TABLE OF CONTENTS Bayes' theorem may be stated as follows: The reliability of a system is equal to the reliability of the system, given that a chosen unit, say Unit A, is good, R s ? A G, times the reliability of Unit A, plus the reliability of the system, given that Unit A is bad, R s ? A B, times the unreliability of Unit A. Mathematically,
R s = ( R s ? A G) R A + ( R s ? A B) Q A.
Bayes' theorem can also be used to determine a system's unreliability, as follows:
Q s = ( Q s ? A G) R A + ( Q s ? A B) Q A,
where
A G = event that Unit A is good,
and
A B = event that Unit A is bad.
Bayes' theorem can be applied to all combinations of units in a system; however, if the combination, as given by the reliability block diagram of the system, is that of series, parallel, and standby units, then the procedures discussed in previous chapters may be used more expediently. Nevertheless, if there is any doubt about the reliability-wise combination of the units, then Bayes' theorem may be used to determine the system's reliability or unreliability very conveniently.
If the terms R s ? A G, R s ?
