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On the Uncertainty Properties of the Conditional Distribution of the Past Life Time
Mohamed Kayid1, Mansour Shrahili1
1Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
Abstract:
For a given system observed at time t, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are n components that have all failed at time t. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system's life-time, which may be useful in a number of practical applications.
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