استعمال بعض التوزيعات المبتورة في بناء نظام خبير لتقدير الفترة المثلى لاستبدال المكائن والمعدات

useing some Trancuted distributions in building an expert system to estimate the optimal period for replacing

Abstract :

The truncated method and combining of probability distributions is considered one of the statistical methods widely used by researchers to construct new probability distributions that are more flexible than standard probability distributions in modeling of phenomena whose data cannot be represented by standard statistical distributions as required. The process of providing appropriate probability distribution models to represent the data is an important factor in the statistical analysis and the conclusions that will follow from it.

According to the above problem, the goal of the thesis is summarized in three aspects:

The first aspect included a proposal for a new probability distribution represented by Left Truncate Gumbel, it’s family, which included two proposed distributions: left truncated Gumbel -exponential and left truncated Gumbel -Weibull distribution, so that the three proposed distributions are appropriate for continuous random variables whose values fall in the period (0 , ∞) including failure times. And the derivation of the properties of the proposed distributions represented by Noncenteral Moment, Centeral moment, skewness coefficient, kortisies coefficient, Mod and Median, as well as the estimation of their parameters in four methods (MLE method, MOM method, P.C method, and Cran method).

As for the second aspect, mathematical models have been proposed to estimate the optimal period of preventive replacement under the criterion of minimum cost and minimum downtime by employing the proposed probability distributions. On the third side, an expert system has been built to estimate the optimal period of preventive replacement.

In order to achieve the goal of the thesis, the results were discussed in the experimental (simulation) and application side, as a simulation method was adopted for comparison between the above four estimation methods to estimate the parameters of the proposed distributions, and simulation experiments were carried out using four different sample sizes (25,50,100,150) and different cases of  Default values for the parameters. The experiment was repeated 1000 times, and the results were compared after organizing them into tables using the standard MSE. The simulation results showed the preference of the Cran estimator among all the four estimators.

As for the application side, after the researcher’s visit to the Salsal Company for Water Desalination and Bottling in Basra and the recording of the data represented by the timing of the blowing mac