비정규 공정의 극소 불량률 관리를 위한 Zp 관리도 적용 방안 연구
On the Application of Zp Control Charts for Very Small Fraction of Nonconforming under Non-normal Process
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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. Zp control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the Zp control chart in order to use under non-normal process. Methods: Zp is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal Zp control chart is designed based on α -risk calculated by cumulative distribution function of Burr distribution. α -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 Zp control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal Zp control chart is able to control not only the very small fraction of nonconforming, but it is also useful when distribution is non-normal distribution.
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. Zp control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the Zp control chart in order to use under non-normal process. Methods: Zp is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal Zp control chart is designed based on α -risk calculated by cumulative distribution function of Burr distribution. α -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 Zp control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal Zp control chart is able to control not only the very small fraction of nonconforming, but it is also useful when distribution is non-normal distribution.
참고문헌 (18)
- Burr, I. W, "Cumulative Frequency Distribution", Annals of Mathematical Statistics, 13, pp.215~232 (1942)
- Burr, I. W, "The Effects of Non-normality on Constants for and R charts", Industrial Quality Control, 23, pp.563~568 (1967)
- Burr, I. W, "Parameter for a General System of Distributions to Match a Grid of and ", Communications in Statistics, 2(1), pp.1~21 (1973)
- Chang, Youngsoon., "Control charts for positively-skewed populations with weighted standard deviations", Quality and Reliability Engineering International, 17(5), pp.397~406 (2001)
- 장영순, "비정규 모집단에 대한 일변량 및 다변량 누적합 관리도의 성능 분석", 품질경영학회지, 34(4), pp.102~109 (2006), 한국품질경영학회
- Cho, Namho., "Real Time Process Control System under 100PPM Management System", Journal of the Korean Society for Quality Management, 25(1), pp.116~134
- Chou, C. Y., "Ranges Control Chart for Non-normal Data", Journal of the Chinese Institute of Industrial Engineers, 14, pp.401~409 (1997)
- Chou, C. Y, "Acceptance Control Charts for Non-normal Data", Journal of Applied Statistics, 32(8), pp.25~36 (2005)
- Joekes, S., "An Improved Attribute Control Chart for Monitoring Non-conforming Proportion in High Quality Processes", Control Engineering Practice, 21(4), pp.407~412 (2013)
- 김정훈, "지역적이고 비정규분포를 갖는 데이터의 공정관리를 위한 지역기반 T2관리도", 품질경영학회지, 40(3), pp.337~346 (2012), 한국품질경영학회[DOI]
- 김종걸, "미세변동공정관리를 위한 가속수명시험관리도 설계", 대한안전경영과학회지, 14(3), pp.167~174 (2012), 대한안전경영과학회
- Kim, Jonggurl., "Controling Method of Very Small Fraction of Nonconforming", Korea patent 10-1538548-0000, ~ (2015)
- 김종걸, "극소불량률 관리를 위한 Zp 관리도 수행도 평가", 대한설비관리학회지, 20(4), pp.29~37 (2015), 대한설비관리학회
- Montgomery, D. C., "Introduction to Statistical Quality Control" (2013), Wiley
- Schilling, E. G., "The Effect of Non-normality on The Control Limits of X-bar charts", Journal of Quality Technology, 8(4), pp.183~188 (1976)
- Um, Sangjoon., "A Simultaneous Control Scheme for Mean and Fraction Nonconforming in Small Process Variation", Communications in Statistics - Theory and Methods (2013)[DOI]
- Yourstone S. A., "Non-normality and Design of Control Charts for Averages", Decision Sciences, 23, pp.1099~1113 (1992)
- Zimmer, W. J., "Variables Sampling Plans Based on Non-normality Popultions", Industrial Quality Control, 20, pp.18~26 (1963)