# Accession Number:

## AD0680008

# Title:

## ON CUMULATIVE DAMAGE AND RELIABILITY OF COMPONENTS

# Descriptive Note:

# Corporate Author:

## SYSTEM DEVELOPMENT CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1968-10-01

# Pagination or Media Count:

## 35.0

# Abstract:

Let T, Xt, 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 Ht,y , so that t sub n and Y sub n are renewal processes. The inequality Ft or Ht,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.

# Descriptors:

# Subject Categories:

- Electrical and Electronic Equipment
- Manufacturing and Industrial Engineering and Control of Production Systems