Statistical design of Shewhart control chart with runs rules

Kim, Young-Bok; Hong, Jung-Sik; Lie, Chang-Hoon

Journal of Korean Society for Quality Management > Volume 36(3); 2008 > Article

Journal of Korean Society for Quality Management 2008;36(3): 34-.

런 규칙이 혼합된 슈와르트 관리도의 통계적 설계

김영복¹, 홍정식², 이창훈¹

¹서울대학교 산업공학과
²서울산업대학교 산업정보시스템공학과

Statistical design of Shewhart control chart with runs rules

Young-Bok Kim¹, Jung-Sik Hong², Chang-Hoon Lie¹

¹Dept. of Industrial Engineering, Seoul National University
²Dept. of Industrial & Information Systems Engineering, Seoul National University of Technology

ABSTRACT

This research proposes a design method based on the statistical characteristics of the Shewhart control chart incorporated with 2 of 2 and 2 of 3 runs rules respectively. A Markov chain approach is employed in order to calculate the in-control and out-of-control average run lengths(ARL). Two different control limit coefficients for the Shewhart scheme and the runs rule scheme are derived simultaneously to minimize the out-of-control average run length subject to the reasonable in-control average run length. Numerical examples show that the statistical performance of the hybrid control scheme are superior to that of the original Shewhart control chart.

Key Words: Shewhart control chart;2 of 2 runs rule;2 of 3 runs rule;ARL;