TY - JOUR
T1 - The asymptotic distribution of the estimated process capability index C̃pk
AU - Chen, Sy Mien
AU - Pearn, W.l.
PY - 1997/1/1
Y1 - 1997/1/1
N2 - Bissell (1990) proposed an estimator Ĉ′pk for the process capability index Cpk assuming that P(μ ≥ m) = 0, or 1, where μ is the process mean, and m is the midpoint between the upper and lower specification limits. Pearn and Chen (1996) considered a new estimator C̃pk, which relaxes Bissell's assumption on the process mean. The evaluation of C̃pk only requires the knowledge of P(μ ≥ m) = p, where 0 ≤ p ≤ 1. The new estimator C̃pk is unbiased, and the variance is smaller than that of Bissell's. In this paper, we investigated the asymptotic properties of the estimator C̃pk under general conditions. We derived the limiting distribution of C̃pk for arbitrary population assuming the fourth moment exists. The asymptotic distribution provides some insight into the properties of C̃pk which may not be evident from its original definition.
AB - Bissell (1990) proposed an estimator Ĉ′pk for the process capability index Cpk assuming that P(μ ≥ m) = 0, or 1, where μ is the process mean, and m is the midpoint between the upper and lower specification limits. Pearn and Chen (1996) considered a new estimator C̃pk, which relaxes Bissell's assumption on the process mean. The evaluation of C̃pk only requires the knowledge of P(μ ≥ m) = p, where 0 ≤ p ≤ 1. The new estimator C̃pk is unbiased, and the variance is smaller than that of Bissell's. In this paper, we investigated the asymptotic properties of the estimator C̃pk under general conditions. We derived the limiting distribution of C̃pk for arbitrary population assuming the fourth moment exists. The asymptotic distribution provides some insight into the properties of C̃pk which may not be evident from its original definition.
KW - Asymptotic distribution
KW - Process capability index
KW - Process mean
KW - Process standard deviation
UR - http://www.scopus.com/inward/record.url?scp=0031245941&partnerID=8YFLogxK
U2 - 10.1080/03610929708832061
DO - 10.1080/03610929708832061
M3 - Article
AN - SCOPUS:0031245941
VL - 26
SP - 2489
EP - 2497
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
IS - 10
ER -