Algorithms for Computing Operating Characteristic and Average Sample Number Functions for Sequential Sampling Plans Based on Binomial Count Models and Revised Plans for European Red Mite (Acari: Tetranychidae) on Apple

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Abstract
Algorithms and computer code (Fortran 77) were developed for computing operating characteristic (OC) and average sample number (ASN) functions for sequential classification sampling plans based on presence-absence counts. Two models that relate the proportion of sample units with more than T (tally threshold) organisms ( PT ) to mean density ( m ) were considered; an empirical model of the form In(-In(l- PT )) = γ + δln(m) where m is the mean density, and the negative binomial distribution (NBD). The algorithms compute OC and ASN for nominal model parameters and for model parameters used to characterize the effect of Pt – m model variability on the OC and ASN functions. Changes in the OC and ASN functions as a result of change in the PT – m model are a measure of the robustness of the sampling procedure. Both PT – m models provided good descriptions of counts of European red mite ( Panonychus ulmi (Koch), on apple trees, Malus domestica (Borkh). The robustness of sampling plans that used T = 0 was poor. Expected OC and ASN functions for sampling plans based on the two PT – m models were similar. Robustness of sampling plans based on NBD improved significantly with larger values of T . When sampling using thresholds of 2.5, 5.0, and 7.5 mites per leaf, recommended values of T are 4, 6, and 6, respectively.

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