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) = 1F(t) 
Binomial  
Poisson  