Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix with Variable Sampling Intervals

Misleading signals in joint schemes for the mean vector and covariance matrix

“…There are fundamentally two types of joint schemes for and . On the one hand, the schemes make use of a single control chart to monitor both parameters; see, for example, Spiring and Cheng, Chen et al, Khoo, Chen and Thaga, Yeh and Lin, Zhang et al On the other hand, the most popular joint schemes that result from running simultaneously two individual charts, one for and another one for , such as the ones discussed by Chen and Thaga, Reynolds and Cho, Hawkins and Maboudou‐Tchao, Machado and Costa, Reynolds and Stoumbos, Zhang and Chang, Costa and Machado, Reynolds and Cho, Ramos et al, Ramos, Ramos et al, Morais et al…”

“…There are fundamentally two types of joint schemes for and . On the one hand, the schemes make use of a single control chart to monitor both parameters; see, for example, Spiring and Cheng, 20 Chen et al, 21 Khoo, 22 Chen and Thaga, 23 Yeh and Lin, 24 Zhang et al 25 On the other hand, the most popular joint schemes that result from running simultaneously two individual charts, one for and another one for , such as the ones discussed by Chen and Thaga, 23 Reynolds and Cho, 26 Hawkins and Maboudou-Tchao, 19 Machado and Costa, 27 Reynolds and Stoumbos, 28 Zhang and Chang, 29 Costa and Machado, 30 Reynolds and Cho, 31 Ramos et al, 32,33 Ramos,34,35 Ramos et al, 36 Morais et al 6 When we use any of these joint schemes, the multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart. Thus, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa.…”

Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

“…Alternatively, the use of two‐chart monitoring schemes has been suggested, which consist of separate mean and variance charts with appropriate control limits (CLs) adjusted to the overall false alarm rate FAR (see, for example, Levinson et al, Reynolds and Stoumbos, and Maboudou‐Tchao and Hawkins). A number of specific approaches have also been developed for the construction of monitoring schemes applicable in miscellaneous situations; typical examples are the likelihood ratio‐based CCs suggested by Zhang et al and Wang et al, the change‐point detection models of Sullivan and Woodall and Zamba and Hawkins, the adaptive schemes that incorporate variable sampling intervals and sequential sampling proposed by Reynolds and Kim and Reynolds and Cho, and so on.…”

Monitoring Correlated Profile and Multivariate Quality Characteristics

“…proposed a nonparametric fault isolation approach based on a one‐class classification algorithm and showed that their proposed method can detect source of variation better than T 2 decomposition in the presence of nonnormal processes. Some kinds of variable sampling rate in multivariate control charts, which lead to overall better performance rather than standard fixed sampling rate, were proposed by Reynolds and Cho . The applications of multivariate control charts in health care were studied by Waterhouse et al …”

“…Some kinds of variable sampling rate in multivariate control charts, which lead to overall better performance rather than standard fixed sampling rate, were proposed by Reynolds and Cho. 12 The applications of multivariate control charts in health care were studied by Waterhouse et al 13 Sometimes, the quality of a product or a process is characterized by a relation between a response variable and one or more independent variables, which is called profile. The most common type of profile is a simple linear profile in which a response variable has a linear relation with an explanatory variable.…”