On the Application of Zp Control Charts for Very Small Fraction of Nonconforming under Non-normal Process

Title & Authors
On the Application of Zp Control Charts for Very Small Fraction of Nonconforming under Non-normal Process
Kim, Jong-Gurl; Choi, Seong-Won; Kim, Hye-Mi; Um, Sang-Joon;

Abstract
Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $\small{Z_p}$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $\small{Z_p}$ control chart in order to use under non-normal process. Methods: $\small{Z_p}$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $\small{Z_p}$ control chart is designed based on $\small{{\alpha}}$-risk calculated by cumulative distribution function of Burr distribution. $\small{{\beta}}$-risk, which is for performance evaluation, obtains in the Burr distribution`s cumulative distribution function and control limit. Results: The control limit for non-normal $\small{Z_p}$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $\small{Z_p}$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $\small{Z_p}$ distribution is non-normal distribution.
Keywords
$\small{Z_p}$ Control Chart;Non-normal Process;Burr Distribution;
Language
Korean
Cited by
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