Transferring biological sequence analysis tools to break‐point detection for on‐line monitoring: A control chart based on the local score

Abstract

The Lindley process defined for the queuing file domain is equivalent to the cumulative sum (CUSUM) process used for break-point detection in process control. The maximum of the Lindley process, called local score, is used to highlight atypical regions in biological sequences, and its distribution has been established by different manners. I propose here to use the local score and also a partial maximum of the Lindley process over the immediate past to create control charts. Stopping time corresponds to the first time where the statistic achieves a statistical significance less than a given threshold in ]0,1[, the instantaneous first error rate. The local score p value is computed using existing theoretical results. I establish here the exact distribution of the partial maximum of the Lindley process. Performance of the control charts is evaluated by Monte Carlo estimation of the average run lengths for an in-control process (ARL 0) and for an out-of-control process (ARL 1). I also use the standard deviation of the run length (SdRL) and the extra quadratic loss (EQL). Comparison with the usual and recent control charts present in the literature shows that the local score control chart outperforms the others with a much larger ARL 0 and ARL 1 smaller or of the same order. Many interesting openings exist for the local score chart: not only Gaussian model but also any of them, Markovian dependance of the data, both location and dispersion monitoring at the same time can be considered. KEYWORDS average run length (ARL), control charts, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), high-quality process monitoring, local score, statistical process control (SPC) 1 STATE OF THE ART INTRODUCTION Statistical quality control is a branch of industrial statistics, which is also largely present in the medical field, business, and many other application domains like bio surveillance. Within statistical quality control, we can distinguish acceptance sampling, statistical process control (SPC), design of experiments, and capability analysis. Control charts are one of the most important and commonly used tools of the SPC tool box, first proposed by Walter Shewhart in 1920. One of the main goals of control charts is to distinguish between the common variation because of chance causes and the variation from Local Score Control Chart