On residual lifetimes in random parallel systems

Date of Publication

1995

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This study is an exposition of the article Residual Lifetimes in Random Parallel Systems by Frederick Solomon. A mathematical explanation on why the last component in a parallel system lives longer than the other components is presented. Two models involving the exponential distribution were particularly studied.The expected fraction of the total system lifetime that the last component lasts after all the others have failed and the ratio of the expected lifetime of the residual component to the expected system lifetime of the parallel system are obtained in the two models. These give the expected amount of time contributed by the last component to the total system lifetime. Without the last component, a parallel system would have lived for a much shorter time. Moreover, the expected time between the (j-l) st component failure and the jth component failure is shown to be less than the expected time between the jth and (j+1)st component failures.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU07041

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

80 leaves

Keywords

Random variables; Variables (Mathematics); Probabilities

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