Simultaneous Test for the Mean and Variance With an Application to the Statistical Process Control

Abstract

In this study, we propose simultaneous tests for the mean and variance under the normality assumption. With formulating the null hypothesis and its alternative, we derive the joint test statistics using the likelihood ratio (LR) principle and combine the individual partial tests into a single one with combining functions including the union–intersection (UI) approach. Then we compare our proposed tests with other one by obtaining empirical powers through a simulation study. We also apply these simultaneous tests to the statistical process control (SPC) with discussion for running the combined charts with an industrial example. We discuss some interesting features as concluding remarks. Finally, in the appendix, we briefly derive the correlation coefficient between two individual LR statistics.

AMS Subject Classification:

• 62G10

Keywords:

• Combined chart
• Combining function
• Likelihood ratio principle
• Partial test
• Union–intersection test

Additional information

Funding

The author wishes to express his sincere appreciations to the editor-in-chief and two anonymous referees for enhancing the quality of this article with providing numerous invaluable advices and suggestions. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2012R1A1A2002042).