Joint Shared Frailty Survival Modeling Approach to Reliability Analysis of Rolls Used in Rolling Mills

Abstract

Reliability of repairable rolls used in Rolling Mills was modeled taking to survival modeling route to address the presence of recurrent failure events, censoring event and terminal event processes observed longitudinally in rolls. All the event processes were influenced by measured and unmeasured covariates. Prior to fitting appropriate model, Archimedean Gumbel and Clayton Copula analyses confirmed that the measured covariates had no significant dependence structure. Since the censoring events were “informative terminations”, joint shared frailty multivariate survival models involving Log-Normal, Gamma and Log Gamma frailty distributions were fitted to recurrent and terminal events data where, the ‘frailty' parameter represented the effect of unmeasured covariates related to condition of rolling operation. Gaussian quadrature method helped in estimating the model parameters. Statistical significance of the frailty parameter and its variance in all the models confirmed existence of heterogeneity across the recurrent failure events within and between rolls on account of unmeasured covariates. The statistically significant positive association between hazard functions of both the recurrent failure events and the terminal events justified joint modeling approach to the recurrent events and the terminal events processes observed in rolls. The joint lognormal shared frailty multivariate survival models were considered appropriate for analyzing the reliability of rolls.