We consider the problem of simultaneously choosing between k systems. Let X₁, …, X_k denote the lifetimes of the systems. We study various criteria including (1) pairwise stochastic precedence and (2) the maximum criterion which prefers system i if q_i = P(X_i = max(X₁, …, X_k)) > q_j for all j ≠ i. We focus on the case where all the systems' components are independent and identically distributed according to a continuous distribution F. Our probability calculations use signature-based formulas. The maximum criterion is particularly useful when pairwise stochastic precedence does not yield a favored system whereas the maximum criterion will make a determination. Various examples are presented to illustrate the advantages and the disadvantages of the criteria we consider.

Keywords: Signature; Stochastic precedence; Maximum lifetime; Simultaneous comparison

Biography: Myles Hollander is Professor Emeritus and Robert O. Lawton Distinguished Professor of Statistics at The Florida State University. His primary research intrests are nonparametric statistics, survival analysis, reliability theory, and biostatistics. He has published over 100 papers and three books on these subjects.