SIMULATION OF RELIABILITY, RELIABILITY INDEX, PROBABILITY DENSITY FUNCTION AND FAILURE FUNCTIONS FROM WEIBULL DISTRIBUTION FOR ENGINEERING APPLICATIONS
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Date
2024-06
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FUDMA Journal of Sciences
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.