Phase-II monitoring and diagnosing of multivariate categorical processes using generalized linear test-based control charts

Niaki

2016

Self Cite

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.

z_{t} = λ F^{*} + ((), 1 - λ) z_{t - 1},

where λ is the smoothing parameter (0 < λ < 1) and z 0 is the EWMA–GLT at time point zero that is equal to the mean of the F * statistic.…”

Section: Problem Statementmentioning

confidence: 99%

“…Furthermore, μ F and σ F are the mean and the standard deviation of the F statistic, determined using the following equations:

\begin{matrix} center \\ center μ_{F} = \frac{ν_{2}}{ν_{2} - 2} & center, σ_{F}^{2} = \frac{ν_{2}^{2} (2 ν_{1} + 2 ν_{2} - 4)}{ν_{1} {((), ν_{2} - 2)}^{2} (ν_{2} - 4)} & center; ν_{2} > 4, \end{matrix}

Section: Problem Statementmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Conclusion and Future Researchmentioning

confidence: 99%

See 3 more Smart Citations

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

Kamranrad

Niaki

2016

Self Cite

Phase‐I monitoring of log‐linear model‐based processes (a case study in health care: Kidney patients)

Kamranrad

Niaki

2019

Self Cite

Processes with multiple correlated categorical quality characteristics are called multivariate categorical processes. These processes are usually shown by contingency tables and are characterized by log-linear models. In this paper, two monitoring approaches including likelihood ratio test (LRT) and F test are developed to monitor multivariate categorical processes based on the contingency table in Phase I. In addition, a change point estimator for multivariate categorical processes is developed in Phase I. The performances of the two proposed approaches are evaluated in terms of probability of signal, while the performance of the proposed change point estimator is evaluated in terms of accuracy and precision criteria through simulation experiments. Meanwhile, we compare the performance of the two proposed control charts with an existing control chart called "−2LRT" control chart for multivariate categorical processes. In the end, a typical application of the proposed methods is illustrated in a real-world health care system.

Monitoring a labeled degree‐corrected stochastic block model

Abossedgh

Saghaei

2022

Self Cite

The stochastic block model (SBM) is a random graph model that focuses on partitioning the nodes into blocks or communities. A degree-corrected stochastic block model (DCSBM) considers degree heterogeneity within nodes. Investigation of the type of edge label can be useful for studying networks. We have proposed a labeled degree-corrected stochastic block model (LDCSBM), added the probability of the occurrence of each edge label, and monitored the behavior of this network. The LDCSBM is a dynamic network that varies over time; thus, we applied the monitoring process to both the US Senate voting network and simulated networks by defining structural changes. We used the Shewhart control chart for detecting changes and studied the effect of Phase I parameter estimation on Phase II performance. The efficiency of the model for surveillance has been evaluated using the average run length for estimated parameters.