Local criteria for testing hypothesis of randomness in laboratory quality control

Abstract

The approach proposed earlier by the authors to a statistically justified search for structures in data of different nature is applied to the problem of statistical quality control. The need to verify that measurement results are independent and identically distributed values (random hypothesis) arises in scientific research, quality control of laboratory analyzes and production processes. Popular tests of randomness or patternless in the existing literature are usually global and do not allow user to identify possibly existing local violations of randomness. The proposed local tests are two-stage. At the first stage, a list of sections is compiled where there is reason to suspect a violation of randomness due to the presence of a certain pattern. Each such section is characterized by two numbers – length and degree of severity. On the plane of parameters (length, severity) a critical region is built, upon entering which this section is declared being significant. The corresponding local modification of the classical runs test is considered. In addition, two more new nonparametric tests have been proposed to search for sections with excessively similar and vice versa strongly fluctuating data. The construction of tests is simplified when the ranks of measured values are replaced by the corresponding empirical p values which are uniformly distributed and nearly independent if hypothesis of randomness is true.