On reliability estimation approaches for a Weibull failure modelling

During the last years, reliability analysis has attracted significant attention due to its vital role in risk and integrity management of hazardous installations. Indeed, estimating accurate probabilities of failure represents a crucial task for developing a cost-effective maintenance plan able to guarantee the safety of the operations. As a result, a sound tool capable of providing precise failure parameters is required. Traditional estimation approaches exploited for practical applications are the Maximum Likelihood Estimation (MLE) and the Least Square Estimation (LSE), while, quite recently, the advances in dedicated opensource software have led to a widespread use of Hierarchical Bayesian Modelling (HBM) for statistical purposes. The aim of this paper is to present and compare the application of the three aforementioned estimation methodologies in order to point out the most accurate one. A case study of five samples is considered to demonstrate and discuss the applicability of the frameworks, while a Weibull distribution is adopted to model the failure behavior of the studied devices. From this research, it emerged that the Bayesian inference is slightly more accurate than the other approaches. The outcomes of this study can help maintenance engineers and asset managers to adopt the most appropriate statistical tool for their analysis.