APPROXIMATION OF BOUNDS ON MIXED-LEVEL ORTHOGONAL ARRAYS

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2011-06-01

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Sezer, Ali Devin
Özbudak, Ferruh

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Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

Subject Keywords

Mixed-level orthogonal array, Rao bound, Gilbert–Varshamov bound, Error block code, Counting, İmportance sampling, Large deviation, Optimal control, Asymptotic analysis, Subsolution approach, Hamilton–Jacobi–Bellman equation

URI

https://hdl.handle.net/11511/32389

Journal

ADVANCES IN APPLIED PROBABILITY

DOI

https://doi.org/10.1017/s0001867800004912

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

A. D. Sezer and F. Özbudak, “APPROXIMATION OF BOUNDS ON MIXED-LEVEL ORTHOGONAL ARRAYS,” ADVANCES IN APPLIED PROBABILITY, pp. 399–421, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32389.