Estimation of the Optimum Period for the Replacement of Machines Using the Age Replacement Model Under the Minimum Cost Criterion

Abstract

Today, as a result of the tremendous technological progress and complexity in the machinery and equipment industry, it has become difficult to determine the appropriate distribution of failure times of machines and equipment based on standard distributions, that is, modeling failure times using new probability distributions is necessary. This, in turn, leads to reaching sound scientific and practical decisions, especially in the matter of maintenance and replacement of machinery and equipment in order to reduce costs and maintain the production process without causing losses. Accordingly, the research aims to employ the Left Truncated Gumbel- weibull probability distribution in the development of mathematical models for estimating the optimal period for the preventive life replacement of machines and equipment under the two criteria of least cost and least downtime, in addition to using the Cran method estimator to estimate the parameters of the mentioned distribution. Then applying those models to real data represented in the stopping times of the machines and equipment of Salsal Water Desalination and Bottling Company in Basra Governorate during the period (1/1/2020-31/12/2020). It has been concluded that the optimal replacement interval for the aforementioned company's machines is four months.