A UNIFIED APPROACH FOR SHEWHART-TYPE PHASE I CONTROL CHARTS FOR THE MEAN

被引：1
|
作者：
Human, S. W. [1 ]
Chakraborti, S. [2 ]
机构：
[1] Univ Pretoria, Dept Stat, Lynnwood Rd, ZA-0002 Pretoria, South Africa
[2] Univ Alabama, Dept Informat Syst Stat & Management Sci, Tuscaloosa, AL 35487 USA
来源：
INTERNATIONAL JOURNAL OF RELIABILITY QUALITY & SAFETY ENGINEERING | 2010年 / 17卷 / 03期
关键词：
Estimation of parameters; false alarm probability (FAP); percentiles; phase II; prospective; retrospective; singular multivariate normal;
D O I：
10.1142/S0218539310003755
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The false alarm probability (FAP) is the metric typically used to design and evaluate the performance of Phase I control charts. It is shown that in situations where the exact or the asymptotic joint p. d. f. of the standardized charting statistics follows a singular standard multivariate normal distribution with a common negative correlation, the FAP of some Shewhart-type Phase I charts for the mean can be expressed as a multiple integral of the joint p.d.f. Hence the required charting constants can be calculated (and the control chart can be implemented) by evaluating this integral. A table with the charting constants is provided for some popular choices of the nominal FAP (denoted FAP(0)) and the number of Phase I samples, m. The proposed methodology is useful to unify some existing Phase I charts and is illustrated with two charts from the literature: the p chart for the fraction nonconforming and the X chart for the mean. A summary and some conclusions are provided.
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页码：199 / 208
页数：10
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