TITLE:
A Modified Replacement Model for Items That Fail Suddenly with Variable Replacement Costs
AUTHORS:
Samuel Ugochukwu Enogwe, Ben Ifeanyichukwu Oruh, Emmanuel John Ekpenyong
KEYWORDS:
Probability Distribution, Failure Times, Variable Replacement Cost, Goodness-of-Fit Test, Group Replacement, Individual Replacement
JOURNAL NAME:
American Journal of Operations Research,
Vol.8 No.6,
November
5,
2018
ABSTRACT: Several researches have been done to provide better alternative to the existing
replacement models, but the research works did not adequately address the
replacement problem for items that fail suddenly. Hence, a modified replacement
model for items that fail suddenly has been proposed using the
knowledge of probability distribution of failure times as well as that of variable
replacement cost. The modified cost functions for implementing both individual
and group replacements were derived. The modified cost functions
were minimized using the principle of classical optimization in order to find
the age at which replacement of items would be appropriate. Conditions under
which the individual and group replacement policies should be adopted
were derived. Two real data sets on failure time of LED bulbs and their replacement
costs were used to validate the theoretical claims of this work. In
essence, goodness-of-fit test was used to select appropriate probability distribution
of failure times as well as that of replacement costs for data sets I and
II respectively. The goodness-of-fit results showed that failure times of LED
bulbs follow the Smallest Extreme Value and Laplace distributions for data
sets I and II respectively. Similarly, it was observed that individual replacement
cost followed the two-parameter Gamma and Largest Extreme Value
distributions for data sets I and II respectively. Further, the group replacement
cost was found to follow the log-normal and two-parameter Weibull
distributions for data sets I and II respectively. Based on the empirical study,
we observed that individual replacement policy is better than group replacement
policy in terms of cost minimization for both existing model and the
proposed model. In view of the results, the proposed replacement policy was
recommended over the existing one because it yielded lower replacement
costs than the existing replacement model.