Order and distance relationships between renewal functions.
01 January 1989
Elementary methods are used to obtain upper and lower bounds for the difference between two renewal functions corresponding to two different life distributions, and to obtain various order relationships between them that follow from order relationships on the underlying life distributions. These bounds are useful mainly in the region where time is small in comparison with the means of the two distributions, and therefore supplement the information that can be obtained for large time using the elementary renewal theorem. These results find major application in reliability modeling of highly reliable systems.