Models and monitoring of zero‐inflated processes: The past and current trends

Quality & Reliability Eng

2019

Self Cite

In the modern era of digitalization, manufacturing industries needed monitoring methods to timely detect an abrupt change in the process. Control charts are widely used online monitoring method and used in several sectors for the surveillance of the process. Usually, control charts are developed for a single study variable, but there exists auxiliary information along with the study variable. Because of the linear relation between the study variable and auxiliary variable, several control chart studies are designed based on the simple linear regression model, but they are restricted to the normally distributed response variable. When the response variable follows an exponential family distribution, then the generalized linear modeling (GLM) approach provides better estimates. Hence, this study is designed to propose GLM‐based control charts when the response variable follows the inverse Gaussian (IG) distribution. In GLM‐based control charts, deviance and Pearson residuals of the IG regression are considered as plotting statistics. For the evaluation purpose, a simulation study is designed, and the performance of the proposed methods is compared with existing counterparts in terms of the run length properties. Moreover, run‐rules are also implemented to gain the efficiency of the Shewhart type GLM‐based control charts under small‐to‐moderate shifts. Finally, an example related to the yarn manufacturing industry is also used to highlight the importance of the stated proposal.

Section: The Data Model For the Glm-based Control Chartmentioning

confidence: 99%

Section: Enhancement Of the Control Charts Using Run-rule Strategiesmentioning

confidence: 99%

Section: Enhancement Of the Control Charts Using Run-rule Strategiesmentioning

confidence: 99%

Section: Enhancement Of the Control Charts Using Run-rule Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

GLM‐based control charts for the inverse Gaussian distributed response variable

Kinat

Amin

Quality & Reliability Eng

2019

Self Cite

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

Appl Stoch Models Bus & Ind

Xie

2021

Self Cite

In this industry 4.0 revolution, most of the manufacturing processes are equipped with the digital devices which are continuously recording the data. To monitor the quality of a manufacturing system, variable about number of conforming or nonconforming items is usually used and statistical analysis based on it is further utilized for developing the policies. In this era of sophisticated and modern technology, most of the manufacturing systems are producing near zero‐defect items. Such processes are known as high‐quality processes, and their dataset consists of excess number of zeros. Generally, the zero excess or near zero‐defect dataset is well fitted by the zero‐inflated distributions, and the zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common models. Most of the time, in high‐quality processes, few covariates are also measured along with defect counts. Hence, to model such processes, generalized linear model (GLM) based on ZIP and ZINB distributions are used to fit the data. In monitoring perspective, data‐based control charts are designed to monitor high‐quality datasets while the GLM‐based control charts based on the residuals of the GLM models are used to monitor a change in the mean of the zero excess datasets. In this study, we have developed memory‐type data‐based and GLM‐based control charts (i.e., exponentially weighted moving average and cumulative sum) to monitor the increasing average defect counts in a high‐quality process. Further, the proposed methods are evaluated using run‐length properties and compared with its competitive charts. Furthermore, to highlight the importance of the study, the proposed methods are implemented on a dataset concerning the number of flight delays between Atlanta and Orlando airports.

A real‐time monitoring approach for bivariate event data

Zwetsloot

Appl Stoch Models Bus & Ind

Taiwo

et al. 2023

Self Cite

Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high‐quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time‐between‐events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time‐to‐signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real‐time. We derive analytical expressions for the control limits and average time‐to‐signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real‐time and that the control limits are based on analytical expressions. The proposed method is implemented on two real‐life datasets from reliability and health surveillance.