1. 1
Failure Rate ≠ for Parallel Systems even with units having a
MTBF
constant failure rate
− dR ( t )
Failure Rate = dt ...(1) The expression to calculate Failure Rate using a Reliability Function
R ( t)
∞
MTBF = ∫ R ( t )dt ...(2) The expression to calculate MTBF using a Reliability Function
0
The Failure Rate & MTBF calculation of a two unit parallel system (1 of 2 required for
system success)
Unit Reliability ... R(t) = e-λt Where λ=Failure Rate; t=Mission Time
λ
System Reliability ... RSP(t) = 2e-λt - e-2λt
λ
System Failure Rate ...... λSP = (2λe-λt - 2λe-2λt)/(2e-λt - e-2λt)
= 2λ(1 - e-λt)/(2-e-λt)
Note: λSP is not constant, and depends on t
2 1 3
System MTBF .... MTBFSP = − =
λ 2λ 2λ
When To Use
If a person says that the reliability of a parallel combination of basic units is 0.9998 for
a mission time of 1 hour, and then say that the
Failure Rate = - ln (0.9998) MTBF = -1 / ln (0.9998)
This person is not correct
The equations (1) & (2) have to be used with the appropriate reliability functions to
calculate Failure Rate & MTBF
For Unit Reliability the exponential is used because of its simplicity and it has been shown in many cases to fit electronic
equipment failure data. For any equipment the Weibul Distribution is the best, but the System calculations will be difficult.
Hilaire Ananda Perera ( www.linkedin.com/in/hilaireperera )
Long Term Quality Assurance