Estimating Hazard Function through Reliability Function and Empirical Methods

Abstract

In this research, the reliability functions are applied to estimate the hazard function of four used car components (tires, brakes, lights, engine), which are inspected by aperiodic vehicles inspection (PVI) established in Erbil city, as a specialized company that conducts the annual technical inspection of vehicles to detect the failure component, that either require repair or replace it with a new one. For our purpose, the data about the failure components of a sample of size (50000) cars are obtained from the Erbil traffic directorate, which are annually inspected for 11 years (2010 – 2020) by a (PVI) company. From the available data the reliability function, hazard function, and probability density function of failure time of each component are found by the non-parametric method and the estimated Rayleigh distribution since the failure rates of the components are the linear functions of time, also the comparison between their reliability values have made by the mean absolute error method.