Multivariate adaptive approach for monitoring simple linear profiles

Adaptive sample size and sampling intervals schemes have been widely used to improve the statistical efficiency of Hotelling T² control chart in detecting small changes when the quality of a product or a process can be characterised by the multivariate distribution of quality characteristics. In this paper, we design a Hotelling T² scheme varying sample sizes and sampling intervals (VSSI-T²) for accelerating the speed of detecting off-target conditions in linear profile parameters. We investigate the statistical performance of the adaptive approach versus its fixed sampling counterparts. To find the optimal setting of the VSSI-T², we build an optimisation model solved using genetic algorithm (GA). Also, average time to signal (ATS) is considered as the objective function of the model and estimated using the Markov chain fundamentals. The comparative studies reveal the potentials of the adaptive scheme in improving the performance of the Hotelling T² control chart in monitoring linear profiles.