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.
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.