Interpreting the out-of-control signal in multivariate control chart - a comparative study

Interpretation of the out-of-control signal poses a persistent problem in multivariate control chart owing to the limitations of available general methods like Hotelling T-2. Many research papers address these problems and present alternative approaches to diagnose faults in out-of-control conditions and to help identify aberrant variables. This work reviews the different methods and attempts to make a comparative study of some of these methods viz. Mason, Tracy and Young method (Journal of Quality Technology 27:99-108, 1995), Murphy method (The Statistician 36:571-583, 1987), Hawkins method (Technometrics 33:61-75, 1991) and Doganaksoy, Faltin and Tucker method (Communications in Statistics - Theory and Methods 20:2775-2790, 1991). A simulation approach was taken to generate data on various out of control situation and to compare the powers of different targeted methods. In control sate was characterised by a multivariate normal with standardised mean and variance assuming intra-class correlation structure. Data were generated for different values of correlation and various out of control situation with respect to the shift of mean in one, two or more variables. Due to the limitations of using average run length as a performance criterion especially in case of skewed distribution of run length it was decided to use power as a measure of comparison. Situations in which the particular method works satisfactorily were identified with respect to correlation structure and pattern of shift of mean.