Logic Differential Calculus for Reliability Analysis Based on Survival Signature

The structure function is an often-used mathematical representation of the investigated system in reliability analysis. It is a binary function that models a system state according to the states of its components. The size of the structure function depends on the number of components and can be enormous for systems with many components. Therefore, the system reliability analysis based on the structure function needs special methods to decrease this dimension and to measure the system reliability. The concept of survival signature provides a useful transformation of the structure function to simplify reliability assessment for systems with many components of specified types. The survival signature is a complete probabilistic description of the system. The new methods and algorithms of system reliability analysis based on this mathematical representation should be developed. The Direct Partial Logic Derivative is one of the approaches that are effective in system reliability evaluation based on the structure function. This approach is used to determine different aspects of system failure depending on system components breakdowns. The development of this derivative for survival signature permits to obtain the new method for the reliability analysis of system failure caused by system component breakdown depending on components types.