ON CUMULATIVE DAMAGE AND RELIABILITY OF COMPONENTS
Abstract
Let T, X(t), and C denote the time to failure, the accumulated damage by time t, and the 'critical' damage. Let F be the distribution function of T. Let 'E' stand for the event of the component undergoing damage and (t sub n) denote the sequence of intervals of time between successive occurrences of 'E'. Let T sub n = summation over n of t sub i and Y sub i denote the amount of damage experienced at time T sub n. Assume (t sub n, Y sub n) is a sequence of independent, identically distributed variables with distribution function H(t,y) , so that (t sub n) and (Y sub n) are renewal processes. The inequality F(t) < or = H(t,infinity) is obtained with equality if and only if C = 0. For 'E', a Poisson process, sufficient conditions are given for F, to be IHR and DMR. The classes of distribution functions are considered with the topology of complete convergence. Empirical estimates for F from observing occurrences of 'E' are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1968
- Accession Number
- AD0680008
Entities
People
- B. P. Lientz
- V. K. Murthy
Organizations
- System Development Corporation