Improved statistical process control using wavelets

There are a number of existing methods for statistical process control (SPC) with Shewhart, CUSUM and EWMA being the most popular for univariate SPC. A Shewhart chart is able to detect large shifts quickly but is not good for detecting small shifts. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts are designed for fast detection of small shifts, but need well-tuned design parameters and are slow in detecting large shifts. Furthermore, CUSUM and EWMA charts are not easy to interpret since they filter the data. Consequently, in practice, it is common to use various control charts together. Another important shortcoming of these control-charting methods is that their performance deteriorates if the measurements are autocorrelated since they give too many false alarms. This paper describes a new approach for SPC based on representing the measurements at multiple scales using wavelets. This approach, called multiscale SPC (MSSPC), provides a common framework for the commonly used methods of Shewhart, CUSUM and EWMA since these methods differ only in the scale at which they represent the measurements. MSSPC exploits the ability of wavelets to separate deterministic and stochastic components and approximately decorrelate autocorrelated. The MSSPC method is explained with examples and average run length (ARL) performance is compared to that of traditional techniques by extensive Monte Carlo simulations. MSSPC does not require much parameter tuning, and is able to retrieve underlying deterministic features in data, enabling the detection of shifts of different types.