Bootstrap-based maximum multivariate CUSUM control chart

ABSTRACT

Maximum multivariate cumulative sum (Max-MCUSUM) is one of the single control charts that plot single statistic as a representation of mean vector and covariance matrix. The Max-MCUSUM statistic has unknown specific distribution. The objective of this paper is to propose bootstrap-based Max-MCUSUM control chart for which reference value is predetermined in Phase I monitoring process. For various numbers of quality characteristics and correlation coefficients, the control limits estimated using bootstrap approach are presented in this paper. Furthermore, the average run lengths of bootstrap-based Max-MCUSUM control chart prove that the proposed control chart tends to be effective for monitoring the small shift in both mean and variance of a process. The illustrative examples are provided to demonstrate the applications of the proposed control chart for both simulation and real data.

KEYWORDS:

• Average run length
• bootstrap
• maximum multivariate CUSUM
• reference value
• single control chart

Acknowledgments

The authors are thankful to the anonymous reviewers and editor for their constructive comments that have significantly improved this paper to a better scientific level.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Research, Technology, and Higher Education Ministry, Republic of Indonesia through PMDSU scheme under Grant [135/SP2H//LT/DRPM/IV/2017].

Notes on contributors

Hidayatul Khusna

Hidayatul Khusna is a PhD student through the Master Program of Education Leading to Doctoral Degree for Excellent Graduates (PMDSU), an accelerated programme for undergraduate prepared to be candidate lecturers or researchers with doctoral degrees. Her research interest includes statistical quality control, and time series analysis.

Muhammad Mashuri

Dr. Muhammad Mashuri is an associate professor in the Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. His research interest includes statistical quality control and multivariate analysis, especially in the industrial field.

Muhammad Ahsan

Muhammad Ahsan is a PhD student through the Master Program of Education Leading to Doctoral Degree for Excellent Graduates (PMDSU), an accelerated programme for undergraduate prepared to be candidate lecturers or researchers with doctoral degrees. His research interest includes statistical quality control computational statistics and network intrusion detection.

Suhartono Suhartono

Dr. Suhartono Suhartono is a senior lecturer whose research interest includes Time series Forecasting, Neural Networks for Data Analysis, Econometrics Time Series Modeling, Spatial Time Series.

Dedy Dwi Prastyo

Dr. Dedy Dwi Prastyo is a senior lecturer whose research interest includes Econometrics, Time Series Analysis, Multivariate Analysis, Computational Statistics and Modeling, Statistics of Financial Market as well as Statistical Learning Theory.