Transformation of the bathtub failure rate data in reliability for using Weibull-model analysis

All statistical methods involve basic model assumptions, which if violated render results of the analysis dubious. A solution to such a contingency is to seek an appropriate model or to modify the customary model by introducing additional parameters. Both of these approaches are in general cumbersome and demand uncommon expertise. An alternative is to transform the data to achieve compatibility with a well understood and convenient customary model with readily available software. The well-known example is the Box–Cox data transformation developed in order to make the normal theory linear model usable even when the assumptions of normality and homoscedasticity are not met.In reliability analysis the model appropriateness is determined by the nature of the hazard function. The well-known Weibull distribution is the most commonly employed model for this purpose. However, this model, which allows only a small spectrum of monotone hazard rates, is especially inappropriate if the data indicate bathtub-shaped hazard rates.In this paper, a new model based on the use of data transformation is presented for modeling bathtub-shaped hazard rates. Parameter estimation methods are studied for this new (transformation) approach. Examples and results of comparisons between the new model and other bathtub-shaped models are shown to illustrate the applicability of this new model.