Abstract :
Two different indexes, the hazard rate and the renewal rate, which are implied by conventional uses of the bathtub-shaped curve, are often noted in reliability. The hazard rate is applicable for a single failure time of each item, such as that of a nonrepairable part; the renewal rate is applicable for multiple failure times of each item, such as those of repairable equipment. Occasionally, remarks are made in the literature concerning the mathematical models for the bathtub-shaped hazard rate but not for the renewal rate. Furthermore, bathtub-shaped hazard and renewal curves as conventionally used are each based on certain assumptions concerning failure time distributions. Little data have been recorded for electronic parts and equipment which would substantiate the widespread use of the conventional implications of the bathtub-shaped hazard and renewal rates. The validity of the assumptions concerning the underlying distributions of failure times affects the accuracy of the results of reliability analyses, such as prediction, data analysis, formal assurance tests, operational planning, and maintenance planning. A study of the applications-oriented literature suggests that the distinction between the hazard rate and the renewal rate, as well as some associated implications, are not generally appreciated. Thus the existing situation is apt to lead engineers astray as well as others with application interests. Basic concepts and definitions are emphasized and extensions and implications are sketched. References are selected and noted for those interested in further pursuit.
