Practical Mathematics K12In the design of multi-stage rockets, electrically-triggered explosive bolts can be used to separate the stages. If the bolt fails to break, the previous stage is still held in place -- and that is typically catastrophic. If the bolt breaks too early then that again can be catastrophic. Having made the part as reliable as possible, further improvement can be made by using series and parallel combinations.

For a series connection of N explosive bolts, if separation failure occurs randomly with probability S for a single bolt, the series assembly fails to separate with probability SN. However, premature separation is N times more likely.

For a parallel connection of N explosive bolts (or explosive bolt series-assemblies) separation failure is N times more likely. Premature separation is less likely by the premature separation probability, P, being raised to the power N.

On a single mission, compare the probability of mission failure with a series chain of two bolts to the probability of mission failure with a single bolt.

(We take the probability of premature separation as 0.0001, and the probability of separation failure as 0.001 for a single bolt.)

by Leslie Green