Delay-time modelling of a critical system subject to random inspections

Abstract

We model the inspection-maintenance of a critical system in which the execution of inspections is random. The models we develop are interesting because they mimic realities in which production is prioritised over maintenance, so that inspections might be impeded or they might be opportunistic. Random maintenance has been modelled by others but there is little in the literature that relates to inspection of a critical system. We suppose that the critical system can be good, defective or failed, and that failure impacts on production, so that a failure is immediately revealed, but a defect does not. A defect, if revealed at inspection, is a trigger for replacement. We compare the cost and reliability of random inspections with scheduled periodic inspections and discuss the implications for practice. Our results indicate that inspections that are performed opportunistically rather than scheduled periodically may offer an economic advantage provided opportunities are sufficiently frequent and convenient. A hybrid inspection and replacement policy, with inspections subject to impediments, is robust to departure from its inspection schedule.

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

“…When an external shock comes, one of two types of shock is incurred according to its effectiveness, that is, Type I shock with a time‐dependent probability p ( t ) (0 ≤ p ( t ) ≤ 1), which increases system degradation level; and Type II shock with a probability q ( t ), which results in a traumatic failure, where p ( t )+ q ( t ) ≡ 1. Most of Type I shocks are avoided owing to the fault tolerant design that is analyzed by the generalized m − δ shock model proposed in Liu et al 30 The system is regarded as failure when the total degradation amount caused by both natural degradation and Type I shock reaches a prescribed threshold or when a Type II shock occurs for the first time, whichever takes place first. In the following contents, the different failure modes are modeled respectively in more details, highlighting the dependence between the traumatic failure and the degradation failure.…”

“…29 Fault tolerance, which is often achieved by some kinds of self-constrained redundancies, is targeted at the development of a system that functions correctly in presence of faults and is most commonly used in computer systems. 30 For example, an onboard error detection and correction (EDAC) device is usually incorporated in memory chips operated in space radiation environments to detect and correct upset errors. This fault tolerant ability is constrained to central process unit (CPU) and random access memory resources, enabling the memory chip to continue more or less its intended operation, possibly at a reduced level.…”

“…Other than maintenance that needs resources outside of a system, fault tolerant design can as well improve a system's resilience to failure, recovering part of the degraded performance and restoring the system to an ameliorative state 29 . Fault tolerance, which is often achieved by some kinds of self‐constrained redundancies, is targeted at the development of a system that functions correctly in presence of faults and is most commonly used in computer systems 30 . For example, an onboard error detection and correction (EDAC) device is usually incorporated in memory chips operated in space radiation environments to detect and correct upset errors.…”

Healthcare Warranty Policies Optimization for Chronic Diseases Based on Delay Time Concept

“…In this study, we developed an optimization model based on a delay time model from the reliability and machine maintenance literature to capture disease-monitoring dynamics. The delay-time model is widely applied to model engineering problems in machine maintenance and inspection; it assumes that a device's life cycle has an increasing failure rate [35][36][37]. The period that starts with the device showing signs of failure, and ending with the final failure, is called the delay time.…”

Imperfect Preventive Maintenance Policies With Unpunctual Execution

“…Yang et al [33] developed a two-phase PM model, where preventive replacement in the second phase is delayed to sufficiently utilize the system's remaining lifetime and facilitate replacement preparations. Scarf et al [34] found that for a critical system, opportunistic inspections may offer an economic advantage against periodic inspections in certain cases. On the other hand, the working cycle of a system that executes successive jobs, might be variable.…”