와이블 고장모형 하에서 경고한계를 고려한 X 관리도의 경제적 설계 = Economic Design of X-Control Charts with Warning Limits under Weibull Failure Model

다국어 초록 (Multilingual Abstract)

Since Duncan(1956) first proposed an economic design of X-control charts, most of the succeeding works on economic design of control charts assumed the exponential failure model like Duncan. Hu(1984), however,assumed a more versatile Weibull failure model to develop an economic design of X-control charts and Banerjee and Rahim(1988) further improved Hu’s design by changing the assumption of fixed-length sampling intervals to variable-length ones. In this article we follow the approach of Banerjee and Rahim(1988) but include a pair of warning limits inside the control limits in order to search for a failure without stopping the process when the sample mean falls between warning and control limits. The computational results indicate that the proposed model gives a lower cost than Banerjee and Rahim’s model unless the early failure probability of a Weibull distribution is relatively large. The reduction in cost is shown to become larger as the cost of production loss outweighs the cost of searches for a failure.

참고문헌 (Reference)

1 이태훈, "대용변수를 이용한 X 관리도의 경제적 설계" 한국품질경영학회 37 (37): 46-57, 2009

2 Duncan, A. J., "The Economic Design of X Charts used to Maintain Current Control of a Process" 51 (51): 228-242, 1956

3 Montgomery, D. C., "The Economic Design of Control Charts : A Review and Literature Survey" 12 (12): 75-87, 1980

4 Ross, S. M., "Stochastic Processes" John Wiley & Sons 1983

5 Yang, S. F., "Multivariate extension to the economical design of X control chart under Weibull shock model" 76 (76): 1035-1047, 2006

6 Rahim, M. A., "Joint Economic Design of X and R Control Charts under Weibull Shock Models" 38 (38): 2871-2889, 2000

7 Montgomery, D. C., "Introduction to Statistical Quality Control, 5th ed" John Wiley & Sons 2004

8 Hu, P. W., "Economic Design of -Control Chart Under Non-Poisson Process Shift" 87-, 1984

9 Chen, Y. S., "Economic Design of X-Control Charts with Weibull in-control times When There are Multiple Assignable Cause" 77 : 17-23, 2002

10 Banerjee, P. K., "Economic Design of X-Control Charts Under Weibull Shock Models" 30 (30): 407-414, 1988

11 Ho, C., "Economic Design of Control Charts : A Literature Review for 1981-1991" 26 (26): 39-53, 1994

12 Hooke, R., "Direct Search Solution of Numerical and Statistical Problems" 8 : 212-229, 1961

13 Page, E. S., "A Modified Control Chart with Warning Limits" 49 (49): 171-176, 1962

14 Rahim, M. A., "A Generalized Model for the Economic Design of X-Control Charts for Production Systems with Increasing Failure Rate and Early Replacement" 40 (40): 787-809, 1993

15 Gordon, G. R., "A Cost model for Economic Design of Warning Limit Control Chart Schemes" 7 (7): 319-329, 1975