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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 0The Failure Rate & MTBF calculation of a two unit parallel system (1 of 2 required forsystem 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 & MTBFFor Unit Reliability the exponential is used because of its simplicity and it has been shown in many cases to fit electronicequipment 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
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