  We define a variant of k-of-n testing that we call conservative k-of-n
testing. We present a polynomial-time, combinatorial algorithm for the problem
of maximizing throughput of conservative k-of-n testing, in a parallel setting.
This extends previous work of Kodialam and Condon et al., who presented
combinatorial algorithms for parallel pipelined filter ordering, which is the
special case where k=1 (or k = n). We also consider the problem of maximizing
throughput for standard k-of-n testing, and show how to obtain a
polynomial-time algorithm based on the ellipsoid method using previous
techniques.
