Abstract
Statistical theory and its applications have played a significant role in the advancement of methodology and techniques for solving various problems in reliability engineering. Different criteria of aging have been introduced for modelling and characterizations of wear properties. Some real life engineering reliability operations arising in maintenance and replacement policies formulations are investigated as convolution, mixture and formation of coherent systems. Shock models are studied for shocks arriving according to Poisson process and causing damages with specific form of aging. Cumulative damage models have been also studied by many researchers. Statistical hypotheses testing are used to test whether a certain, censored or uncensored data has exponential or a specific aging propety.
In this paper we present a unified state of the art type of survey for the research and developments in these problems. In particular we expose the main recent contributions, trace the trend of research and highlight the possible direction of further research.