A BATHTUB ADDITIVE FAILURE RATE MODEL FOR ACTUARIAL RELIABILITY

The actuarial approach to hardware reliability plays an important role in providing balanced avenue and fair play in dealing with multi-unit systems and dual failures occurring in such complex settings. In statistical reliability perspective, the additive failure rate methodology is believed to adequately adapt to the actuarial approach for effective system reliability. In line with this hypothetical subject, this paper introduces a lifetime model named Hybrid Weibull-Exponential Power model, based on the later phenomenon vis-à-vis the former approach. The failure rate (FR) of the proposed model displayed suitable compound trends such as increasing-decreasing and various complex forms of bathtub-curve, with and without the lingering useful life period. The consistency of its quantile function in producing effective samples was validated by simulation study, despite its non-closed form. Other reliability properties of the model were also provided. The paper employs the maximum likelihood estimation procedure for estimating the unknown parameters of model, due to its reputable robustness in the aspect of applied statistics. The adequacy of the proposed estimator was evaluated by means of simulation study, where, negligible biases and declining MSEs were observed. The real-life performance of the proposed model in relation to three similar-structured models was weighed using bathtub failure times, where, least values of information criteria and pvalues of goodness-of-fit statistics were obtained for the model. Highest loglikelihood value of the model was also observed. The additive failure rate model proposed in this paper allows for actuarial reliability analysis of compound systems, due to its outstanding performance on the dataset. The MLEs used for estimating the model parameters were proven consistent since insignificant biases and declining MSEs were obtained in all cases. Also, on the premise of the results obtained for the information criteria, the p-values for the goodness-of-fit statistics and the loglikelihood value, we infer that the new established model can better be employed over the compared models, for the dataset. Subsequently, effective system reliability with similar datasets can be achieved using the model. Succinct guide on the recent developments of the emerging family of additive FR models and their application in multi-unit system modelling, is also given.