Sampling Plans in Insect Pest Management Based on Wald's Sequential Probability Ratio Test

Abstract

Equations for the stopping boundaries, and operating characteristic (OC) and average sample number (ASN) functions, of Wald's sequential probability ratio test (SPRT) are presented for the binomial, negative binomial, normal, and Poisson distributions. The effects of errors in Wald's OC and ASN equations due to overshooting the decision boundaries, and errors due to truncating, postponing decisions beyond the first stage, and taking more than one observation at each stage of the decision process are discussed. Monte Carlo procedures are used to show that Wald's equations overestimate the true error probabilities and underestimate the true ASN for a two-decision sampling plan based on the negative binomial distribution. A Monte Carlo procedure for modifying the decision boundaries to yield actual OC and ASN functions approximately equal to the desired ones is presented. Monte Carlo procedures are also used to examine the errors in Wald's OC and ASN functions when used to describe the OC and ASN functions of a composite three-decision sampling plan based on two single SPRT's using the negative binomial distribution. Wald's equations, in general, overestimate the true error probabilities and underestimate the true ASN even more for the three-decision case compared with the two-decision case. Recommendations are given as to the seriousness of the errors inherent in Wald's equations in relation to all of the other errors that are associated with the sampling process, and the choice between Wald's and Monte Carlo OC and ASN functions to describe the properties of a sampling plan.