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A Modified Replacement Model for Items That Fail Suddenly with Variable Replacement Costs

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Document pages: 17 pages

Abstract: Several researches have been done to provide better alternative to the existingreplacement models, but the research works did not adequately address thereplacement problem for items that fail suddenly. Hence, a modified replacementmodel for items that fail suddenly has been proposed using theknowledge of probability distribution of failure times as well as that of variablereplacement cost. The modified cost functions for implementing both individualand group replacements were derived. The modified cost functionswere minimized using the principle of classical optimization in order to findthe age at which replacement of items would be appropriate. Conditions underwhich the individual and group replacement policies should be adoptedwere derived. Two real data sets on failure time of LED bulbs and their replacementcosts were used to validate the theoretical claims of this work. Inessence, goodness-of-fit test was used to select appropriate probability distributionof failure times as well as that of replacement costs for data sets I andII respectively. The goodness-of-fit results showed that failure times of LEDbulbs follow the Smallest Extreme Value and Laplace distributions for datasets I and II respectively. Similarly, it was observed that individual replacementcost followed the two-parameter Gamma and Largest Extreme Valuedistributions for data sets I and II respectively. Further, the group replacementcost was found to follow the log-normal and two-parameter Weibulldistributions for data sets I and II respectively. Based on the empirical study,we observed that individual replacement policy is better than group replacementpolicy in terms of cost minimization for both existing model and theproposed model. In view of the results, the proposed replacement policy wasrecommended over the existing one because it yielded lower replacementcosts than the existing replacement model.

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