Optimal Selection of Imperfect Tests for Fault Detection and Isolation

In this paper, we propose new formulations for the problem of test selection in the presence of imperfect tests in order to minimize the total costs of tests subject to lower bound constraints on fault detection and fault isolation. Our formulation allows tests to have multiple outcomes and delays caused by fault propagation, reporting, and transmission. Since the test selection problem is NP-hard even in the presence of perfect binary tests with no delays, we propose genetic algorithm (GA) and Lagrangian relaxation algorithm (LRA) to solve this problem. GA is a general approach for solving the problem with imperfect tests, including the scenarios with delayed and multiple test outcomes. The LRA is suitable for problems with perfect tests, including multiple outcomes. A key advantage of the LRA approach is that it provides an approximate duality gap, which is an upper bound measure of suboptimality of the solution. Our formulations and algorithms are tested on various real-world and simulated systems, and comparisons are made with previous test selection methods developed for perfect tests with no delays. The results show that our methods can efficiently solve the imperfect test selection problem. In addition, they have better performance (measured in terms of the number of tests used) than the methods in the literature for the perfect test selection cases. Finally, the GA has better computational efficiency than the LRA for all of the scenarios with perfect tests.