In the context of process capability analysis, the results of most processes are dominated by two or even more quality characteristics, so that the assessment of process capability requires that all of them are considered simultaneously. In recent years, many researchers have developed different alternatives of multivariate capability indices using different approaches of construction.In this paper, four of them are compared through the study of their ability to correctly distinguish capable processes from incapable processes under a diversity of simulated scenarios, defining suitable minimum desirable values that allow to decide whether the process meets or does not meet specifications. In this sense, properties analyzed can be seen as sensitivity and specificity, assuming that a measure is sensitive if it can detect the lack of capability when it actually exists and specific if it correctly identifies capable processes. Two indices based on ratios of regions and two based on the principal component analysis have been selected for the study. The scenarios take into account several joint distributions for the quality variables, normal and non-normal, several numbers of variables, and different levels of correlation between them, covering a wide range of possible situations.The results showed that one of the indices has better properties across most scenarios, leading to right conclusions about the state of capability of processes and making it a recommendable option for its use in real-world practice.
Observations with missing data are a typical predicament in the context of multivariate statistical process control (MSPC). When process control is performed using a T2 control chart of the principal components (PCs), several score imputation methods have been proposed. Some of these lead to estimators with good properties. However, there are no detailed studies pertaining the performance of Phase II Hotelling's T2 and squared prediction error (SPE) charts when such imputation methods are used. In this paper, a simulation study was conducted to assess the consequences of the estimation of incomplete observations using score imputation methods on T2 and SPE control charts. The study involves several scenarios that combine different correlation structures for the PCA model, methods of score estimation, percentages of missing data and patterns of incomplete information. Results show that the charts' standard control limits are adequate only for small percentages of missing values and that their average run lengths (ARLs) tend to be larger than expected in out‐of‐control situations. To illustrate the conclusions of the study, we present two examples. Our findings lead us to suggest a modification that may result in an improvement in the performance of the T2 and SPE control charts.
Multivariate capability analysis has been the focus of study in recent years, during which many authors have proposed different multivariate capability indices. In the operative context, capability indices are used as measures of the ability of the process to operate according to specifications. Because the numerical value of the index is used to conclude about the capability of the process, it is essential to bear in mind that almost always that value is obtained from a sample of process units. Therefore, it is really necessary to know the properties that the indices have when they are calculated on sampling information, in order to assess the goodness of the inferences made from them. In this work, we conduct a simulation study to investigate distributional properties of two existing indices: NMCpm index based on ratio of volumes and Mp2 index based on principal component analysis. We analyze the relative bias and the mean square error of the estimators of the indices, and we also obtain their empirical distributions that are used to estimate the probability that the indices classify correctly a process as capable or as incapable. The results allow us to recommend the use of one of these indices, as it has shown better properties. Copyright © 2016 John Wiley & Sons, Ltd.
Los estudios de repetibilidad y reproducibilidad fueron diseñados con el propósito de analizar la bondad de los sistemas de medición, análisis cuya importancia radica en el hecho que un sistema inadecuado introducirá variabilidad adicional ocasionando que las mediciones no reflejen el verdadero comportamiento del proceso. El análisis se basa en la cuantificación de la variabilidad asociada al sistema de medición y su posterior comparación con la variabilidad total observada, siendo requerimiento fundamental para ello que resulte factible obtener mediciones repetidas de una misma unidad bajo las mismas condiciones experimentales, de lo contrario, la variabilidad en las mediciones estará confundida con la variabilidad propia de las partes medidas. Tal es el caso en que los ensayos de medición son “destructivos”, esto es, las unidades no son robustas frente al proceso de medición, o bien, las unidades no son temporalmente estables. En este trabajo se exponen diversas alternativas para el caso de estudios R&R con ensayos destructivos y una aplicación particular en un problema real sobre estimación de tiempos de producción en una empresa metalúrgica. El empleo de Modelos Lineales Generalizados permitió obtener estimaciones adecuadas de ciertas Componentes de Variancia, que advirtieron sobre características importantes a mejorar en el proceso de medición.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.