Contributions to the study on ageing of life distributions based on failure rate and applications

Abstract

The thesis mainly focuses on the development of new lifetime distributions which are parsimonious and explores their ageing properties based on failure rate. The principle of parsimonious modeling of lifetimes has regained its importance recently, and the value of stochastic modeling in dealing with the inevitable un-certainty and risk is nowadays highly appreciated. In this thesis, we propose a transformation called Kavya-Manoharan (KM) transformation for obtaining a new class of parsimonious distributions and study its properties. Next, we construct three new lifetime models using exponential, Weibull and Lomax as the baseline distributions in the transformation, respectively known as KM- Exponential, KM-Weibull and KM-Lomax distributions, and investigate their ageing behaviour and other properties. The models introduced here have mono- tone failure rate functions. Comparing the proposed models with other models in the literature using a real-life data set, the newly introduced models show better fit to the data sets. We generalize the transformation and develop a new lifetime model using the exponential distribution as the baseline distribution, and the new model is called Generalized KM Exponential (GKME) distribution. The new model shows both monotone and non-monotone failure rate. With the help of real-life data sets, we show that the proposed model is more suitable compared to other distributions mentioned in this study. Estimation of stress- strength reliability for the newly proposed model is an other major work of the thesis, followed by a discussion on the asymptotic distribution of stress-strength reliability, simulation study and application. The thesis concludes by emphasizing the importance of ageing concepts in reliability theory and outlining future research directions.