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Effective Failure Rate of One Standby Offline Unit with "n" Active On-line Units Required for Success. (with Repair)

This tool calculates the effective failure rate of a configuration that has a single off-line standby unit ("cold spare") with "n" active on-line units required for success. The off-line spare unit is assumed to have a failure rate of zero while it is in a non-operating state. All on-line units are assumed to have equal failure and repair rates. Upon failure of one of the on-line units, the standby off-line unit is switched in with a probability of "P," the probability that that the switching mechanism works properly. For perfect switching, P=1. The calculation implements Equation 3 shown on page 90 of the United States Air Force Rome Laboratory Reliability Engineer's Toolkit (1993). See this page for additional details on time inputs (Mct) for system restoration.

Reliability Block Diagram:

Reliability Block Diagram showing one cold standby spare unit with n active on-line units, all of which are required for success.

Calculation Inputs:

Number of active on-line units (n):
Mean corrective maintenance time (Mct), hours:
Probability that switch will work correctly (P, range 0 to 1.0):
Decimal places:

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  1. United States Air Force Rome Laboratory Reliability Engineer's Toolkit (1993).
  2. MIL-HDBK-338, Electronic Reliability Design Handbook.
  3. Klion, Jerome, A Redundancy Notebook, Rome Air Development Center, RADC-TR-77-287, December 1987.
  4. Reliability Modeling and Prediction, MIL-STD-756B, November 1981.
  5. McGregor, Malcolm A., Approximation Formulas for Reliability with Repair, IEEE Transactions on Reliability, Volume R-12, Number 4, December 1963.