Modelling of unexpected shift in SPC

Optimal statistical process control (SPC) requires models of both in-control and out-of-control process states. Whereas a normal distribution is the generally accepted model for the in-control state, there is a doubt as to the existence of reliable models for out-of-control cases. Various process models, available in the literature, for discrete manufacturing systems (parts industry) can be treated as bounded discrete-space Markov chains, completely characterized by the original in-control state and a transition matrix for shifts to an out-of-control state. The present work extends these models by using a continuous-state Markov chain, incorporating non-random corrective actions. These actions are to be realized according to the SPC technique and should substantially affect the model. The developed stochastic model yields a Laplace distribution of a process mean. An alternative approach, based on the Information theory, also results in a Laplace distribution. Real-data tests confirm the applicability of a Laplace distribution for the parts industry and show that the distribution parameter is mainly controlled by the SPC sample size.Control charts, Markov chain, mixture distribution, information distance,

Loss-based optimal control statistics for control charts

This work proposes a means for interconnecting optimal sample statistics with parameters of the process output distribution irrespective of the specific way in which these parameters change during transition to the out-of-control state (jumps, trends, cycles, etc). The approach, based on minimization of the loss incurred by the two types of decision errors, leads to a unique sample statistic and, therefore, to a single control chart. The optimal sample statistics are obtained as a solution of the developed optional boundary equation. The paper demonstrates that, for particular conditions, this equation leads to the same statistics as are obtained through the Neyman-Pearson fundamental lemma. Application examples of the approach when the process output distribution is Gamma and Weibull are given. A special loss function representing out-of-control state detection as a pattern recognition problem is presented.

Quality control of wastewater treatment: A new approach

This paper presents a new approach to quality control of wastewater treatment. The first part formulates basic principles of statistical process control (SPC) and Taguchi Method. Then it is shown that the classical SPC technique used in industry, cannot be to applied to wastewater treatment plants without adaptation and that the Taguchi Method is inapplicable in this case. This is followed by an example from literature, which demonstrates the problems of applying the SPC method to wastewater treatment. The third part of the paper presents a case study where the performance of a greywater treatment plant is examined. The performance is analyzed by means of cross-correlation between input and output parameters. A new approach to SPC of wastewater treatment, either "Dynamic SPC" or "linear regression SPC", is presented, and a permeability coefficient is developed (the ratio of the output and input energies). Both are proposed as monitoring tools for wastewater treatment systems.