Extending Coverage Modeling to Voter Behavior for Spacecraft Reliability Modeling

Embedded computer-based systems, or digital systems, are used in applications, such as spacecraft, which require high reliability. Meeting the reliability requirements at the lowest possible cost, typically involves trade studies that aim to quantify the value of different mechanisms for obtaining high reliability. One of these mechanisms is fault tolerance, which involves the detection, location, isolation, and recovery of the system upon occurrence of a fault. The coverage parameter has been defined as the likelihood of successfully recovering from a fault that has occurred. If the fault and error handling mechanisms cannot successfully cover all the faults in the system, then the coverage factor is less than one and the system has imperfect coverage. An accurate reliability analysis of the system thus must take into consideration the coverage parameter, for systems with imperfect coverage. Methods for incorporation of the coverage parameter in system reliability analysis have been developed. These methods consider the uncovered failure of components both at the subsystem and system level. At the subsystem level, and in the context of hierarchical systems, the uncovered failure of a component can cause the failure of a given subsystem. At the systems level, the uncovered failure of a component can cause systems level failures. One of the mechanisms for including fault tolerance in the system is masking faults using voters. We propose to extend the existing methods for coverage modeling to consider the behavior of voters and their contribution to the prevention of uncovered failures. We consider that the system can have three states: successful, fail covered and fail uncovered and find the likelihood of each of these states as a function of the likelihood of the coverage parameter for each component as well as the likelihood of successful fault masking by the voter.