Control charts are the most popular tool of statistical process control for monitoring variety of processes. The detection ability of these control charts can be improved by introducing various transformations. In this study, we have enhanced the performance of CUSUM charts by introducing a link relative variable transformation technique. Link relative variable converts the original process variable in a form which is relative to its mean. So, the link relative represents the relative positioning of the observations. Average run length (ARL) is used to compare our technique with the previous studies. The comparison shows the overall good detection performance of our scheme for a span of shifts in the mean. A real‐world example from the electrical engineering process is also included to demonstrate the application of proposed control chart.
As product quality has increased rapidly in recent years, monitoring and control of products have become more and more difficult. The items were produced with zero defects, and zero‐inflated distributions are used to fit the defect count data. Recently, many studies were designed for the estimation and monitoring methods based on the zero‐inflated distributions. As zero‐inflated models are useful in the modeling of high‐yield and rare health‐related processes, so, the stated study is designed to provide a summary of past and current trends of monitoring methods under the zero‐inflated models. Moreover, a review is done on the several zero‐inflated models and their applications in different industries. Finally, some future directions are also highlighted to overcome existing unsolved issues.
Emerge in technology brought well‐organized manufacturing systems to produce high‐quality items. Therefore, monitoring and control of products have become a challenging task for quality inspectors. From these highly efficient processes, produced items are mostly zero‐defect and modeled based on zero‐inflated distributions. The zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common distributions, used to model the high‐yield and rare health‐related processes. Therefore, data‐based control charts under ZIP and ZINB distributions (i.e., Y‐ZIP and Y‐ZINB) are proposed for the monitoring of high‐quality processes. Usually, with the defect counts, few covariates are also measured in the process, and the generalized linear model based on the ZIP and ZINB distributions are used to estimate their parameters. In this study, we have designed monitoring structures (i.e., PR‐ZIP and PR‐ZINB) based on the ZIP and ZINB regression models which will provide the monitoring of defect counts by accounting the single covariate. Further, proposed model‐based charts are compared with the existing data‐based charts. The simulation study is designed to access the performance of monitoring methods in terms of run length properties and a case study on the number of flight delays between Atlanta and Orlando during 2012–2014 is also provided to highlight the importance of the stated research.
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.
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