Comments on Finite-Period Applications of Age-Based Replacement Models

The age-based replacement problem is considered when a finitetime zone is placed upon the duration of the process and, accordingly,for which an asymptotic model could be of questionable validity.Three models to be optimized with respect to the decision variableare considered: first, the commonly used limiting asymptoticcost per unit time; secondly, the refined asymptotic cost perunit time; and thirdly, the exact expected cost. These modelsare investigated in the case of a negative exponential and Weibullfailure-time distribution. In both cases, it is found that theestimated cumulative cost resulting from the refined model approachesquickly that of the exact formulation. The practical use and decision consequences of this result areinvestigated for a Weibull failure distribution. It is arguedthat, because of the essential illconditioned nature of theage based replacement model, for short time-zone applications,the model should be extended to accommodate non-zero replacementtimes.     

Modelling maintenance practice of production plant using the delay-time concept

In this paper we present a study carried out for a copper productsmanufacturing company, developing and applying the delay-timemodelling technique to model and thus optimize preventive maintenance(PM) of the plant. A key machine in the plant is used to illustratethe modelling process and management reaction. The parameter values of the process by which faults arise andof the delay-time distribution are estimated from maintenancerecord data of failures and faults found at PM, using the methodof maximum likelihood. A test of the model fit to data is carriedout. Based upon the estimated model parameters and the failuredelay time, an inspection model is proposed to describe therelationship between the total downtime and the PM interval.     

A Recent Mathematical Development in Maintenance Theory

This paper introduces the mathematics of delay-time analysisand places it in context. Both the nature of and the scope fordelay-time models are indicated, and example prototype modelsdeveloped in the context of inspection policies. The essentialrole of subjective estimation is indicated, and the need toconsider revisions of both the prior delay-time distributionand the delay-time model highlighted. An unavoidable bias thatarises when estimating delay-time is discussed and the appropriatedistribution of biased estimates derived. A mechanism for correctingthis bias when estimating a delay-time distribution is proposed,based upon maximum-likelihood considerations. Finally, generalcomments are made concerning other developments and applicationsof the technique.     

The delay-time modelling of preventive maintenance of plant given limited PM data and Selective repair at PM

This paper presents a maintenance-modelling case study of aplant manufacturing brake linings. A delay–time modelis developed and applied to model and optimize preventive maintenance(PM). A key subsystem in the plant is used to illustrate themodelling process and management reaction. Defects identifiedat PM may not all be removed. This incomplete response to PMis a feature which has not been modelled before. The parametervalues of the delay-time process are estimated from objectivedata from maintenance records of failures, using the methodof maximum likelihood. This is aided by a theorem extendingresults on the NHPP arival rate of failures in a perfect-inspectioncase to the non-perfect-inspection case. Problems of parameterestimation given inadequate data collected at PMs are discussed,and the necessity to augment objective data with subjectiveassessments highlighted. Based upon the estimated model parametersand delay-time distribution, an inspection model is constructedto describe the relationship between the total unit downtimeand the PM interval. The response of management is discussed.     

Prototype modelling of irregular condition monitoring of production plant

The previously reported modelling of inspection-maintenanceproblems utilizing the delay-time concept is here extended toembrace condition-monitoring checks. The main requirements arethe relaxation of regular periodic inspections, and the requirementthat the initial point of a defect be measured as the time fromthe as-new condition and not, as previously, as the time sincea previous inspection. An expression for the probability ofa defect arising as a breakdown and as an inspection repairis constructed for a general inspection policy, under the assumptionof both perfect and imperfect repair. The revised role of theseprobability expressions in modelling the process of maintenancefor cost-effective production is discussed, various modellingalternatives are outlined, and a numerical example is presented.Parallels are drawn between condition monitoring in an industrialsetting and in the delivery of health care.     

An Integral-Equqtion Approach for Replacement Modelling Over Finite Time Horizons

An integral-equation approach to calculating the exact and asymptoticestimates of expected costs in stochastic replacemnet problemsis advocated. The method is based upon the known solution tothe generalized renewal integral equation and upon the key renewaltheorem. The basic failure-bsed and age-based replacement policiesare taken as illustrative examples for the method, and the relationshipto more conventional methods of calculation is highlighted.The benefit of the integral-equation format is that it providesa relatively clear procedure for evaluating more complex stochastitreplacement situations.     

A delay-time-based maintenance model of a multi-component system

There is a well established literature on delay-time modelsof regular inspection policies where inspections may or maynotbe perfect, and where the initial point u of a defect arisesas a homogeneous Poisson process. This paper extends the modellingin two ways. The first is to include the observed practice wherethe multi-component system is inspected not only on a plannedbasis, but also when a component fails. The second extensionis to use a nonhomogeneous Poisson process to describe defectarrivals in the system. An inspection–replacement modelbased upon these two extensions is then developed for a multi-componentsystem. The total expected cost per unit time is minimized withrespect to theinspection intervals and the system replacementtime. The likelihood function of the time of failures and thenumber of defects found at inspections is established, in orderto estimate model parameters based upon routinely collectedmaintenance data. As a special case of the general model, aninspection model—based upon a homogeneous Poisson processof defects arising—is also proposed, which has a relativelysimple structure. Both simulated and real-life data of failuresand defects identified at inspections are used to test the modelsand parameter-estimating procedure.