Modelling and analysis of lifetime data using various failure rate distributions Name of the Researcher

Abstract

Lifetime data analysis plays a vital role in elds such as reliability engineering, biostatistics, and quality control by focusing on the time to occurrence of speci c events like system failure, death, or recovery. The key objective in modelling such data is to uncover insights into the causes of failure or survival, enabling risk assess- ment and informed decision-making. A central element of this analysis is selecting appropriate failure rate distributions that capture the diverse patterns observed in real-world systems-ranging from monotonic to non-monotonic failure rates. This thesis, titled Modelling and Analysis of Lifetime Data Using Various Failure Rate Distributions , is organized into ten chapters. Chapter 1 introduces essential concepts of lifetime data and failure rate modelling. Chapter 2 develops a new exible distribution using the DUS transformation and the Kumaraswamy distribution, e ectively capturing a wide range of failure rate behaviors. The appli- cability of the model is demonstrated using both simulation and real data studies. Chapter 3 introduces another novel distribution derived via the DUS trans- formation with the inverse Kumaraswamy distribution, o ering strong modelling capabilities for non-monotonic hazard rates. Its utility is veri ed through charac- terizations, reliability analysis, and real data applications. Chapter 4 presents a bi- variate model based on the Farlie-Gumbel-Morgenstern copula with inverse Weibull marginals, designed to capture weakly dependent lifetime data, and demonstrates its applicability through a real-life medical dataset. Chapters 5 to 7 focus on censoring mechanisms in life-testing experiments. Chapter 5 analyzes progressive Type-II censoring, progressive Type-II hybrid cen- soring, and adaptive progressive Type-II censoring schemes using the exponential Power distribution, comparing parameter estimation via maximum likelihood and Bayesian methods. Chapter 6 applies the joint adaptive progressive Type-II censor- ing scheme to the generalized Lindley distribution, emphasizing e cient estimation using Markov Chain Monte Carlo and bootstrap techniques. Chapter 7 proposes a novel T1-T2 mixture censoring scheme based on the Weibull distribution, o er- ing advantages in maximizing the number of failures within a given supplementary time. All the above models are illustrated using real-world data to ensure practical relevance and applicability. Chapter 8 addresses long-term survivors through cure fraction modelling using the exponentiated Weibull distribution under mixture and non-mixture frameworks. Both frequentist and Bayesian approaches are employed, and the models are validated using cancer survival data from Kerala, India. Finally, Chapter 9 summarizes the key contributions of the thesis, highlighting the development of new lifetime distributions, innovative censoring schemes, and their practical applications. These contributions provide valuable tools for real- world lifetime data analysis and lay the foundation for future research in this field.