Abstract
This study is concerned with the two-parameter Weibull distribution which has and is still being used as a model in life testing and reliability engineering. We seek to find out whether Rank Regression Method can be a good alternative to that of the world publicised traditional method known as Maximum Likelihood for estimating two parameters of the Weibull distribution. The methods under consideration are: Maximum Likelihood Estimation, Least Square Estimation on Y and that of Least Square Estimation on X. These estimators are derived for Random Type-I censored samples. These methods were compared using Mean Square Error and Mean Percentage Error through simulation study with small, medium and large sample sizes in estimating the Weibull parameters under Type-I censored data. The observations that are made based on this study are that Maximum Likelihood Estimator stands out when estimating the scale parameter followed by Least Square Estimator on X but for the shape parameter Least Square Estimator on X performed better than Maximum Likelihood Estimator thereby making it a good alternative method to MLE.
Highlights
As a result of the versatility in fitting time-tofailure of a very extensive variety to complex mechanisms, the Weibull distribution has lately assumed the centre stage especially in the field of lifetesting and reliability analysis
We have considered the estimation of the parameters under Least Square estimators on X (LSX), which is used to minimize the horizontal distance between the data points and the straight line that is fitted to the data and lastly, the Least Square estimators on Y (LSY) which is used to minimize
The main objective of this study is to determine whether Rank Regression Method can be a good alternative to that of the world publicised traditional method known as Maximum Likelihood for estimating two parameters of the Weibull distribution
Summary
As a result of the versatility in fitting time-tofailure of a very extensive variety to complex mechanisms, the Weibull distribution has lately assumed the centre stage especially in the field of lifetesting and reliability analysis. They have not been many studies that look at the potentials of the two Rank Regression methods against that of the Maximum Likelihood method, these methods have very good characteristics or properties that could be used as an alternative to Maximum Likelihood Estimator, the review of these methods in this study.
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