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Engineering Reliability Statistical Models

Engineering Statistics and Probability Knowledge

There are many standard statistical distributions which may be used to model the various engineering and reliability parameters. It has been found that a relatively small number of statistical distributions satisfies most needs in engineering and reliability work. The particular distribution used depends upon the nature of the data, in each case.

The following are some of the distributions most commonly used in engineering and reliability analysis, criteria for their use, and examples of application. The tables below, Table A and B are summaries of the shape of common failure density, reliability, and hazard rate functions for the distributions described. 

Table A
Type of Distribution Probability Density Function, f(t)

Reliability Function
R(t) = 1 - f(t)

Hazard Function
 

Exponential
Gamma
Lognormal
Normal
Weibull

Table B

Type of Distribution

Parameters Probability of Density Function f(x) Reliability Function
R(x) = 1-F(t)
Binomial

Sample data used to plot charts shown

Poisson
Sample data used to plot charts shown

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