A reliability and survival model for one and two failure modes system with applications to complete and censored datasets

Lifetime distributions that have bathtub-shaped failure rates with low and long constant region at the mid-time period are more realistic for modelling failure time datasets with similar failure rates. In this paper, we introduce a new model named flexible additive Chen–Gompertz distribution. The model has increasing and bathtub-shaped failure rate with or without low and long constant region, and can be adequately used in reliability context. Some distributional properties of the model are obtained. We present a complete Bayesian analysis of the proposed model for censored and non-censored datasets and provide the Bayes estimators of the model parameters using the Metropolis–Hastings algorithm by utilizing the square error loss function. We have also given the maximum likelihood estimators of the model parameters for complete and right-censored datasets and performed simulations on the two methods for different settings of the parameters and sample sizes. The applicability of the proposed distribution is demonstrated by fitting three different failure time datasets each with bathtub failure rate from reliability and survival analysis. The results of the applications illustrate that the model provides a good fit to all the three datasets compared to the other well-known Chen and Weibull extended distributions as evidenced by some goodness-of-fit tests.