Contributions to the lifetime distributions

Abstract

The research presented in this thesis, Contributions to the Lifetime Distributions introduces newlineinnovative statistical models and estimation techniques for analyzing lifetime data. newlineThe thesis significantly advances the field by developing new distributions and exploring newlinetheir practical applications. newlineOne primary contribution is the Arvind distribution, a new continuous lifetime model newlinedemonstrating flexibility through diverse density and hazard rate functions. This model newlineeffectively handles data related to climate, COVID-19, and reliability, showcasing its newlinepractical relevance. Additionally, the DBHE distribution is proposed for managing overdispersed, newlinepositively skewed, and decreasing failure rate data, proving useful for complete newlineand censored datasets. Another notable development is the ExDLi distribution, which newlineprovides a versatile approach for analyzing count data with various dispersion and skewness newlinecharacteristics. newlineThe thesis extends stress-strength reliability models to complex systems with multiple newlinestress and strength variables. For the NML distribution under progressive Type-II censoring, newlinethe effectiveness of these models for real-world reliability assessments is highlighted. newlineIt also explores the MRS function, enhancing our understanding of system remaining newlinestrength. Implementing these models in real-time monitoring systems for climate analysis, newlinepandemic tracking, and mechanical systems is proposed to enhance their practical newlineutility. Additionally, methods for estimating the S-S reliability parameter in scenarios newlinewhere the system s strength is bounded by two stresses (lower and upper), particularly newlinefor Rayleigh distributions under PFF censoring, are presented. The superior performance newline145 newlineChapter 7. Conclusions and Future Perspectives 146 newlineof Bayesian estimators with informative priors, especially for smaller values of and#951;, is emphasized. newlineThe thesis suggests applying new stress-strength setups to fields like medical newlineresearch, finance, and environmental studies to address complex real-world data scenarios.