Some contributions to reliability theory and survival analysis

Abstract

Reliability and survival analysis are widely used in systems engineering and clinical trial experiments. Innovations in reliability methods enhance the safety and reliability of complex technological systems, like engineering systems and offshore pipelines. Survival analysis is generally defined as a set of methods for analyzing data where the outcome variable is the time until an event of interest occurs. It can be a death, illness, failure, or completion of a mission. The time to event or survival time can be measured in days, weeks, years, etc. The notion of ageing plays a significant role in reliability theory. Ageing has a direct impact on the failure rate function behavior. They can be used in maintenance planning, replacement planning, resource allocation, etc. The increasing failure rate (IFR), decreasing failure rate (DFR), and bathtub failure rate (BFR) distributions are widely used in reliability engineering. Birnbaum and Saunders (1969) proposed a failure time distribution for fatigue failure caused by cyclic loading. It was also assumed that the failure was due to the development and growth of a dominant crack. Univariate Birnbaum-Saunders (BS) distribution has been used to analyze positively skewed lifetime data. It has received a lot of attention in the last few years. One of the most widely used approaches to reliability estimation is the well-known stress-strength (SS) model. Several physics and engineering applications use this model, including strength failure and the collapse of systems. The step-stress model is a widely accepted accelerated life testing model. This accelerated testing reduces the time to failure. The data collected from such an accelerated test may then be extrapolated to estimate the underlying distribution of failure times under normal conditions. The step-stress experiment is a special case of accelerated testing that allows for different conditions at various intermediate stages of the experiment.