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Reliability and Effective Failure Rate of "n" Active Redundant Units, with "m" Required for Success, and "n-m" Cold Standby Units

This tool calculates the reliability function and effective failure rate for "m of n" units, where n-m units are "cold standby" spares. It assumes:

The tool also calculates system mean time to failure (MTTF) for the case where the system is operated without renewal. It is similar to this tool, but is more comprehensive in that it handles an arbitrary number of cold standby spares, computes the reliability, and uses numerical integration to compute the effective mean time between failure (MTBF), sometimes referred to as the mean time between critical failure (MTBCF). For additional details, click here.

Reliability Block Diagram:

Reliability Block Diagram showing n total units with m units required for success and n-m cold standby spare units

Calculation Inputs:

1. Number of units required for mission success (m):
2. Total number of units (n):
3. Probability that switch will work correctly (P, range 0 to 1.0):
4. Maintenance interval for system renewal (T), hours:
6. Decimal places:
7. Format for R(t) output:
8. Options:


Without renewal
With renewal ( renewal interval)
Compare to single unit
Compare to all active (spares are hot), without renewal
Zoom plot


Additional outputs:
Series MTBF

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  1. United States Air Force Rome Laboratory Reliability Engineer's Toolkit (1993).
  2. Reliability Toolkit: Commercial Practices Edition, United States Air Force Rome Laboratory and the DoD Reliability Analysis Center, (1995). Available from:
  3. MIL-HDBK-338, Electronic Reliability Design Handbook.
  4. Klion, Jerome, A Redundancy Notebook, Rome Air Development Center, RADC-TR-77-287, December 1987.
  5. Reliability Modeling and Prediction, MIL-STD-756B, November 1981.
  6. McGregor, Malcolm A., Approximation Formulas for Reliability with Repair, IEEE Transactions on Reliability, Volume R-12, Number 4, December 1963.
  7. Bazovsky, Igor, Reliability Theory and Practice.
  8. O'Connor, Patrick, D. T., Practical Reliability Engineering.