General formula for parallel MTBF of n components with disparate failure rates, where λᵢ = 1/MTBFᵢ is the failure rate of component i.

MTBF parallel = ∑ i=1 n 1 λi − ∑ i<j 1 λi + λj + ∑ i<j<k 1 λi + λj + λk − ⋯ + (−1) n+1 1 λ1 + λ2 + ⋯ + λn

For the special case of n identical components (all with the same MTBF), the formula simplifies to the harmonic series, where Hₙ = 1 + 1/2 + 1/3 + ... + 1/n is the nth harmonic number.

MTBF parallel = MTBF × ( 1 + 1 2 + 1 3 + ⋯ + 1 n ) = MTBF × H n