Electrical Circuit Reliability

A model can be used for many things, and one of them is the possibility to calculate the reliability for the system modeled. With information about the lifetime of each component, the lifetime of the complete system can be studied. In this example, we look at how heat affects the mean time to failure (MTTF) for an amplifier.

To run this example, you'll need

SystemModeler 5 and Mathematica 10 or 11.

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Construct a model for simulation and reliability estimation. Four components in this circuit, three resistors and one operational amplifier, are annotated with their lifetime distributions. A Boolean expression representing which components are needed for the system to work is also provided. In this case, all four components are needed.
Operational amplifier with limits.

Parameters from MIL-HDBK-217F

In this example, the reliability handbook MIL-HDBK-217F is used to find parameters for the electrical components. The parameters are added to the model, and the reliability for the complete system can be computed, as well as the mean time to failure (MTTF).
Parameters from MIL-HDBK-217F inserted into the model annotations.
Four common measures used in reliability are the survival function, the hazard function, the PDF, and the CDF. To calculate which components are the most important to improve or contribute the most to system failure, different importance measures can be used.
Four common properties for a system of components.
The importance of the components after 500,000 hours of operation according to the Birnbaum importance measure.

Compare Similar Circuits in Different Operating Temperatures

Reliability of electrical circuits is highly dependent on the temperature at which they’re are operating in. Adjusting the temperature factor results in different parameters for the components and a new system reliability.
Comparison of the same electrical circuit, with two different temperatures and their respective mean time to failure.

Perform reliability calculations

Annotate model components with reliability parameters and configuration to use the system with ReliabilityDistribution, FailureDistribution, and more.