Sampling efficiency for an alternating poisson process

The efficiency of schemes for sampling an alternating Poisson process (0,1 observations) is evaluated by the inverse ratio of the variance of the proportion estimate, p, to the binomial variance. The variance ratio presented by D.R. Cox (in Renewal Theory) for fixed interval sampling is generalized to accommodate random sampling and random sampling after a time delay equal to a fixed proportion, γ , of the mean time between observations, δ. The result is a sampling design tool that provides quantifications for the effect of various spacings between observations and of fixed vs. random sampling. Direct application is made to thes field of work sampling.