Reliability characteristics based on aging and longevity applications

Submitted in partial fulfilments of the requirements for the Doctor of philosophy degree in the department of Statistic at the College of Science, King Saud UniversityIt is known that reliability theory was historically developed to describe failure and aging of complex electronic (military) equipments. Even so the theory itself is very widely applicable in many real life situations. Reliability concepts in their present mathematical formulation and their physical meaning form a recent discipline. The root of these concepts goes back to the interest of research investigating the failure of American rockets and first commercial jet aircraft in the 1950's. Many researchers have considered the paper of Epstein and Sobel (1953) studying the exponential distribution to be the main basic contribution in the theory of reliability. The actual beginning of reliability theory as a separate topic has started with the publication of the paper by Birnbaum, Esary and Saunders (1961). In fact, the development of Boeing 707 airplanes and the crash of the British de Havilland comets have motivated the Boeing Scientific Research Laboratories (BSRL) in Seattle began to emphasize reliability theory in their mathematics division. Also, Professor Z. W. Birnbaum from the University of Washington was a consultant at the BSRL. Birnbaum is known for his strong mathematical background and his ability to formulate mathematical model for system problems. Birnbaum, with other known researchers as well, has introduced significant contributions to reliability theory