TY - JOUR
T1 - Robust multivariate control charts based on Birnbaum–Saunders distributions
AU - Marchant, Carolina
AU - Leiva, Víctor
AU - Cysneiros, Francisco José A.
AU - Liu, Shuangzhe
PY - 2018/1/2
Y1 - 2018/1/2
N2 - Multivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard methodology. This study reports the good performance of our methodology. An illustration with real-world air quality data of Santiago, Chile, is provided. This illustration shows that the methodology is useful for alerting early episodes of extreme air pollution, thus preventing adverse effects on human health.
AB - Multivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard methodology. This study reports the good performance of our methodology. An illustration with real-world air quality data of Santiago, Chile, is provided. This illustration shows that the methodology is useful for alerting early episodes of extreme air pollution, thus preventing adverse effects on human health.
KW - Average run length
KW - bootstrapping
KW - Hotelling statistic
KW - Mahalanobis distance
KW - maximum likelihood method
KW - Monte Carlo simulation
KW - multivariate non-normal distributions
KW - R software
UR - http://www.scopus.com/inward/record.url?scp=85031109941&partnerID=8YFLogxK
U2 - 10.1080/00949655.2017.1381699
DO - 10.1080/00949655.2017.1381699
M3 - Article
AN - SCOPUS:85031109941
SN - 0094-9655
VL - 88
SP - 182
EP - 202
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 1
ER -