This thesis aims to estimate the parameters of the modified weighted Pareto distribution type one. This distribution is considered as important distribution in the field of reliability analysis and failure data modeling, given the flexibility of its probability density function, which has three parameters: two of them are shape parameters, the other is a scale parameter. Three statistical methods were employed to estimate the parameters: maximum likelihood estimation (MLE), ordinary least squares estimation (OLS), and rank set sampling estimation (RSS). The thesis relied on a Monte Carlo simulation procedure to evaluate the efficiency of each estimation method. This was achieved by generating empirical data with different sample sizes, repeating the simulation 1,000 times for each case, and using different sets of assumed values ​​for the three parameters. The calculations was performed using the program MATLAB

The performance of each method was evaluated based on the mean square error criterion to measure the accuracy of parameter estimation, as well as the reliability function. The results were presented in comparison tables to determine the most efficient and accurate estimation method. In the applied aspect, real data from the Ministry of Industry and Minerals – General Company for Automotive Industry/Battery Factory were used to estimate the reliability function, the cumulative distribution function, and the hazard function, which contributes to verifying the suitability of modified weighted Pareto distribution type one in the reliability analysis of real data in industrial systems.

very good