Reliability aspects of relevation transforms with special emphasis to extreme models

Abstract

This thesis investigates the reliability properties and theoretical developmentsof the relevation and reversed relevation transforms, with emphasis on theirapplications in reliability theory and extreme value analysis.The studyexamines these transforms under modified proportional hazards and proportionalreversed hazards frameworks, analyzing their aging characteristics, stochasticordering properties, and characterization results.It introduces multi-phaseauto-relevation and reversed auto-relevation transforms, establishing their con-nections with stochastic processes such as the non-homogeneous Poisson process.Several new distributional models, including generalizations of the exponential,log-logistic, Fréchet, and half-logistic distributions, are developed and analyzedin terms of reliability behavior, tail properties, and applicability to both completeand censored data. The work further incorporates quantile-based formulationsand information measures to provide deeper structural insights, with applicationsin risk assessment and stress–strength reliability analysis using real data. Inthe context of extreme value theory, the truncated generalized extreme valuedistribution and its reversed auto-relevation version are studied. Parameterestimation of the generalized extreme value distribution is addressed throughregression-based methods, supported by a review of existing techniques and theconstruction of bootstrap confidence intervals, with performance evaluated viasimulation studies. Overall, the thesis provides a comprehensive framework forrelevation transform based reliability modeling, combining theoretical advance-ments with practical applicability.