Errors in Inspection: Integer Parameter Maximum Likelihood in a Finite Population

Abstract

In a probability model for possible errors in the inspection of a finite lot containing defective items, it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement. These changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter. A new method for the bounding of the integer solution is introduced. The results show that the parameter estimates in the inspection model are generally stable under wide changes in the sampling framework. Conditions for instability of the solution are identified. Some apparently new relations for discrete distributions are derived in the process of the investigation.

Key Words:

• Misclassification
• Sampling without replacement
• Binomial mixture