New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II

Abstract

In some statistical process control (SPC) applications, quality of a process or product is characterized by contingency table. Contingency tables describe the relation between two or more categorical quality characteristics. In this paper, two new control charts based on the WALD and Stuart score test statistics are designed for monitoring of contingency table‐based processes in Phase‐II. The performances of the proposed control charts are compared with the generalized linear test (GLT) control chart proposed in the literature. The results show the better performance of the proposed control charts under small and moderate shifts. Moreover, new schemes are proposed to diagnose which cell corresponding to different levels of categorical variables is responsible for out‐of‐control signal. In addition, we propose EWMA–WALD and EWMA–Stuart score test control charts to improve the performance of Shewhart‐based control charts in detecting small and moderate shifts in contingency table parameters. Meanwhile, we compare the performances of two proposed EWMA‐based control charts with the ones of three existing control charts called EWMA–GLT, EWMA–GLRT and an EWMA‐type control chart for multivariate binomial/multinomial processes along with the ones of the corresponding Shewhart‐based control charts. A numerical example is given to show the efficiency of the proposed methods. Finally, the effect of parameter estimation in Phase I based on m historical contingency table on the performance of the Shewhart‐based control charts is studied. Copyright © 2016 John Wiley & Sons, Ltd.

Assessing Response Quality by Using Multivariate Control Charts for Numerical and Categorical Response Quality Indicators

“…For multivariate numerical variables, the 2 statistic can be calculated based on the mean vector and the covariance matrix of the variables. On the other hand, for multivariate categorical data, a contingency table is the most efficient tool with which to study the relationships of the categorical variables by presenting the count of the combinations of different levels of variables (Kamranrad 2017). However, for a dataset including both numerical and categorical variables, existing literature details few methods with which to deal with them simultaneously.…”

Data Consumption Analysis by Two Ordinal Multivariate Control Charts

“…The multivariate ordinal processes include more than one ordered factor, for which multivariate categorical control charts based on the OLLM are used. Statistical Process Monitoring (SPM) uses contingency tables to monitor multivariate category processes simultaneously [2]. As well as, OLLM used to demonstrate the relevance between ordinal variables and correlative observations in an ordinal contingency table (OCT) cell.…”

“…In phase II, they showed that the proposed control chart was robust to detect different shifts. Afterwards, the GLT statistic proposed to monitor multivariate processes in phase-II by Kamranrad et al [2]. As well as, GLT is mixed with an EWMA statistic to enhance performance in small and medium shifts.…”

Simultaneous Monitoring of a Large Number of Heterogeneous Categorical Data Streams

“…There are also control charts developed for multivariate categorical data. One may refer to Patel (1973), Marcucci (1985), Lu et al (1998), Li et al (2012;2014a), and Kamranrad et al (2017). As for monitoring multivariate Poisson counts, recent works include Chiu and Kuo (2008), He et al (2014) and Wang et al (2017).…”