María Dolores Berrade

Optimal inspection and preventive maintenance of units with revealed and unrevealed failures

Abstract The maintenance of a single unit system that alternates operating and idle periods is studied. In the former case the failures are detected as soon as they occur and only by special testing or inspection in the latter. This paper aims at minimizing the cost per unit of time for an infinite time span by selection of a unique interval, for both inspection and maintenance. A special feature of this model is the possibility of a less than perfect testing as the inspections may fail and give a wrong result. It is further assumed that both preventive and corrective maintenance make the unit as good as new with the durations of inspections and maintenances being negligible. The existence of an optimum interval and how it depends on both the cost parameters and the reliability characteristics of the unit is discussed.

Imperfect inspection and replacement of a system with a defective state: A cost and reliability analysis

We consider a system with three possible states, good, defective and failed. Failures are detected as soon as they occur; the defective state, which is only revealed by inspection, does not prevent the system from fulfilling the function for which it was designed. We present a maintenance model consisting of periodic inspections to check the state of the system, in which inspections are subject to error. At a false positive inspection the system is unnecessarily replaced; at a false negative inspection a defect remains unrevealed with reliability implications for future operation. The model is illustrated with an example from the railways. In this context, we suppose that system lifetime is heterogeneous so that the time the system spends in the defective state is a random variable from a mixed distribution. We determine under what circumstances the cost of maintenance cannot be justified by its efficacy, and suggest that when there is the possibility that replacement is poorly executed (lifetime heterogeneity) the natural response to imperfect inspection of increasing the inspection frequency can be counter-productive.

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.

Aging properties of the additive and proportional hazard mixing models

Abstract We carried out a study of the aging characteristics in two mixing models having additive and proportional hazards, respectively. The relation between aging properties of such mixtures and that of an exponential mixture is described. The effect of mixing on the properties of the stochastic aging as well as the relation between the mixture and the distributions within are also analyzed.

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.

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.

ON THE BEHAVIOR OF AGING CHARACTERISTICS IN MIXED POPULATIONS

Bounds for aging properties in mixtures and their derivatives are provided. Such bounds allow control of the behavior of those characteristics through the aging properties of the distributions in the mixture. We also obtain some results for discrete mixtures involving exponential distributions. In addition, well-known mixture-preserving properties for several distribution classes are derived with little algebraic complexity.

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.

Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair

Abstract We analyze the optimal replacement policy for a system subject to a general failure and repair model. Failures can be of one of two types: catastrophic or minor. The former leads to the replacement of the system, whereas minor failures are followed by repairs. The novelty of the proposed model is that, after repair, the system recovers the operational state but its condition is worse than that just prior to failure (worse than old). Undertrained operators or low quality spare parts explain this deficient maintenance. The corresponding failure process is based on the Generalized Polya Process which presents both the minimal repair and the perfect repair as special cases. The system is replaced by a new one after the first catastrophic failure, and also undergoes two sorts of preventive maintenance based on age and after a predetermined number of minor failures whichever comes first. We derive the long-run average cost rate and study the optimal replacement policy. Some numerical examples illustrate the comparison between the as bad-as-old and the worse than old conditions.