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Two-Parameter Lifetime Distributions for Reliability Studies of Renewal Processes |
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by B. J. Flehinger, P. A. Lewis
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Probability functions are defined for use in reliability studies of equipments which are maintained over a long period of time through replacement of components. These are: lifetime distribution function, lifetime density function, probability of survival, hazard, expected number of replacements, and renewal rate. Theoretical results of renewal theory are adapted to reliability studies of complex systems. The "exponential law" is equivalent to the assumption that survival probability for any given time interval is independent of the age of a component at the beginning of the interval. It seems more realistic, however, to assume that this survival probability is a monotonically decreasing function of initial age, or, equivalently, that the hazard is a monotonically increasing function of the age of the component. Consequently, three two-parameter models of distribution functions, with the properties: (1) initial lifetime density greater than zero, and (2) monotonically increasing hazard, are proposed and discussed. The lifetime behavior associated with these models ranges from complete determinacy to complete randomness. An entropic measure of this randomness is introduced. The expected number of replacements is numerically calculated and plotted as a function of time for several different parameter values in each model. |
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| Related Subjects: Reliability |
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