Optimism Replacement of a System Subject to Shocks

Article Abstract:

A system is subject to shocks that arrive according to a Poisson process. Each shock weakens the system and makes it more expensive to run. It is desirable to determine a replacement policy for the system. The possibility of periodic replacement of the system is considered. A necessary and sufficient condition for the existence of an optimal finite period is discussed. The problem is investigated for both finite and infinite time horizons. A particular model for a system that fails on a second shock is studied.

Mathematical models, Poisson distribution, Models, Simulation, Optimization, Systems, Replacement Policy

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Percentile Residual Life Functions

Article Abstract:

Biometry, acturial science, and reliability researchers study the mean residual life function. The median and other percentiles are also used, especially where the underlying distribution is skewed. Life distributions are often categorized according to different aging properties. Two distributions are analyzed, the decreasing mean residual life (DMRL) and the new better than used in expectation (NBUE) distribution.

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When Does the Bth Percentile Residual Life Function Determine the Distribution

Article Abstract:

Knowledge of the Bth percentile residual life function does not uniquely determine the underlying distribution. Additional information about the tail behavior of the distribution is needed. Knowledge of both the B1 and B2 percentile residual life functions does not uniquely determine the distribution provided that B1 and B2 are noncommensurate. This corrects and extends the results of Schmittlein and Morrison.

Statistical Analysis, Residual Values

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