Estimating an instrument's counting efficiency by repeated measurements of one sample

Abstract

Suppose a device, a counter, inspects a sample having an unknown number (N*) of identical objects, such as particles or defects. Assume further that the probability that any one object will be detected in one inspection is p, which remains constant. From the sample mean and sample variance of the counts obtained in repeated readings, the counting efficiency (the probability p) can be estimated. The uncertainty in the estimates is predicted to depend on the number of replications made (M) but not on the unknown true count (N*), for N* ≫ 10. Monte Carlo simulations were carried out that confirmed the analysis (p = 0.1, 0.5, and 0.9; M = 10, 100, and 1000; N* = 100, 1000, and 10,000). Experiments were performed with Tencor Surfscan (TM) 4500 and Tencor Surfscan (TM) 5500 surface particle counters. The detection efficiencies calculated with this method were in good agreement with those measured, except at very low fractions counted and near the noise threshold. © 1991.