Defect Signal Detection Model Based on Variable Confidence

Abstract

A person is assumed to have varying levels of confidence that a defect or a target exists. He will say that a defect or target exists when his confidence (x) is equal to or exceeds a criterion level (c). For a single criterion level, he will say that no target or defect exists when his confidence is below c. For a double criterion level, he will say “no” when his confidence is below a lower value than c. Otherwise, he will try again.

When a defect exists, the confidence frequency function (f₁) increases with increasing confidence. When no defect is present, a different (decreasing) function (f_o) describes the behavior. Confidence (x) varies between 0 and 1. For a given frequency function, reliability (R) is calculated as a function of the relative number of defects (r) and the criterion level. The optimum criterion level and maximum reliability (R_m) are found. Operating characteristic (OC) curves are presented. For a single criterion level, results are given for the following types of frequency functions: linear, exponential, normal, step, and arbitrary. Discrete distributions are also considered. An example for a double criterion level is also presented.