Standard inspection methods underestimate the true number of defects or nonconformities in a complex product (e.g., automobile, mobile home, airplane, circuit board, computer program) when an inspector is unable to identify every defect with certainty. A nonlinear statistical model with a nonlinear constraint is developed for estimating the unknown number of defects in a product when inspection is imperfect. A sequential defect removal sampling plan is defined in which two or more inspectors examine in sequence a product or sample of products and then mark or correct any observed defects prior to the next inspection. The number of defects identified by each inspector provides the information needed to estimate the number of defects in the product in addition to the number of defects that have eluded all inspectors. A goodness-of-fit test of model assumptions is presented. A test of hypothesis regarding the unknown number of defects in quality improvement experiments also is described.