Life Distributions, Models and Their Characteristics

  • Shelemyahu Zacks
Part of the Springer Texts in Statistics book series (STS)


A typical experiment in life testing of equipment consists of installing a sample of n similar units on appropriate devices and subjecting the units to operation under specified conditions until failure of the equipment is observed. We distinguish between two types of data. The first type is obtained under continuous monitoring of a unit until failure is observed. In this case we have exact information on the length of life, or time till failure, T, of that unit. The observed random variable, T, is a continuous variable, i.e., it can assume any value in a certain time interval. The second type of data arises when the units are observed only at discrete time points t 1, t 2, ···. The number of failures among the n tested units is recorded for each inter-inspection time interval. Let N 1, N 2, ···, denote the number of units failing in the time intervals [0, t1), [t 1, t 2), ···. These are discrete random variables representing failure counts.


Probability Density Function Cumulative Distribution Function Exponential Distribution Weibull Distribution Normal Approximation 
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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Shelemyahu Zacks
    • 1
  1. 1.Department of Mathematical SciencesState University of New York at BinghamtonBinghamtonUSA

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