  As a type of search design, a detecting array can be used to generate test
suites to identify and detect faults caused by interactions of factors in a
component-based system. Recently, the construction and optimality of detecting
arrays have been investigated in depth in the case where all the factors are
assumed to have the same number of levels. However, for real world
applications, it is more desirable to use detecting arrays in which the various
factors may have different numbers of levels. This paper gives a general
criterion to measure the optimality of a mixed level detecting array in terms
of its size. Based on this optimality criterion, the combinatorial
characteristics of mixed level detecting arrays of optimum size are
investigated. This enables us to construct optimum mixed level detecting arrays
with a heuristic optimization algorithm and combinatorial methods. As a result,
some existence results for optimum mixed level detecting arrays achieving a
lower bound are provided for practical use.
