Reliability models of repairable systems considering the effect of operating conditions

Abstract

The proportional hazard modeling is a useful technique to investigate the effects of diagnostic variables associated with a system on its life period. Most of the reliability models consider failure time as the only factor that influence reliability characteristics of a system during its operation. It is possible to include the effect of operating conditions like type of failure, stress etc. in the reliability function. These conditions when quantified are called covariates and the model is known as proportional hazard model (PHM). The proportionality of hazard rates at different covariates is the underlying assumption. Two types of failure data are studied; renewal process data and non-renewal process data. Different methods of estimation of cumulative hazard rate (CHR) function are discussed under nonparametric and parametric models. Goodness of fit tests are used to verify the assumption of PH model. Parametric models like Weibull distribution or power law process are fitted to check the results obtained using nonparametric models. The parameters of life distributions are obtained by regressing the reliability function using multiple regression analysis or by maximum likelihood estimators (MLEs). The study involves failure data of an electro-mechanical equipment in all underground coal mine and failure times of a small DC motor in accelerated life testing using PHM techniques to assess their failure behavior at different operating conditions. The study also involves evaluation of optimum preventive maintenance interval in a thermal power unit based on graphical methods using PH models.