  Locating arrays (LAs) can be used to detect and identify interaction faults
among factors in a component-based system. The optimality and constructions of
LAs with a single fault have been investigated extensively under the assumption
that all the factors have the same values. However, in real life, different
factors in a system have different numbers of possible values. Thus, it is
necessary for LAs to satisfy such requirements. We herein establish a general
lower bound on the size of mixed-level $(\bar{1},t)$-locating arrays. Some
methods for constructing LAs including direct and recursive constructions are
provided. In particular, constructions that produce optimal LAs satisfying the
lower bound are described. Additionally, some series of optimal LAs satisfying
the lower bound are presented.
