On residual lifetimes in random parallel systems

• Main Authors: Arjona, Mary Rose N., Lumabi, Belinda S.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Random variables; Variables (Mathematics); Probabilities
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16241
• Institution: De La Salle University

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.