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. 

Type of Distribution	Probability Density Function, f(t)
Exponential
Gamma
Lognormal
Normal
Weibull

 

Table A
Type of Distribution	Reliability Function R(t) = 1 - f(t)
Exponential
Gamma
Lognormal
Normal
Weibull

 

Type of Distribution	Hazard Function
Exponential
Gamma
Lognormal
Normal
Weibull

 

Type of Distribution	Parameters
Binomial
	Sample data used to plot charts shown
Poisson
	Sample data used to plot charts shown

Type of Distribution	Probability of Density Function f(x)
Binomial
Poisson

Type of Distribution	Reliability Function R(x) = 1-F(t)
Binomial
Poisson