Some issues in statistical process control: Change-point techniques

Quality improvement and Statistical Quality Control face many challenges. A major issue in statistical process control is the detection of changes in the location and in scale parameters of a process with unknown mean (μ _o) and unknown standard deviation (σ₀) that undergoes a small shift of unknown size (δ). Small shifts in quality deserve more than a usual attention and failure to diagnose them if they persist for a long time can be more damaging than large shifts. These challenges however become crucial when faced with multivariate processes (more than 2 quality characteristics), and when the multivariate process performance is based on the behavior of a set of interrelated variables. These problems are further compounded by a lack of sophisticated tools especially when it comes to processes with modest data to start with, thereby misleading engineers in the calibration step of processes. Along with these, there is also a need of avoiding the harmful effect of imprecision in the parameter estimation and solving the dichotomy between the phase I (calibrating) and phase II (charting) methods in quality.; Even though there exist several optimal techniques to capture small shifts in quality, they are restrictive in that they require an advance knowledge of the true parameters of the process (information frequently unavailable). An attractive technique that will not require knowledge about the parameters is the change-point formulation. Our approach to the change-point technique advances the classical fix-sample or static formulation. We develop an approach based on sequential estimates using a dynamic procedure.; Both univariate and multivariate aspects of this new approach have been covered. We also suggest a moving window with update approach in large sample situation.; The benefits we have found from this work are: Solving the problem of small shifts in Industrial Processes; removing the (sometimes artificial) dichotomy between phase I and phase II methods in quality; and finding a multivariate tool for both processes with small and large historical data set.