Browse Prior Art Database

Renewal Function Estimation

IP.com Disclosure Number: IPCOM000053074D
Original Publication Date: 1981-Aug-01
Included in the Prior Art Database: 2005-Feb-12
Document File: 2 page(s) / 13K

Publishing Venue

IBM

Related People

Haugh, LD: AUTHOR [+2]

Abstract

This article sets forth a more efficient algorithm to estimate the renewal function under multi-censoring of systems.

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Renewal Function Estimation

This article sets forth a more efficient algorithm to estimate the renewal function under multi-censoring of systems.

In a group of N systems where each system consists of similar components, the failure of a component causes the systems to cease operation. However, the system can be immediately restored to operation by replacement of the failed component with another component from the same population. The systems may have different entry times into operation, resulting in different current operating times. Thus there is progressive or multiple censoring of groups of component lifetimes.

The renewal function M(t) is defined as the expected number of component renewals or replacements by time t at a single component position. By pooling the system failure data, the renewal function necessary for the evaluation of field reliability can be estimated.

An unbiased estimator of M(t), for a single system of c components, is just: See original. where n(t) is the number of renewals on all component positions by time t. Similarly, if Q systems have not experienced any censoring (losses) by time t, an unbiased estimator is M(t) = n(t)/cQ, where n(t) is now the total number of renewals on all systems by time t.

For multiple systems after one or more systems have been lost, however, a choice of methods for estimating M(t) arises. For example, suppose there are two systems each containing c components and t > T(1), T(1) being the loss time for system 1. A "reduced sample approach' would specify using the second system alone, after T(1); that is, See original. where n(2)(t) is the number of renewals by time t on system 2. This estimate is unbiased.

An alternative is ca...