Modeling lifetime of parallel components system with covariate, right and interval censored data

Abstract

This research aims to model the lifetime of parallel components system with covariates, right, and interval censored data. The lifetimes of the components are assumed to follow the exponential distribution, with constant failure rates. A simulation study is conducted to assess the performance of the maximum likelihood estimates, without and with midpoint imputation method at various sample sizes, censoring proportions, and number of components in the system. The combination which produces the best parameter estimates is then identified by comparing the bias, standard error and root mean square error of these estimates. The simulation results indicate that the midpoint imputation method produces more efficient and accurate parameter estimates with smaller bias, standard error and root mean square error. Also, in general, better estimates are obtained at low censoring levels, large sample sizes, and a high number of parallel components in the system. The proposed model is then fitted to a modified real data of diabetic retinopathy patients. Following that, the non-parametric log-rank test and Wald hypothesis test are carried out to check the significance of the covariate, age in the model. The results show that the model fits the data rather well and the age of patients has no significant effect on the survival time of the patients’ eyes.