Robust kernel distance multivariate control chart using support vector principles

It is important to monitor manufacturing processes in order to improve product quality and reduce production cost. Statistical Process Control (SPC) is the most commonly used method for process monitoring, in particular making distinctions between variations attributed to normal process variability to those caused by ‘special causes’. Most SPC and multivariate SPC (MSPC) methods are parametric in that they make assumptions about the distributional properties and autocorrelation structure of in-control process parameters, and, if satisfied, are effective in managing false alarms/-positives and false- negatives. However, when processes do not satisfy these assumptions, the effectiveness of SPC methods is compromised. Several non-parametric control charts based on sequential ranks of data depth measures have been proposed in the literature, but their development and implementation have been rather slow in industrial process control. Several non-parametric control charts based on machine learning principles have also been proposed in the literature to overcome some of these limitations. However, unlike conventional SPC methods, these non-parametric methods require event data from each out-of-control process state for effective model building. The paper presents a new non-parametric multivariate control chart based on kernel distance that overcomes these limitations by employing the notion of one-class classification based on support vector principles. The chart is non-parametric in that it makes no assumptions regarding the data probability density and only requires ‘normal’ or in-control data for effective representation of an in-control process. It does, however, make an explicit provision to incorporate any available data from out-of-control process states. Experimental evaluation on a variety of benchmarking datasets suggests that the proposed chart is effective for process mo

Bootstrap Confidence Intervals of the Modified Process Capability Index for Weibull distribution

The objective of the paper is to modify the existing process capability index (PCI) for a Weibull distribution and to construct bootstrap confidence intervals (BCIs) for the newly proposed index. Three BCIs that consist of standard, percentile and bias-corrected percentile bootstrap (BCPB) confidence intervals are constructed for the newly proposed index and the existing Pearn and Chen index. The efficiency of the newly proposed index CGPK is compared with Pearn and Chen index using their coverage probabilities and average widths. The coverage probabilities and average width of three BCIs were calculated using Monte Carlo simulation studies. The newly proposed index shows better performance than Pearn and Chen index. The results indicate that BCPB confidence interval was more efficient in both cases and outperform other two confidence intervals in all situations. The comparison of average width of BCPB apparently shows that the proposed index performed better in all cases. A real-life example is also provided for a practical application.11sciescopu