A general inspection and opportunistic replacement policy for one-component systems of variable quality

We model the influence of opportunities in a hybrid inspection and replacement policy. The base policy has two phases: an initial inspection phase in which the system is replaced if found defective; and a later wear-out phase that terminates with replacement and during which there is no inspection. The efficacy of inspection is modelled using the delay time concept. Onto this base model, we introduce events that arise at random and offer opportunities for cost-efficient replacement, and we investigate the efficacy of additional opportunistic replacements within the policy. Furthermore, replacements are considered to be heterogeneous and of variable quality. This is a natural policy for heterogeneous systems. Our analysis suggests that a policy extension that allows opportunities to be utilised offers benefit, in terms of cost-efficiency. This benefit is significant compared to those offered by age-based inspection or preventive replacement. In addition, opportunistic replacement may simplify maintenance planning

A study of postponed replacement in a delay time model

We develop a delay time model for a one component system with postponed replacement to analyze situations in which maintenance might not be executed immediately upon discovery of a defect in the system. Reasons for postponement are numerous: to avoid production disruption or unnecessary or ineffective replacement; to prepare for replacement; to extend component life; to wait for an opportunity. This paper explores conditions that make postponement cost-effective. We are interested in modelling the reality in which a maintainer either prioritizes functional continuity or is not confident of the inspection test indicating a defective state. In some cases more frequent inspection and a longer time limit for postponement are recommended to take advantage of maintenance opportunities, characterized by their low cost, arising after a positive inspection. However, when the cost of failure increases, a significant reduction in the time limit of postponement interval is observed. The examples reveal that both the time to defect arrival and delay time have a significant effect upon the cost-effectiveness of maintenance at the limit of postponement. Also, more simply, we find that opportunities must occur frequently enough and inspection should be a high quality procedure to risk postponement

Conditional inspection and maintenance of a system with two interacting components

In this paper we consider the inspection and maintenance of a two-component system with stochastic dependence. A failure of component 1 may induce the defective state in component 2 which in turn leads to its failure. A failure of component 1 and a defect in component 2 are detected by inspection. Our model considers a conditional inspection policy: when component 1 is found to have failed, inspection of component 2 is triggered. This opportunistic inspection policy is a natural one to use given this stochastic dependence between the components. The long-run cost per unit time (cost-rate) of the conditional inspection policy is determined generally. A real system that cuts rebar mesh motivates the model development. The numerical examples reveal that when the ratio of the cost of corrective system replacement, that is on failure, to the cost of preventive system replacement is large there exists a finite optimum policy in most cases. Moreover, for the studied system wherein inspections of component 2 are expensive relative to those of component 1, having a reliable indicator of the defective state in component 2 is a good strategy to avoid costly failures of component 2, particularly when its time to failure is short

Modelling inspection and replacement quality for a protection system

An inspection and replacement policy for a protection system is described by a mathematical model that incorporates multiple aspects of maintenance quality. A three-state component failure model is assumed, with a defective state preceding failure. The quality of maintenance intervention is modelled by supposing that inspections may misclassify defects (false positives and false negatives) and further that an inspection may induce a defect. The quality of replacement is modelled by supposing that a component arises from a heterogeneous population, composed of weak and strong items and with the mixing parameter determining quality. Isolation valves used in water distribution systems motivate the model development, and a case study is considered in this context. We evaluate the impact of these aspects of the quality of maintenance upon cost and production losses. Defect induction is found to be a key determinant of the cost-optimal policy. The proposed model allows us to verify conditions that justify investment in higher quality maintenance, and thus to provide guidance for prioritization of this investment

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

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. Keywords: Maintenance; reliability; random inspection; production; qualit

Maintenance scheduling of a protection system subject to imperfect inspection and replacement

An inspection and replacement policy for a protection system is described in which the inspection process is subject to error, and false positives (false alarms) and false negatives are possible. We develop two models: one in which a false positive implies renewal of the protection system; the other not. These models are motivated by inspection of a protection system on the production line of a beverage manufacturer. False negatives reduce the efficiency of inspection. Another notion of imperfect maintenance is also modelled: that of poor installation of a component at replacement. These different aspects of maintenance quality interact: false alarms can, in a worst case scenario, lead to the systematic and unnecessary replacement of good components by poor components, thus reducing the availability of the system. The models also allow situations in which maintenance quality differs between alternative maintainers to be investigated

Some insights into the effect of maintenance quality for a protection system

This paper considers an inspection and preventive replacement policy for a one-component protection or cold standby system. Inspection is imperfect, and subject to false positives and negatives; preventive replacement may also be of poor quality. We determine conditions relating to the quality of the inspection and preventive replacement under which a maintained system would not benefit from the execution of inspections and preventive maintenance. We present examples with decreasing failure rate component lifetimes in which preventive replacement is cost-optimal, contrary to the classic policy. Such cases arise when inspections do not necessarily detect the failed state

Modelling imperfect inspection over a finite horizon

This paper models imperfect inspection policies for a system with a finite operational time requirement. Two types of maintenance policy are considered: that in which an alarm (a positive inspection) is followed by a check of the validity of the alarm at additional cost, and if the system is good it continues in service and if failed it is retired; and that in which a positive inspection leads to retirement of the system regardless of the true system state. False negative inspections may also occur. The cost implications and applicability of these policies are different, but the mathematical analyses of the models are related. We also allow aperiodic inspection. The models we describe are general and allow one to explore maintenance planning options for systems that are close to retirement

Preventive replacement with defaulting

This paper models age replacement and block replacement when there is the possibility of defaulting on the planned maintenance. A default occurs when a planned preventive replacement is not executed, and we discuss how defaults can arise in practice. Our aim is to study the robustness of block replacement and age replacement, bearing in mind that (a) these policies are frequently used in practice, (b) in the standard scenario (no defaulting) age replacement has a lower economic cost rate than block-replacement and (c) block replacement is simple to manage because component age does not have to be monitored. We model defaults as independent Bernoulli trials. We prove that a cost-minimizing critical age for replacement in the age policy with defaulting exists if the time to failure distribution has an increasing failure rate. A numerical study of the policies indicates that: age replacement is effective if maintenance control is good, that is, when there is only a small chance of defaulting; block replacement is relatively robust to defaulting (postponement), but less so to lack of knowledge about component reliability