ROOTCASTLE / ENGINEERING LAB
Reliability lab
MTBF, Weibull life and redundancy maths.
LOCAL CALCULATION · EDUCATIONAL MODEL
MTBF and availability
- Mission reliability R(t)
- 64.53 %
- Expected failures in mission
- 0.438
- Availability A
- 99.96 %
- Number of nines
- 3.4
- Expected downtime per year
- 3.5 h
- λ · FIT
- 5.00e-5 /h · 50,000
Model and assumptions
Constant failure rate (exponential distribution): R(t) = e^(−t/MTBF), λ = 1/MTBF. Inherent availability A = MTBF/(MTBF+MTTR); logistics and waiting time are not included. The probability of surviving to the MTBF is always 36.8 %: MTBF is not a guaranteed life.
R(t) = e^(−t/MTBF); A = MTBF / (MTBF + MTTR); downtime = (1 − A) · 8760 h
What it is for
To look at the same numbers when discussing how long equipment will be down per year, what a redundant unit really buys, or where a part’s replacement interval should start. The MTBF, Weibull and redundancy maths is shown with its equations; change the assumptions and see how sensitive the result is.
Limitations
Manufacturer MTBF figures are usually predictions for a given temperature and load; different field conditions give different results. The redundancy maths assumes units fail independently; common causes such as a shared power supply, the same software bug or the same maintenance error reduce the real benefit. Safety functions need a separate assessment under IEC 61508 / ISO 13849.
References
IEC 61703:2016 (mathematical expressions for reliability, availability, maintainability) · IEC 61649:2008 (Weibull analysis) · P. D. T. O’Connor, A. Kleyner, Practical Reliability Engineering, 5th ed. · NIST/SEMATECH e-Handbook, Assessing Product Reliability
Educational model. Results are not sufficient to diagnose a machine or establish safe operating limits.