of-n system structure.…”

Identificação do intervalo ótimo de inspeções via conceito de delay time

“…Passando inclusive por análises sobre as recentes inovações neste tipo de modelagem (WANG, 2012a). Dentre as aplicações, destacam-se aquelas associadas à definição de intervalos de manutenções preventivas (foco deste trabalho); em que particularmente, pode-se ressaltar o trabalho de Wenbin Wang (WANG, 2012;LU et al, 2012;WANG, 2011;WANG, 2011a).…”

A myopic policy for optimal inspection scheduling for condition based maintenance

“…The authors of [22,24] in particular use a delay-time model, whose main purpose is to schedule inspections in time to detect faults prior to failures. The scheduled inspections need not be periodic, but they are not dynamically scheduled; a vector of inspections times is produced as a result of delay-time models [25,26]. A PHM is more general, incorporating complex system state information, rather than a binary defect/no-defect component.…”