On the Confidence Region of Vector-valued Process Capability Indices $C_p$& $C_pk$

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Journal of Korean Society for Quality Management > Volume 30(4); 2002 > Article

Journal of Korean Society for Quality Management 2002;30(4): 44-.

2차원 벡터 공정능력지수 $C_p$와 $C_pk$의 근사 신뢰영역

박병선¹, 이충훈², 조중재³

¹충북대학교 전자계산학과
²LG전자(주) DRM 사업부
³충북대학교 통계학과

On the Confidence Region of Vector-valued Process Capability Indices $C_p$& $C_pk$

ABSTRACT

In this paper we study two vector-valued process capability indices $C_{p}$＝($C_{px}$, $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) considering process capability indices $C_{p}$ and $C_{pk}$. First, we derive two asymptotic distributions of plug-in estimators (equation omitted) and (equation omitted) under. some proper. conditions. Second, we examine the performance of asymptotic confidence regions of our process capability indices $C_{p}$＝( $C_{px}$ , $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) under BN($mu$$_{x}$, $mu$$_{y}$, $sigma$$^2$$_{x}$, $sigma$$^2$$_{y}$,$ ho$)$ ho$)EX>)EX>)EX>)

Key Words: Process Capability Index;Asymptotic distribution;Bivariate normal distribution;Confidence region;Plug-in estimator;Monte-carlo experiment;