Cusum Control Chart for Monitoring Process Variance

Lee, Yoon-Dong; Kim, Sang-Ik

Journal of Korean Society for Quality Management > Volume 33(3); 2005 > Article

Journal of Korean Society for Quality Management 2005;33(3): 149-.

공정분산 관리를 위한 누적합 관리도

이윤동, 김상익

건국대학교 응용통계학과

Cusum Control Chart for Monitoring Process Variance

Yoon-Dong Lee, Sang-Ik Kim

Department of Applied Statistics, Konkuk University

ABSTRACT

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

Key Words: CUSUM;Process Variance;Erlang Distribution;