Inspection and replacement models for reliability and maintenance: filling in gaps
Date
2017
Authors
Chipoyera, Honest Walter
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Abstract
The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit.
The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored.
Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174.
A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored.
The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge.
Description
A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017.
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Citation
Chipoyera, Honest Walter (2017) Inspection and replacement models for reliability and maintenance: filling in gaps, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23607>