Locating Arrays

Abstract

The purpose of a screening experiment is to identify significant factors and interactions on a response for a system. Engineered systems are complex in part due to their size. To apply traditional experimental designs for screening in complex engineered systems requires either restricting the factors considered, which automatically restricts the interactions to those in the set, or restricting interest to main effects, which fails to consider any possible interactions. To address this problem we propose a locating array (LA) as a screening design. Locating arrays exhibit logarithmic growth in the number of factors because their focus is on identification rather than on measurement. This makes practical the consideration of an order of magnitude more factors in experimentation than traditional screening designs. We present preliminary results applying an LA for screening the response of TCP throughput in a simulation model of a mobile wireless network. The full-factorial design for this system is infeasible (over 1043 design points!) yet an LA has only 421 design points. We validate the significance of the identified factors and interactions independently using the statistical software JMP. Screening using locating arrays is viable and yields useful models.

Locating Arrays with Mixed Alphabet Sizes

“…Compared to exhaustive full-factorial designs, using locating arrays as experimental designs greatly decreases the number of design points, thus reducing the cost of experiments. In [13], mixed-level LAs were applied to the screening experiment for TCP throughput of a mobile wireless network.…”

“…LAs have been utilized in measurement and testing [13][14][15]; however, theoretical studies on LAs are still in an early stage. For example, when the number of factors is arbitrary, only the minimum number of tests in (1, 1)-LA and ( 1, 1)-LA is known precisely [16].…”

Finding Minimum Locating Arrays Using a SAT Solver

“…The notion of locating arrays was proposed by Colbourn and McClary in [4]. Concrete applications of locating arrays are discussed in [13,4,14,15]. At present there is not much work on locating arrays.…”

Locating one pairwise interaction: Three recursive constructions

“…Here we focus on locating arrays. Although locating arrays have been successfully applied in applications to measurement and testing [1], few constructions are known. Martínez et al [9] develop adaptive analogues and establish feasibility conditions for a locating array to exist.…”