Avaliação de sistemas de medição binária com erros de classificação empregando o método de estimação do mínimo qui-quadrado

Abstract

Binary measurement systems (BMS) are tools frequently using in classification problems when is there only two possible responses. In medicine, are used in diagnostic tests, and in quality control, when the interest is assess the quality of manufacturing items by an inspection. However, the BMSs are not perfect and can result in misclassification. For example, in quality control, a BMS can judge a “conform” item as “nonconforming” with probability e1 or a “nonconforming” item as “conform” with probability e2 during the inspection. Such errors can influence critical decisions to be taken in the process and in quality of manufacturing items, which makes it essential to carry out a rigorous study to evaluate the quality of measurement system in use. The assessment consist in estimate the errors e1 and e2, and the proportion of conform items in the process, denoted by p. However, only items classified as “conform” and “nonconforming” are observed, and these may pass or fail during an inspection with the BMS, that is, the true state of the items is not observable (latent). An alternative is to perform r repeated classifications of each item using the BMS and employ a latent class model. The proposal of this paper is to evaluate a BMS using the so-called minimum chi-square apporach, which has been little discussed in estimation problems, however, Joseph Berkson (1899-1982) defends its use, questioning the sovereignty of the maximum likelihood. In this paper, it is shown that the minimum chi-square estimators are competitive with of Moments and Maximum Likelihood, if compared according to the mean squared error, and equivalent when the number of repeated classifications is three.