### Bootstrapping Vector-valued Process Capability Indices

Cho, Joong-Jae;Park, Byoung-Sun

• 발행 : 2003.08.01
• 40 4

#### 초록

In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, some vector-valued ${PCI}_p$ ${C}_p$=(${C}_{px}$, ${C}_{py}$),${C}_{pk}$=(${C}_{pkx}$, ${C}_{pky}$) and ${C}_{pm}$=(${C}_{pmx}$, ${C}_{pmy}$) considering univariate PCIs ${C}_p$,${C}_{pk}$ and ${C}_{pm}$ are studied. First, we propose some asymptotic confidence regions of our vector-valued PCIs with bootstrap. And we examine the performance of asymptotic confidence regions of our vector-valued PCIs ${C}_p$ and ${C}_{pk}$ under the assumption of bivariate normal distribution BN($\mu_{x}$, $\mu_{y}$, $\sigma_{x}^{2}$, $\sigma_{y}^{2}$, $\rho$) and bivariate chi-square distribution Bivariate $x^2$(5,5,$\rho$).

#### 키워드

Vector-valued Process Capability Index;Asymptotic Distribution;Consistency of Bootstrap;Confidence Region

#### 참고문헌

1. Process Capability Indices(1st ed.) Kotz,S.;Johnson,N.L.
2. Journal of Quality Technology v.24 pp.196-210 Bootstrap Lower Confidence Interval Limits for Capability Indices Franklin,L.A.;Wasserman,G.S.
3. Unpublished manuscript Cho,J.J.;Park,B.S.
4. Quality Progress v.22 no.3 pp.108-109 The Use and Abuse of $C_{pk}$ : Part2 Gunter,B.H.
5. Communication in Statistics : Theory and Methods v.20 pp.2529-2547 Process capability indices : Bivariate Normal distribution Kocherlakota,S.;Kocherlakota,K. https://doi.org/10.1080/03610929108830648
6. Korean Communications in Statistics v.8 no.3 pp.697-709 On Statistical Estimation of Multivariate (Vector-valued) Process Capability Indices with Bootstrap Cho,J.J.;Park,B.S.;Lim,S.D.
7. Journal of the Korean Society for Quality Management v.30 no.4 pp.44-57 On the Confidence Region of Vector-valued Precess Capability Indices $C_{p}$ and $C_{pk}$ Park,B.S.;Lee,C.H.;Cho,J.J.
8. Korean Journal of Applied Statistics v.12 no.1 pp.45-65 Better Nonparametric Bootstrap Confidence Interval for Process Capability Index $C_{pk}$ Cho,J.J.;Kim,J.S.;Park,B.S.
9. Annals of Statistics v.16 pp.927-953 Theoretical Comparison of Bootstrap Confidence Intervals Hall,P. https://doi.org/10.1214/aos/1176350933