Estimating reliability function for modified extension Weibull distribution using type three (progressively) censored samples and Monte Carlo simulation

This article defines modified extension Weibull distribution, reliability, and hazard functions. There are many types of censored data: left-censored, interval-censored, and right-censored. The right censored data is divided into three types, which are as follows: a-type one censoring data,b-type two censoring data, and C-type three (progressively) censoring data. We explain the maximum likelihood method under the Type Three(Progressively) censoring sample. The censored samples play an important role in lifetimes. In this article, estimating and deriving the three parameters of modified extension Weibull distribution under the Type Three(Progressively) censored samples by maximum likelihood estimation method depends on the Newton-Raphson method. After that, the simulation procedure was applied using the Monte-Carlo technique to find the reliability function under different sample sizes and various initial values for the parameters for all estimated parameters of the modified extension Weibull model by applying the initial values in the MATLAB program. Then, compare the estimated Reliability function with the empirical Reliability function using the mean squares error procedure. Finally, finding the probability density function f(t), Reliability function R(t), and hazard function h(t) for real data which get it from (Diyala State Company) is one of the formations of the Ministry of Industry and Minerals.