Maximum weighted adaptive CUSUM charts for simultaneous monitoring of process mean and variance

ABSTRACT

In this paper, we propose maximum weighted adaptive Crosier CUSUM (MaxWACCUSUM) charts with three different unbiased estimators of the process mean and variance shifts for joint monitoring of the mean and variance of a normal process. The MaxWACCUSUM charts provide an overall good performance for detecting a range of joint mean and dispersion shift sizes. The run length characteristics of the proposed charts are computed using the Monte Carlo simulation method. A detailed comparative study is conducted to compare the run length performances of the proposed and existing charts. It is found that the MaxWACCUSUM charts are more sensitive than the maximum EWMA, double EWMA and CUSUM charts when detecting a range of joint shift sizes. Real datasets are considered to support the theory.

Keywords:

• Average run length
• maximum EWMA
• maximum double EWMA
• maximum CUSUM
• Monte Carlo simulation
• process mean and dispersion
• weighted adaptive CUSUM
• statistical process control

2010 Mathematics Subject Classification:

• 62N10

Acknowledgments

The authors are thankful to the associate editor and the anonymous reviewer for providing useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.