8.
Assessing Product Reliability
8.1. Introduction 8.1.6. What are the basic lifetime distribution models used for non-repairable populations?
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Weibull Formulas |
Formulas and Plots
The Weibull is a very flexible life distribution model with two parameters.
It has CDF and PDF and other key formulas given by:
with
The cumulative hazard function for the Weibull is the integral of the failure
rate or
A more general three-parameter form of the Weibull includes an additional
waiting time parameter
NOTE: Various texts and articles in the literature use a variety
of different symbols for the same Weibull parameters. For example, the
characteristic life is sometimes called
Special Case: When
Depending on the value of the shape parameter |
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Weibull data "shapes" |
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From a failure rate model viewpoint, the Weibull is a natural
extension of the constant failure rate exponential model since the
Weibull has a polynomial failure rate with exponent { |
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Weibull failure rate "shapes" |
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The Weibull is very flexible and also has theoretical justification in many applications |
Uses of the Weibull Distribution Model
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Weibull probability plot |
We generated 100 Weibull random variables using ![]()
We can comput the PDF and CDF values for failure time Functions for computing Weibull PDF values, CDF values, and for producing probability plots, are found in both Dataplot code and R code. |