# Analysis and Application of Selected Control Charts Suitable for Smart Manufacturing Processes
## 1 Introduction  
Statistical process monitoring methods have an irreplaceable position in smart process control. Various control charts were developed for monitoring processes. Classical parametric control charts (CC) assume the presence of data normality, constant mean and variance and data independence [1; 2; 3]. However, such prerequisites for data are quite often not met in practical conditions, which is a frequent situation in smart manufacturing processes with complex structure, various monitored characteristics and the need to process big data. In conditions of big data, which have already been enabled by massive deployment of various sensors, large amounts of processed data with various structures and high frequency of collection have led to the fact that statistical properties of data such as data non-normality of various types or data dependence are more typical of modern manufacturing processes than they were of previous manufacturing systems. However, improper application of parametric control charts, including Shewhart's control charts, in such situations can lead to wrong conclusions about a process's statistical stability. Thus, more dependable nonparametric control charts were designed for these situations [4; 5]. Nonparametric control charts (NPCC) have shown great potential for monitoring processes in conditions of smart manufacturing due to their ability to overcome the shortcomings of classical parametric control charts [6; 7; 8; 9], as they were developed for situations when the distribution of the analyzed process is arguable or unknown. The main benefits of NPCCs are as follows: it is not necessary to presume a particular distribution for the analyzed process, they are greatly efficient in detecting changes when data are not normally distributed, they are more robust and resistant to outliers, and itis not required to assess the variance when constructing a control chart for the location parameter [10; 11]. However, practical utilization of NPCC is very rare, predominantly because of a deficiency in software support and a lack of simple but complete instructions for their application. The introduction of such a manual is the main output of this paper. The heart of this developed methodology can be found in the phase of selection of the most effective NPCC. The main goal of the research described in this paper is the selection of the most effective NPCC in relation to various considered deviations from data preconditions and the determination of the most robust NPCC. The phase mentioned above is based on the authors' simulations and comparison of the performance of 6 various univariable NPCCs not only for monitoring location but also for monitoring process variability: the Shewhart sign control chart (SSCC), the nonparametric exponentially weighted moving average signed-rank control chart (NP-EWMA), the nonparametric sign cumulative sum chart based on the Mann-Whitney statistic (NP-CUSUM), the nonparametric progressive mean control chart (NP-PM), the nonparametric control chart based on the Mood statistic for dispersion (NP-MOOD) and the nonparametric control chart based on the median absolute deviation (NP-MAD). In contrast to the study described in this paper, other similar studies compare fewer control charts, and very often they compare NPCCs to some classical Shewhart control chart. For instance, in [12], the author makes a comparison between an NPCC based on a two-sample rank-sum test with the classical Shewhart S chart. In [13], an NPCC based on Mann-Whitney statistics is compared to the classical Shewhart X-bar chart. [PERSON] [14] designed an NPCC with simultaneous monitoring of location and scale and compared it with classical Shewhart control charts. In [15], Shewhart S charts and NP-MAD charts are compared. In [16], authors put the stress on the performance of three control charts--median, bootstrap and Hodges-Lehmann control charts [17; 18] in contrast to a Shewhart X-bar control chart with estimated control limits.