Location-Scale Rank Testing with Application in Quality Control

The best known and most used rank test for the location-scale problem is the Lepage (1971) test. The idea of Lepage is to use a statistic which is the sum of the squares of the standardized Wilcoxon and Ansari-Bradley statistics. There is also another rank test, due to Cucconi (1968) that is earlier but neither known in the literature nor applied in practice. The test is of interest since, contrary to the other location-scale tests, it is not a quadratic form of a test on location and a test on scale and it is easier to be computed than that of Lepage, and other tests. The Cucconi test is based on squared ranks and squared counter-ranks. It should be noted that the power of the Lepage test, contrary to that of the Cucconi test, has been widely studied, even recently. For this reason power and size of the Cucconi test are studied, and comparisons with the Lepage test are assessed. Simulations show that the test of Cucconi maintains the size very close to a and is more powerful than the Lepage test, and therefore should be taken into account as a better alternative. An application of the tests in the context of quality control and industrial statistics is discussed.