Efficient adaptive CUSUM control charts based on generalized likelihood ratio test to monitor process dispersion shift

Abstract

In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out‐of‐control signal against these control charts. Moreover, real‐life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts.

New Hybrid EWMA Charts for Efficient Process Dispersion Monitoring with Application in Automobile Industry

“…For this purpose, the real-life data are considered, representing the inside diameter of the cylinder bores in an engine block. These real-life data are used by [46,47] in their studies. The data comprise 30 samples, each size n = 5 given in Table 7.…”

Novel nonparametric control charts for monitoring dispersion of count data

“…As a matter of fact, the dispersion of the observed count data changes over time in practice, reflecting the time-varying impact of certain latent confounding risk factors on the count data, and it is highly desirable to monitor the dispersion of the observed count data since the performance of the process under monitoring depends heavily on the dispersion level. 17 More specifically, an increase in dispersion often implies deterioration of the process, and a decrease indicates improvement in the process. In addition, it could be meaningless to detect a mean shift without ensuring that the dispersion is in-control (IC).…”

“…Although some of them consider the data dispersion, they assume that the dispersion parameter does not change over time, which may not be true in practice. As a matter of fact, the dispersion of the observed count data changes over time in practice, reflecting the time‐varying impact of certain latent confounding risk factors on the count data, and it is highly desirable to monitor the dispersion of the observed count data since the performance of the process under monitoring depends heavily on the dispersion level 17 . More specifically, an increase in dispersion often implies deterioration of the process, and a decrease indicates improvement in the process.…”