SIMULATION OF RELIABILITY, RELIABILITY INDEX, PROBABILITY DENSITY FUNCTION AND FAILURE FUNCTIONS FROM WEIBULL DISTRIBUTION FOR ENGINEERING APPLICATIONS

Abstract

In modelling and simulating future rainfall for a selected location, the probability distributions have been established to be an effective tool. In this study, the different methods utilised in the estimation of the probability distributions’ parameters were evaluated and presented using Weibull's two parameters. Different estimator methods (mean rank, median rank, symmetric, graphical, least square, empirical, maximum likelihood, general probability, modified maximum likelihood, Mabchour, alternative maximum likelihood, equivalent energy, moment expression, Lysen and Moment methods) were used to determine probability density function, reliability, reliability index and failure functions of rainfall data from Maiduguri. The performances of these different methods were compared probability density function, reliability, reliability index and failure functions of Weibull two parameters. The study revealed that the values of probability distribution dimensionless shape variables were between 1.0193 and 4.205, and probability distribution scale factor constants were between 0.302 and 7.254. These values are all positive (non-negative values or less than zero) values. It was established that there were significant differences (F108, 1728 was 162.1976 and the probability (p) was zero) between the individual reliabilities and Weibull estimators (F15, 1620 was 14928.98 and probability was zero) at a 95 % confidence level (p less than 0.05).  It was concluded that caution must be taken in the utilization of general probability, equivalent energy, Alternative Maximum Likelihood Method and moment expression methods in any engineering applications to prevent failure of devices or infrastructure.