| We propose various "run tests" for a sequence of nominal data with more than two classes. Specifically, we derive recursive equations and find the probability distributions of the total number of runs and the maximum run length. Based on the two types of test statistics and two different sampling methods, various run tests can be classified into four cases. Numerous researchers have derived the probability distributions in many different ways, treating each case separately. In the paper, we propose a unified approach which is based on recurrence arguments of mutually exclusive sub-sequences. The run tests can be applied to many practical situations, such as testing changes in process variation, developing non-parametric multivariate control charts, and comparing the shapes and locations of more than two continuous distributions. |
Updated 02/21/2015