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Basic reliability cookbook

Parallel Reliability

Parallel reliability is used when only one of several elements needs to be functional for the combination to be useful.  Given a set of elements, the unreliability of the combination is the product of the individual unreliability of the elements.  The reliability of the combination is the unreliability of the combination subtracted from one.

Elements E1, E2, … EN have individual reliability P1, P2 … PN.  The unreliability of each element is (1-P1), (1-P2), … (1-PN).  The combined unreliability of the elements is (1-P1) * (1-P2) * … (1-PN).  The combined reliability of the elements is 1-((1-P1) * (1-P2) * … (1-PN)). 

For example, E1 has reliability 0.9, E2 has reliability 0.85 and E3 has reliability 0.95.  The parallel reliability of a system composed of E1, E2 and E3 is 1-((1-0.90) * (1-0.85) * (1-0.95)) = 0.99925.

In the special case where all of the elements are identical, the parallel reliability of N elements with reliability P is 1-(1-P)N.  For example, five identical elements with reliability 0.8 have a combined parallel reliability of 0.99968.

The reliability of a system composed of parallel elements is always greater than or equal to the reliability of the most reliable element.

Failure Rate | Serial Reliability | Parallel Reliability | K of N Reliability | Standby Reliability | Duty Cycle Reliability

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