Luiz Henrique da Conceição Leal, Werickson Fortunato de Carvalho Rocha
{"title":"Model Adequacy Checking in Homogeneity and Stability Studies","authors":"Luiz Henrique da Conceição Leal, Werickson Fortunato de Carvalho Rocha","doi":"10.1007/s12647-023-00695-1","DOIUrl":null,"url":null,"abstract":"<div><p>The production of reference materials necessitates, among other factors, evaluations of homogeneity and stability. The aim of the homogeneity study is to ensure uniformity in property values across all samples. On the other hand, stability pertains to a sample’s ability to retain its property value over time. ISO Guide 35 dictates that homogeneity, between and within samples, is appraised using a one-way random effects analysis of variance, while stability is gauged by a univariate linear regression model. Both these statistical techniques presuppose the normality and homoscedasticity of the residuals. Notably, the ISO Guide 35 standard omits any reference to the assumption of homoscedasticity in its prescribed statistical methods. This communication introduces the Shapiro–Wilk and Koenker–Bassett tests as tools to verify the assumptions of normality and homoscedasticity, respectively. Moreover, it advances the feasible generalized least squares method as a remedy for instances where these assumptions are breached. Initial findings suggest that, in certain scenarios, breaches in statistical model assumptions might influence evaluations of homogeneity and/or stability.</p></div>","PeriodicalId":689,"journal":{"name":"MAPAN","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"MAPAN","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s12647-023-00695-1","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 0
Abstract
The production of reference materials necessitates, among other factors, evaluations of homogeneity and stability. The aim of the homogeneity study is to ensure uniformity in property values across all samples. On the other hand, stability pertains to a sample’s ability to retain its property value over time. ISO Guide 35 dictates that homogeneity, between and within samples, is appraised using a one-way random effects analysis of variance, while stability is gauged by a univariate linear regression model. Both these statistical techniques presuppose the normality and homoscedasticity of the residuals. Notably, the ISO Guide 35 standard omits any reference to the assumption of homoscedasticity in its prescribed statistical methods. This communication introduces the Shapiro–Wilk and Koenker–Bassett tests as tools to verify the assumptions of normality and homoscedasticity, respectively. Moreover, it advances the feasible generalized least squares method as a remedy for instances where these assumptions are breached. Initial findings suggest that, in certain scenarios, breaches in statistical model assumptions might influence evaluations of homogeneity and/or stability.
期刊介绍:
MAPAN-Journal Metrology Society of India is a quarterly publication. It is exclusively devoted to Metrology (Scientific, Industrial or Legal). It has been fulfilling an important need of Metrologists and particularly of quality practitioners by publishing exclusive articles on scientific, industrial and legal metrology.
The journal publishes research communication or technical articles of current interest in measurement science; original work, tutorial or survey papers in any metrology related area; reviews and analytical studies in metrology; case studies on reliability, uncertainty in measurements; and reports and results of intercomparison and proficiency testing.