Modeling Failures at the Component Level
As discussed in Chapter 1, a system is a collection of parts and failure of the system is related to failure of its parts. In Chapter 4, we discussed the modeling of part failure based on the black-box characterization, under which a part is characterized in terms of two states—working or failed. Typically, a part starts in its working state and changes to a failed state after a certain time. The time to failure is a random variable and in Chapter 4 we looked at modeling of the time to failure by a failure distribution function.
The failure of a part occurs due to a complex set of interactions between the material properties and other physical properties of the part and the stresses that act on the part. The process through which these interact and lead to a part failure is complex and is different for different types of parts (for example, failure mechanisms that lead to failure of mechanical parts are different from those that lead to failure of electrical parts). In this chapter, we briefly discuss the different mechanisms that lead to failure at the part level. We then develop models for first failure based on the physics of failure.
Subsequent failures of a part depend on the type of rectification actions taken. These in turn depend on whether the part is repairable or not. In the case of a nonrepairable part, a failed part needs to be replaced by a new one. In the case of a repairable part, subsequent failures ...