Equation 4 of Table 6.2.1-3 is *** not *** for m-of-n standby systems.
Equation 4 relates to non-repairable systems of ‘n’ units where ‘q’ number of units are allowed to fail; that is, ‘n-q’ units are required to remain operational for ‘success’. All ‘n’ units are active.
As such, there are no dormant units per the system of Equation 4.
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The last equation in table 6.2.1-2 addresses Standby redundancy where m of n units must be working. It accommodates mission time, but not dormant failures.
In all cases shown in the Toolkit’s equations, standby units are assumed to have a dormant failure rate of ‘0’.
To include dormancy, you would need to know:
The dormant failure rate
The probability that a standby unit being switched in is ‘good’ (has not failed in dormancy)
The time at which the reliability is desired to be known
As a result, one could include dormancy if the reliability over a given time frame, t, is desired.
The following website purports to provide a ‘solution’ that includes dormancy for a single standby unit, and of other time-dependent situations.
http://reliawiki.com/index.php/Time-Dependent_System_Reliability_%28Analytical%29#Standby_Components
