How do you calculate the reliability of two systems in series?

To calculate the reliability of two systems that are configured in series, you multiply the individual reliabilities of each system. This method is grounded in the understanding that for series systems, the failure of any one component leads to the failure of the entire system. Therefore, the overall reliability of the system depends on the reliability of each component working successfully without failure.

For example, if System A has a reliability of 0.9 (90%) and System B has a reliability of 0.8 (80%), the overall reliability of the system in series would be calculated as:

Reliability = Reliability of A × Reliability of B

Reliability = 0.9 × 0.8 = 0.72 (or 72%)

This calculation illustrates how the performance of each system is interdependent; if either system fails, the entire system fails. This is crucial for understanding system reliability and risk management in engineering contexts.

Other methods, such as averaging or adding reliabilities, do not account for the dependency of the systems in series and would not yield accurate results for overall system reliability. Subtracting values also overlooks the correct mathematical relationships that define how series systems operate.