A Change Point Method for Monitoring Generalized Linear Profiles in Phase I

Abstract

The Phase I applications of the statistical profile monitoring have recently been extended to the case when the response variable is binary. We are motivated to undertake the current research in an attempt to try to provide a unified framework for the Phase I control in the context of statistical profile monitoring that can be used to tackle a large class of response variables, such as continuous, count, or categorical response variables. The unified framework is essentially based on applying the change point model to the class of generalized linear models. The proposed Phase I control chart is assessed and compared with the existing charts under binomial and Poisson profiles. Some diagnostic procedures are also discussed. A real data set obtained from a test lab concerning the dispersion of carbon black filler in a rubber mix is used to demonstrate how the proposed chart can be used in practical applications. Some future research directions are also discussed.

Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

“…Hence, Equation 11 is a linear regression model that has hypothesis of homoscedasticity in the error terms. The estimated β parameters by weighted least squares (WLS) method and the covariance matrix for the parameters can be expressed by the following equations 49,50…”

“…For practical applications, we can mention the articles by Stover and Brill, Kang and Albin, Mahmoud and Woodall, Woodall et al, Wang and Tsung, Williams et al, and Shang et al For Phase I analysis, the authors such as Mestek et al, Kang and Albin, and Kim et al could be named who have proposed the methods for monitoring linear profiles. Amiri et al applied 3 methods, namely, T 2 , likelihood ratio test, and F method, and Shadman et al used a change point method to control the generalized linear models (GLMs). Niaki et al studied the autocorrelated simple linear profiles based on the principal component analysis.…”

Phase I outlier detection in profiles with binary data based on penalized likelihood

“…Yeh et al first studied such a problem and proposed five T 2 control charts, among which the chart performs best in detecting outliers. Besides, Shadman et al proposed a change‐point (CP) approach chart, but their simulation results show that the CP approach chart is less effective than the chart in detecting the presence of outlying observations. Therefore, the chart will be used as the benchmark in the following simulation study.…”

“…The authors constructed the control chart via a likelihood‐ratio test derived from a change‐point model (LRT CP ) based on the risk‐adjustment logistic regression. Recently, Shadman et al proposed a unified framework combining a change point model with a generalized linear model, which can be used to develop Phase I control charts for profiles with continuous, count, or categorical data.…”

Monitoring of linear profiles using generalized likelihood ratio control chart with variable sampling interval

“…Also, GLR charts do not need to tune additional parameters such as EWMA and CUSUM charts, which is another advantage of them. Many researchers have used the GLR charts for monitoring the process (see for example, Reynolds and Lou, Reynolds et al in the case of univariate processes, Wang and Reynolds in the case of multivariate processes, Xu et al in the case of linear profiles, and Shadman et al in the case of generalized linear profiles). However, there has been very sparse research on GLR charts with adaptive features.…”