Pub Date : 2023-04-05DOI: 10.1080/00224065.2023.2185558
E. V. Thomas
Abstract Sensitivity testing often involves sequential design strategies in small-sample settings that provide binary data which are then used to develop generalized linear models. Model parameters are usually estimated via maximum likelihood methods. Often, confidence bounds relating to model parameters and quantiles are based on the likelihood ratio. In this paper, it is demonstrated how the bias-corrected parametric bootstrap used in conjunction with approximate pivotal quantities can be used to provide an alternative means for constructing bounds when using a location-scale model. In small-sample settings, the coverage of bounds based on the likelihood ratio is often anticonservative due to bias in estimating the scale parameter. In contrast, bounds produced by the bias-corrected parametric bootstrap can provide accurate levels of coverage in such settings when both the sequential strategy and method for parameter estimation effectively adapt (are approximately equivariant) to the location and scale. A series of simulations illustrate this contrasting behavior in a small-sample setting when assuming a normal/probit model in conjunction with a popular sequential design strategy. In addition, it is shown how a high-fidelity assessment of performance can be attained with reduced computational effort by using the nonparametric bootstrap to resample pivotal quantities obtained from a small-scale set of parametric bootstrap simulations.
{"title":"Use of the bias-corrected parametric bootstrap in sensitivity testing/analysis to construct confidence bounds with accurate levels of coverage","authors":"E. V. Thomas","doi":"10.1080/00224065.2023.2185558","DOIUrl":"https://doi.org/10.1080/00224065.2023.2185558","url":null,"abstract":"Abstract Sensitivity testing often involves sequential design strategies in small-sample settings that provide binary data which are then used to develop generalized linear models. Model parameters are usually estimated via maximum likelihood methods. Often, confidence bounds relating to model parameters and quantiles are based on the likelihood ratio. In this paper, it is demonstrated how the bias-corrected parametric bootstrap used in conjunction with approximate pivotal quantities can be used to provide an alternative means for constructing bounds when using a location-scale model. In small-sample settings, the coverage of bounds based on the likelihood ratio is often anticonservative due to bias in estimating the scale parameter. In contrast, bounds produced by the bias-corrected parametric bootstrap can provide accurate levels of coverage in such settings when both the sequential strategy and method for parameter estimation effectively adapt (are approximately equivariant) to the location and scale. A series of simulations illustrate this contrasting behavior in a small-sample setting when assuming a normal/probit model in conjunction with a popular sequential design strategy. In addition, it is shown how a high-fidelity assessment of performance can be attained with reduced computational effort by using the nonparametric bootstrap to resample pivotal quantities obtained from a small-scale set of parametric bootstrap simulations.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"6 1","pages":"442 - 462"},"PeriodicalIF":2.5,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89887387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-05DOI: 10.1080/00224065.2023.2186288
Chun-Yen Wang, Dennis K. J. Lin
Abstract In an order-of-addition (OofA) experiment, the response is a function of the addition order of components. The key objective of the OofA experiments is to find the optimal order of addition. The most popularly used model for OofA experiments is perhaps the pairwise ordering (PWO) model, which assumes that the response can be fully accounted by the pairwise ordering of components. Recently, the PWO model has been extended by adding the interactions of PWO factors, to account for variations caused by the ordering of sets of three or more components, where the interaction term is defined by the multiplication of two PWO factors. This paper introduces a novel class of conditional PWO effect to study the interaction effect between PWO factors. The advantages of the proposed interaction terms are studied. Based on these conditional effects, a new model is proposed. The optimal order of addition can be straightforwardly obtained via the proposed model.
{"title":"Interaction effects in pairwise ordering model","authors":"Chun-Yen Wang, Dennis K. J. Lin","doi":"10.1080/00224065.2023.2186288","DOIUrl":"https://doi.org/10.1080/00224065.2023.2186288","url":null,"abstract":"Abstract In an order-of-addition (OofA) experiment, the response is a function of the addition order of components. The key objective of the OofA experiments is to find the optimal order of addition. The most popularly used model for OofA experiments is perhaps the pairwise ordering (PWO) model, which assumes that the response can be fully accounted by the pairwise ordering of components. Recently, the PWO model has been extended by adding the interactions of PWO factors, to account for variations caused by the ordering of sets of three or more components, where the interaction term is defined by the multiplication of two PWO factors. This paper introduces a novel class of conditional PWO effect to study the interaction effect between PWO factors. The advantages of the proposed interaction terms are studied. Based on these conditional effects, a new model is proposed. The optimal order of addition can be straightforwardly obtained via the proposed model.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"47 1","pages":"463 - 468"},"PeriodicalIF":2.5,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79357274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-28DOI: 10.1080/00224065.2023.2170839
Sebastian Ottenstreuer, C. Weiß, M. Testik
Abstract Qualitative, more specifically, ordinal data generating processes are common in real-world process control implementations. In this study, a survey of control charts for the sample-based monitoring of independent and identically distributed ordinal data is provided together with critical comparisons of the control statistics, for memory-less Shewhart-type and for memory-utilizing exponentially weighted moving average (EWMA) and cumulative-sum types of control charts. New results and proposals are also provided for process monitoring. Using some real-world quality scenarios from the literature, a simulation study for performance comparisons is conducted, covering sixteen different types of control chart. It is shown that demerit-type charts used in combination with EWMA smoothing generally perform better than the other charts, which may rely on quite sophisticated derivations. A real-world data example for monitoring flashes in electric toothbrush manufacturing is discussed to illustrate the application and interpretation of the control charts in the study.
{"title":"A review and comparison of control charts for ordinal samples","authors":"Sebastian Ottenstreuer, C. Weiß, M. Testik","doi":"10.1080/00224065.2023.2170839","DOIUrl":"https://doi.org/10.1080/00224065.2023.2170839","url":null,"abstract":"Abstract Qualitative, more specifically, ordinal data generating processes are common in real-world process control implementations. In this study, a survey of control charts for the sample-based monitoring of independent and identically distributed ordinal data is provided together with critical comparisons of the control statistics, for memory-less Shewhart-type and for memory-utilizing exponentially weighted moving average (EWMA) and cumulative-sum types of control charts. New results and proposals are also provided for process monitoring. Using some real-world quality scenarios from the literature, a simulation study for performance comparisons is conducted, covering sixteen different types of control chart. It is shown that demerit-type charts used in combination with EWMA smoothing generally perform better than the other charts, which may rely on quite sophisticated derivations. A real-world data example for monitoring flashes in electric toothbrush manufacturing is discussed to illustrate the application and interpretation of the control charts in the study.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"49 1","pages":"422 - 441"},"PeriodicalIF":2.5,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77637769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-22DOI: 10.1080/00224065.2023.2171320
Zhanpan Zhang
This clear and well-structured book is the second edition of the same authors’ 2014 book, Bayesian Networks With Examples in R. In addition to the core material covered in the first edition, the new edition expands several topics such as conditional Gaussian Bayesian networks, dynamic Bayesian networks, and general Bayesian networks, etc. It’s worth mentioning that there is a website for this book and the related R package, “bnlearn”, in which the R code used in the book can be downloaded and additional examples are provided. This book can be suitable for an introductory Bayesian network course at the MS or PhD level. Chapters 1 to 4 follow a similar structure to introduce several types of Bayesian network. Each chapter presents graphical and probabilistic representation of Bayesian network, parameter estimation, structure learning, inference, and Bayesian network plotting. Chapter 1 focuses on multinomial Bayesian network for discrete data, whereas Chapter 2 on Gaussian Bayesian network for continuous data. In these two chapters, all the variables follow probability distributions belonging to the same family, either multinomial or normal. Chapter 3 introduces conditional Gaussian Bayesian network that is a “mixture of normals” model in which continuous nodes can have both continuous and discrete parents while discrete nodes can only have discrete parents. This chapter demonstrates an initial step to combine different families of probability distributions in building a Bayesian network. Chapter 4 discusses dynamic Bayesian network for dynamic problems in which some variables can evolve over time, therefore a variable measured at different times can be treated as different nodes in Bayesian network. Chapter 5 presents general Bayesian network in which each variable is modeled by its most suitable distribution rather than limited to follow multinomial or normal distribution. Since this is a more general case for Bayesian network building, Stan (an open source software for Bayesian statistical inference using Markov chain Monte Carlo sampling) and its R interface, “rstan”, are adopted to perform random sampling and parameter estimation. Chapter 6 covers theoretical foundations for Bayesian network, in which the formal definition of a Bayesian network and its properties are introduced, and the algorithms for Bayesian network learning and inference are included. This chapter also discusses two important topics: what are the assumptions and challenges in learning a causal Bayesian network; and what considerations are needed to evaluate a Bayesian network. Chapter 7 provides an overview of software packages for Bayesian network development. A number of R packages are listed in a table, along with information on each package’s capability to handle discrete and/or continuous data, as well as its support for structure learning, parameter learning, and inference. Stan and its features are discussed, and several commercial software packages are briefly menti
{"title":"Bayesian networks with examples in R","authors":"Zhanpan Zhang","doi":"10.1080/00224065.2023.2171320","DOIUrl":"https://doi.org/10.1080/00224065.2023.2171320","url":null,"abstract":"This clear and well-structured book is the second edition of the same authors’ 2014 book, Bayesian Networks With Examples in R. In addition to the core material covered in the first edition, the new edition expands several topics such as conditional Gaussian Bayesian networks, dynamic Bayesian networks, and general Bayesian networks, etc. It’s worth mentioning that there is a website for this book and the related R package, “bnlearn”, in which the R code used in the book can be downloaded and additional examples are provided. This book can be suitable for an introductory Bayesian network course at the MS or PhD level. Chapters 1 to 4 follow a similar structure to introduce several types of Bayesian network. Each chapter presents graphical and probabilistic representation of Bayesian network, parameter estimation, structure learning, inference, and Bayesian network plotting. Chapter 1 focuses on multinomial Bayesian network for discrete data, whereas Chapter 2 on Gaussian Bayesian network for continuous data. In these two chapters, all the variables follow probability distributions belonging to the same family, either multinomial or normal. Chapter 3 introduces conditional Gaussian Bayesian network that is a “mixture of normals” model in which continuous nodes can have both continuous and discrete parents while discrete nodes can only have discrete parents. This chapter demonstrates an initial step to combine different families of probability distributions in building a Bayesian network. Chapter 4 discusses dynamic Bayesian network for dynamic problems in which some variables can evolve over time, therefore a variable measured at different times can be treated as different nodes in Bayesian network. Chapter 5 presents general Bayesian network in which each variable is modeled by its most suitable distribution rather than limited to follow multinomial or normal distribution. Since this is a more general case for Bayesian network building, Stan (an open source software for Bayesian statistical inference using Markov chain Monte Carlo sampling) and its R interface, “rstan”, are adopted to perform random sampling and parameter estimation. Chapter 6 covers theoretical foundations for Bayesian network, in which the formal definition of a Bayesian network and its properties are introduced, and the algorithms for Bayesian network learning and inference are included. This chapter also discusses two important topics: what are the assumptions and challenges in learning a causal Bayesian network; and what considerations are needed to evaluate a Bayesian network. Chapter 7 provides an overview of software packages for Bayesian network development. A number of R packages are listed in a table, along with information on each package’s capability to handle discrete and/or continuous data, as well as its support for structure learning, parameter learning, and inference. Stan and its features are discussed, and several commercial software packages are briefly menti","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"72 1","pages":"523 - 523"},"PeriodicalIF":2.5,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83561003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-27DOI: 10.1080/00224065.2022.2161434
Konstantinos Bourazas, F. Sobas, P. Tsiamyrtzis
Abstract The online quality monitoring of a process with low volume data is a very challenging task and the attention is most often placed in detecting when some of the underline (unknown) process parameter(s) experience a persistent shift. Self-starting methods, both in the frequentist and the Bayesian domain aim to offer a solution. Adopting the latter perspective, we propose a general closed-form Bayesian scheme, where the testing procedure is built on a memory-based control chart that relies on the cumulative ratios of sequentially updated predictive distributions. The theoretic framework can accommodate any likelihood from the regular exponential family and the use of conjugate analysis allows closed form modeling. Power priors will offer the axiomatic framework to incorporate into the model different sources of information, when available. A simulation study evaluates the performance against competitors and examines aspects of prior sensitivity. Technical details and algorithms are provided as supplementary material.
{"title":"Predictive ratio CUSUM (PRC): A Bayesian approach in online change point detection of short runs","authors":"Konstantinos Bourazas, F. Sobas, P. Tsiamyrtzis","doi":"10.1080/00224065.2022.2161434","DOIUrl":"https://doi.org/10.1080/00224065.2022.2161434","url":null,"abstract":"Abstract The online quality monitoring of a process with low volume data is a very challenging task and the attention is most often placed in detecting when some of the underline (unknown) process parameter(s) experience a persistent shift. Self-starting methods, both in the frequentist and the Bayesian domain aim to offer a solution. Adopting the latter perspective, we propose a general closed-form Bayesian scheme, where the testing procedure is built on a memory-based control chart that relies on the cumulative ratios of sequentially updated predictive distributions. The theoretic framework can accommodate any likelihood from the regular exponential family and the use of conjugate analysis allows closed form modeling. Power priors will offer the axiomatic framework to incorporate into the model different sources of information, when available. A simulation study evaluates the performance against competitors and examines aspects of prior sensitivity. Technical details and algorithms are provided as supplementary material.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"67 1","pages":"391 - 403"},"PeriodicalIF":2.5,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86077818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-27DOI: 10.1080/00224065.2023.2165463
Hon Keung Tony Ng
"Statistical Methods for Reliability Data." Journal of Quality Technology, ahead-of-print(ahead-of-print), pp. 1–3
可靠性数据的统计方法。质量技术杂志，印刷前(印刷前)，第1-3页
{"title":"Statistical Methods for Reliability Data","authors":"Hon Keung Tony Ng","doi":"10.1080/00224065.2023.2165463","DOIUrl":"https://doi.org/10.1080/00224065.2023.2165463","url":null,"abstract":"\"Statistical Methods for Reliability Data.\" Journal of Quality Technology, ahead-of-print(ahead-of-print), pp. 1–3","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-27DOI: 10.1080/00224065.2022.2161435
Konstantinos Bourazas, F. Sobas, P. Tsiamyrtzis
Abstract In statistical process control/monitoring (SPC/M), memory-based control charts aim to detect small/medium persistent parameter shifts. When a phase I calibration is not feasible, self-starting methods have been proposed, with the predictive ratio cusum (PRC) being one of them. To apply such methods in practice, one needs to derive the decision limit threshold that will guarantee a preset false alarm tolerance, a very difficult task when the process parameters are unknown and their estimate is sequentially updated. Utilizing the Bayesian framework in PRC, we will provide the theoretic framework that will allow to derive a decision-making threshold, based on false alarm tolerance, which along with the PRC closed-form monitoring scheme will permit its straightforward application in real-life practice. An enhancement of PRC is proposed, and a simulation study evaluates its robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, and binomial) illustrate its implementation in practice. Technical details, algorithms, and R-codes reproducing the illustrations are provided as supplementary material.
{"title":"Design and properties of the predictive ratio cusum (PRC) control charts","authors":"Konstantinos Bourazas, F. Sobas, P. Tsiamyrtzis","doi":"10.1080/00224065.2022.2161435","DOIUrl":"https://doi.org/10.1080/00224065.2022.2161435","url":null,"abstract":"Abstract In statistical process control/monitoring (SPC/M), memory-based control charts aim to detect small/medium persistent parameter shifts. When a phase I calibration is not feasible, self-starting methods have been proposed, with the predictive ratio cusum (PRC) being one of them. To apply such methods in practice, one needs to derive the decision limit threshold that will guarantee a preset false alarm tolerance, a very difficult task when the process parameters are unknown and their estimate is sequentially updated. Utilizing the Bayesian framework in PRC, we will provide the theoretic framework that will allow to derive a decision-making threshold, based on false alarm tolerance, which along with the PRC closed-form monitoring scheme will permit its straightforward application in real-life practice. An enhancement of PRC is proposed, and a simulation study evaluates its robustness against competitors for various model type misspecifications. Finally, three real data sets (normal, Poisson, and binomial) illustrate its implementation in practice. Technical details, algorithms, and R-codes reproducing the illustrations are provided as supplementary material.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"20 1","pages":"404 - 421"},"PeriodicalIF":2.5,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81607131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-27DOI: 10.1080/00224065.2023.2171319
Joseph D. Conklin
The ability to harness data for actionable insight is increasingly essential for nearly every sector of the economy. We are awash in data, yet companies and organizations don’t always know how best to leverage their data to meet strategic goals, improve outcomes, or simply gain deeper understanding of their operations. This stackable graduate certificate in analytics and modeling focuses on foundational skills and knowledge for those working in or hoping to work in data science and analytics in any industry.
{"title":"Data Science: A First Introduction","authors":"Joseph D. Conklin","doi":"10.1080/00224065.2023.2171319","DOIUrl":"https://doi.org/10.1080/00224065.2023.2171319","url":null,"abstract":"The ability to harness data for actionable insight is increasingly essential for nearly every sector of the economy. We are awash in data, yet companies and organizations don’t always know how best to leverage their data to meet strategic goals, improve outcomes, or simply gain deeper understanding of their operations. This stackable graduate certificate in analytics and modeling focuses on foundational skills and knowledge for those working in or hoping to work in data science and analytics in any industry.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"74 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80512385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-23DOI: 10.1080/00224065.2022.2139783
Yuhui Yao, S. Chakraborti, X. Yang, J. Parton, Dwight Lewis, M. Hudnall
Abstract Phase I or retrospective process monitoring plays a key part in an overall statistical process monitoring (SPM) regime and is increasingly emphasized in the recent literature. At present, a lot of the data in a variety of settings (public and private sector organizations) are collected individually and sequentially and thus are serially correlated (or autocorrelated). Though a reasonable amount of work is available in the control charting literature for prospective (Phase II) autocorrelated data monitoring, very little work exists for the retrospective phase (Phase I). In this article, we present a Shewhart-type control chart for Phase I monitoring of individual autocorrelated data, assuming normality, with estimated parameters. The methodology, while developed and presented for the first-order autoregressive (AR(1)) model for simplicity, may be adapted to more general time series models. The correct charting constants, adjusted for autocorrelation and parameter estimation, are derived, and tabulated for a nominal in-control (IC) false alarm probability (FAP). Simulation results show that the proposed chart is favorably IC FAP robust and effective for reasonably small sample sizes, moderate autocorrelation, and some model miss-specifications, compared to other approaches. An illustration using some public health data involving prescription fentanyl transactions is provided to show the potential for broader areas of applications of the proposed methodology. Along with a summary and recommendations, some future research areas are indicated. An R package is developed and made available for implementing the proposed methodology on demand.
{"title":"Phase I control chart for individual autocorrelated data: application to prescription opioid monitoring","authors":"Yuhui Yao, S. Chakraborti, X. Yang, J. Parton, Dwight Lewis, M. Hudnall","doi":"10.1080/00224065.2022.2139783","DOIUrl":"https://doi.org/10.1080/00224065.2022.2139783","url":null,"abstract":"Abstract Phase I or retrospective process monitoring plays a key part in an overall statistical process monitoring (SPM) regime and is increasingly emphasized in the recent literature. At present, a lot of the data in a variety of settings (public and private sector organizations) are collected individually and sequentially and thus are serially correlated (or autocorrelated). Though a reasonable amount of work is available in the control charting literature for prospective (Phase II) autocorrelated data monitoring, very little work exists for the retrospective phase (Phase I). In this article, we present a Shewhart-type control chart for Phase I monitoring of individual autocorrelated data, assuming normality, with estimated parameters. The methodology, while developed and presented for the first-order autoregressive (AR(1)) model for simplicity, may be adapted to more general time series models. The correct charting constants, adjusted for autocorrelation and parameter estimation, are derived, and tabulated for a nominal in-control (IC) false alarm probability (FAP). Simulation results show that the proposed chart is favorably IC FAP robust and effective for reasonably small sample sizes, moderate autocorrelation, and some model miss-specifications, compared to other approaches. An illustration using some public health data involving prescription fentanyl transactions is provided to show the potential for broader areas of applications of the proposed methodology. Along with a summary and recommendations, some future research areas are indicated. An R package is developed and made available for implementing the proposed methodology on demand.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":"97 1","pages":"302 - 317"},"PeriodicalIF":2.5,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78769800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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