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Reliability Prediction Tool

Predict system reliability from component MTBF values using a series model with optional parallel redundancy.

Tool Purpose and README

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Inputs

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Component table

Component ? MTBF (hours) ? Series count ? Parallel count ?
Use series count for repeated components. Advanced options add parallel redundancy.

Advanced options include parallel redundancy and a separate reliability allocation scenario.

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Key results

Provide inputs and click calculate to see results.

System Reliability Derivation
Equation (1): Component reliability
$$ R = e^{-\lambda t} $$
R: reliability \lambda: failure rate t: mission time
Equation (2): Parallel redundancy
$$ R_{parallel} = 1 - (1 - R)^n $$
n: parallel count
Equation (3): Series system reliability
$$ R_{sys} = \prod R_i $$
R_i: block reliability
Substituted values
Equivalent Failure Rate Derivation
Equation (4): Effective failure rate
$$ \lambda_{eq} = -\frac{\ln R_{sys}}{t} $$
\lambda_{eq}: equivalent failure rate R_{sys}: system reliability t: mission time
Substituted values
Equivalent MTBF Derivation
Equation (5): Equivalent MTBF
$$ MTBF_{eq} = \frac{1}{\lambda_{eq}} $$
MTBF_{eq}: equivalent MTBF \lambda_{eq}: equivalent failure rate
Substituted values

Reliability allocation

Provide allocation inputs to compute required component targets.

Allocation Reliability Derivation
Equation (6): Equal allocation
$$ R_{comp} = R_{sys}^{1/N} $$
R_{comp}: component reliability R_{sys}: system reliability N: component count
Substituted values
Allocation Failure Rate Derivation
Equation (7): Required failure rate
$$ \lambda_{req} = -\frac{\ln R_{comp}}{t} $$
\lambda_{req}: required failure rate R_{comp}: component reliability t: mission time
Substituted values
Allocation MTBF Derivation
Equation (8): Required MTBF
$$ MTBF_{req} = \frac{1}{\lambda_{req}} $$
MTBF_{req}: required MTBF \lambda_{req}: required failure rate
Substituted values

Component summary

Component MTBF (hours) Series Parallel Failure rate (1/hr) Block reliability

System reliability curve

Background and Theory

Contents

Overview

This tool assumes independent component failures and uses an exponential reliability model with constant failure rates. Series blocks multiply reliability, while parallel redundancy assumes independent units with no repair during the mission time.

Assumptions

  • Component failures follow an exponential distribution with constant hazard rate.
  • Redundancy is cold or hot standby without repair during the mission.
  • Components are statistically independent.

References

  • O'Connor, P.D.T. and Kleyner, A. Practical Reliability Engineering, 5th ed.
  • Ebeling, C.E. An Introduction to Reliability and Maintainability Engineering.
  • IEC 60300-3-1: Dependability management - Application guide.