Conditional design of the EWMA median chart with estimated parameters

ABSTRACT

The exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.

KEYWORDS:

• EWMA median chart
• Estimated parameters
• Standard Deviation of Average Run Length
• Bootstrap method.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N10
• 62P30
• 62F03

Acknowledgement

The authors thank the anonymous referees for their valuable suggestions, which helped to improve the quality of the this manuscript.

Additional information

Funding

XueLong Hu's work was supported by the Natural Science Foundation of JiangSu Province under Grant No. BK20170894; Humanity and Social Science Youth foundation of Ministry of Education of China under Grant No. 17YJC630043; Social Sciences Foundation of Nanjing University of Posts and Telecommunications under Grant No. NYY217007, and XiaoJian Zhou's work was supported by the National Nature Science Foundation of China under Grant No. 71401080; Social Science Foundation of Jiangsu Province under Grant No.17GLB016; the State Scholarship Fund of China under Grant No. 201508320059 and 1311 Talented Foundation of NJUPT.