Optimization of alarm threshold and sequential inspection scheme

An item is subject to gradual degradation. The degradation can be represented by a measurable, non-negative and non-decreasing quantity. The item can be in one of three different states: normal (when the degradation quantity is smaller than a threshold of alarm or potential failure), functional failure (when the degradation quantity is larger than a functional failure threshold) and in-between or potential failure (when the degradation quantity is larger than the alarm threshold and smaller than the functional failure threshold). A sequential inspection scheme is implemented to determine the state of the item so as to prevent a functional failure. The paper presents a flexible degradation model and two cost models to optimize the alarm threshold and the sequential inspection scheme. The usefulness and appropriateness of the proposed models are illustrated by examples.