

MILHDBK338B: Electronic Reliability Design Handbook 
 

5.5.1 Bayes’ Theorem
5.5.1 Bayes’ Theorem
From basic probability theory, Bayes’ Theorem is given by
In the specific framework and context of reliability, the
various terms in the equation may be motivated and defined as follows:
A 

An hypothesis or statement of belief.
(“The reliability of this component is 0.90.”) 
B 

A piece of evidence, such as a
reliability test result that has bearing upon the truth or credibility
of the hypothesis. (“The component failed
on a single mission trial.”) 
Pr [A] 

The prior probability: the probability we
assign to the hypothesis A before evidence B becomes available. (“We
believe, based on engineering experience, that there is a 5050 chance
that the reliability of this component is about 0.90, as opposed to
something drastically lower, e.g., Pr [A] = 0.5.”) 
Pr [BA] 

The likelihood: the probability of the
evidence assuming the truth of the hypothesis. (“The probability of
the observed failure, given that the true component reliability is
indeed 0.90, is obviously 0.10.”) 
Pr [B] 

The probability of the evidence B,
evaluated over the entire weighted ensemble of hypotheses
A_{i} 
Pr [AB] 

The posterior probability of A, given the
evidence B 
The posterior probability is the end result of the
application of Bayes' Equation. The following examples illustrate the use of
Bayesian statistics in reliability
analysis.




 
 