Extraction and organization of statistical distribution functions for simulation of variations and patterns in the variability control charts

Abstract

Although the existence of natural variations in process control charts is inevitable, the formations of significant patterns associate out-of-control conditions. Hence, the detection of unnatural patterns is essential to increase the sensitivity of Shewhart’s control charts. In the previous years, numerous models have been offered for recognizing and analysing non-random patterns. These models commonly have applied the simulated samples for training, testing and evaluating, and often have simulated and supervised behaviours in the mean control chart. The serious problem for these models is that they have not simultaneously controlled the process variability and the process mean, while the control of variability chart is main prerequisite for the control of mean chart in the monitor of the variable quality characteristics. On the other hand, few classifier models of the variability control chart patterns have merely applied the unrealistic predefined simulators. In an overview, extraction of the known statistical distributions for the simulation of variations and patterns in the variability control charts has not yet been reported in the literature. Therefore, our paper organizes simulators of non-patterned and patterned samples in the variability control charts. In this work, we extract the known statistical distribution functions for simulation of natural variations in the variability control charts. Then the generating functions of significant patterns and their corresponding numerical parameters are described for these charts. Also, the organized simulator functions are compared with simulators applied by the previous papers. The guideline introduced in this research provides required tools for reliable simulations of samples in the variability control charts.