Applications of the Weibull distribution in the study of reliability

Abstract

Introduction: To solve many problems in the field of maintenance management and Reliability in Physical Assets is solved by analyzing data through statistical processes, one of these applications is the Distribution of Weibull. Objective: The present study aims to quote some of the Weibull distribution applications and its use in the field of reliability. Applying the Weibull distribution versatility, the calculation model of the reliability estimators for repairable and non-repairable equipment is presented, therefore the method of least squares is used, considering the Weibull bi-parametric equation. Methodology: A sample of 119 failures of forty generator sets of the same mark was used, the steps for calculating the distribution parameters with the method of least squares using Excel software are clearly described, the probability density functions, cumulative failure probability, survival, and instantaneous failure rate were plotted, finally several test times were evaluated to demonstrate future estimates of reliability. As a second application of resolving the time of the Reliability equation R(t) it is possible to obtain for a certain failure mode the change frequency time of a replaceable asset after the occurrence of a failure.  The third application is the third parameter of the Weibull distribution determination  with a graphical method, for which a sample of 130 failures was taken, data grouping was initially used through the class ranges defined in a frequency history, then random values ​​​​close to the first fault were selected to test them by contrasting data between the last data of each class range with each of the estimated data, when graphing them, it is determined which of them best approximates a straight line. Result: three applications were obtained where the Weibull distribution is applied, different databases were used for the analysis of each case. Conclusions: The Weibull distribution is very adaptable, it can cover other distributions such as exponential and normal distributions, it can also work whit little or a lot of data, based on its multiple applications have been developed in the field of Reliability.