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.
Statistical methods for monitoring the operation of cathodic protection stations