Tools › Reliability › System Models › System Reliability › Example
MIL-HDBK-338B §6.4.4.2.1.3: reliability of a bridge-type network with repeated elements
| Tool | System Reliability |
| Source | U.S. Department of Defense (1998). Electronic Reliability Design Handbook. MIL-HDBK-338B, 1 October 1998. Section 6.4.4.2.1.3, equation 6.30. |
| Level | Undergraduate |
Problem
Five units with probabilities of success P_A = 0.3, P_B1 = P_B2 = 0.1 and P_C1 = P_C2 = 0.2 are connected so that the system works if A works with either C1 or C2, or B1 works with C1, or B2 works with C2. Find the probability of system success, compare it with the equivalent series model, and rank the units by importance.
Inputs to Enter
- Components (loaded by default): A fixed 0.3; B1 fixed 0.1; B2 fixed 0.1; C1 fixed 0.2; C2 fixed 0.2
- Structure: (A and (C1 or C2)) or (B1 and C1) or (B2 and C2)
- Mission time 100 hours (the fixed probabilities do not depend on it)
Answers
- P_S = 0.13572 (equation 6.30); the equivalent series model P_A P_B² P_C² = 0.00012
- Pivot on A: P_S(A good) = 2P_C − P_C² = 0.36, P_S(A failed) = 0.0396
- Birnbaum importance I_B(A) = 0.36 − 0.0396 = 0.3204; criticality I_C(A) = 0.3204 × 0.7/(1 − 0.13572); I_B(C1) = I_B(C2) by symmetry
- Equal apportionment of a 0.9 target to the five units: 0.9^(1/5) each
Notes
The tool's default inputs are this example; press Submit. C1 and C2 appear twice in the structure and are handled by pivotal decomposition.