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# Accession Number:

## ADA193526

# Title:

## Analysis of the Effect of Faulty Spares on the Performance of Diagnostic Algorithms in Reliable Systems.

# Descriptive Note:

## Master's thesis,

# Corporate Author:

## NAVAL POSTGRADUATE SCHOOL MONTEREY CA

# Report Date:

## 1987-12-01

# Pagination or Media Count:

##
141.0

# Abstract:

## Previous research of systems diagnosis algorithms have assumed that replacement processors are fault-free. In practical applications, however, faults can occur in spare processors. It is shown that faulty spare processors have a surprisingly large deleterious effect on the speed of diagnosis in the universal diagnosis Algorithm analyzed by Smith. This Algorithm is described as follows Replace a processor if it fails at least one test. The speed of diagnosis is nearly independent of the distribution of fault processors. That is, as long as the total number of fault processors is constant, the probability of repair is relatively unaffected by whether more faulty processors are in the spares or in the system. This thesis derives an asymptotic approximation to the probability of repair when faulty spares are present. An exact value can be obtained from previously known results. However, the calculations are extremely time consuming with a time complexity of order 04n, where n is the number of processors. Our asymptotic approximations yield good estimates that can be calculated quickly. The analysis was performed by formulating the probability of repair calculations as a multiplication of matrices and by deriving approximations to the largest eigenvalues of these matrices. Also, faster calculations were achieved by an aggregation operation on the states of the system.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#