No abstract

Classical parametric statistical methods are based on several basic assumptions about data (normality, independence, constant mean and variance). Unfortunately, these assumptions are not always fulfilled in practice, whether due to problems arising during manufacturing or because these properties are not typical for some processes. Either way, when we apply parametric methods to such data, whether Shewhart’s or other types of parametric control charts, it is not guaranteed that they will provide the right results. For these cases, reliable nonparametric statistical methods were developed, which are not affected by breaking assumptions about the data. Nonparametric methods try to provide suitable procedures to replace commonly used parametric statistical methods. The aim of this paper is to introduce the reader to an alternative way of evaluating the statistical stability of the process, in cases where the basic assumptions about the data are not met. First, possible deviations from the data assumptions that must be met in order to use classical Shewhart control charts were defined. Subsequently, simulations were performed to determine which nonparametric control chart was better suited for which type of data assumption violation. First, simulations were performed for the in-control process. Then simulations for an out-of-control process were performed. This is for situations with an isolated and persistent deviation. Based on the performed simulations, flow charts were created. These flow charts give the reader an overview of the possibilities of using nonparametric control charts in various situations. Based on the performed simulations and subsequent verification of the methodology on real data, it was found that nonparametric control charts are a suitable alternative to the standard Shewhart control charts in cases where the basic assumptions about the data are not met.

Nonparametric control charts (NPCC) have shown great potential for monitoring processes in conditions of smart manufacturing with complex structures, various monitored characteristics and the need to process big data. Practical applications of NPCCs are very rare. The main reasons for this situation are a deficiency in software support and a lack of simple but complete instructions for their application. The introduction of such manual, which is based on the authors’ own simulations of performance of wide spectrum of NPCCs in conditions of different violations of data prerequisites, leading to recommendations for the selection of the most effective NPCC in various practical situations, is the main goal of this paper. Compared to other similar studies, this approach covers a wider range of control charts, and it was applied to a wider spectrum of data assumption violations. As an integral part of these analyses, an examination of various control chart performance indicators such as ARL, MRL, x5 and x95 was performed using simulations to select the best of them. The designed methodology was verified using real data.

This paper deals with the methodology for practical application of nonparametric control charts. This topic is very important for two reasons: firstly nonparametric control charts are very effective instruments for the realization of the statistical process monitoring phase I due to their robustness against various deviations from the data assumptions that must be met when applying model-based control charts. Secondly nonparametric control charts have very weak SW support and also they are not taught in the frame of training courses not even of the university study programmes. For that reason the practitioners do not know them and do not use them. The paper offers the proposal how to practically apply these control charts which is based on the complex simulation study of various nonparametric control charts performance when various data assumptions have not been met. The study has covered these nonparametric control charts: Shewhart sign control chart, nonparametric EWMA and nonparametric CUSUM control charts, nonparametric progressive mean control chart, control chart based on Mood statistics and robust median absolute deviation control chart. All charts have been studied in condition of not normally distributed data, autocorrelated data and data with nonconstant distribution parameters. The simulations were realized for statistically stable (ICin control) and also statistically unstable (OCout of control) processes. For the evaluation of the control charts performance median run length, 0.05-quantile, and 0.95-quantile were used.

This paper deals with the methodology for practical application of nonparametric control charts. This topic is very important for two reasons: firstly nonparametric control charts are very effective instruments for the realization of the statistical process monitoring phase I due to their robustness against various deviations from the data assumptions that must be met when applying model-based control charts. Secondly nonparametric control charts have very weak SW support and also they are not taught in the frame of training courses not even of the university study programmes. For that reason the practitioners do not know them and do not use them. The paper offers the proposal how to practically apply these control charts which is based on the complex simulation study of various nonparametric control charts performance when various data assumptions have not been met. The study has covered these nonparametric control charts: Shewhart sign control chart, nonparametric EWMA and nonparametric CUSUM control charts, nonparametric progressive mean control chart, control chart based on Mood statistics and robust median absolute deviation control chart. All charts have been studied in condition of not normally distributed data, autocorrelated data and data with nonconstant distribution parameters. The simulations were realized for statistically stable (IC – in control) and also statistically unstable (OC – out of control) processes. For the evaluation of the control charts performance median run length, 0.05-quantile, and 0.95-quantile were used.