Monotone Likelihood Ratio of a .Faulty-Inspection. Distribution

Let X denote the number of items declared defective in a sample of size n selected without replacement from a batch of N items containing . defectives, where testing is fallible.In this note it is shown that the density of X, p(x, .), has a monotone likelihood ratio (MLR) in x, and the relevance of this fact to inference is discussed in detail.In addition, an interesting connection is made between the MLR property and the suitability of X as a proxy for the .true. number of defectives in regression modeling.