Beta Control Chart for Monitoring Proportions With Application.
Abstract
In this paper we use a beta Chart to monitor fracture data. The beta Chart displays its control limits based on the beta probability distribution. This Chart was applied to a data set of contaminated peanut proportions. With toxic substances for 34 batches weighing 120 pounds and then comparing it with the traditional Shewart Chart ( p- Chart ), then a sensitivity study is performed to compare both Charts in two cases: under control and out of control. Using several values of average ratios and with different sample sizes, the evaluation is based on one of the criteria that measures the efficiency of the the evaluation is done based on one of the criteria that measures the efficiency of the Chartwhich is the Average Run Length (ARL) for both cases. , and the operating average in the first case is a function of the type one error is for comparing Charts and in order to discover the shift in the proof the first type and in the second case it is a function of the type two error The second cases Sensitivity analysis using several values of the fracture rate confirmed the superior performance of the beta Chart compared to the p Chart, resulting in the proposed approximation the value of the average operating length of ARLo in the control condition slightly greater and that the value of the average operating length in an out sidesce nario ARL1 controlismuchsmaller
References
- -Al-Sadhan, Abdullah Ibrahim, Peanuts are among the most famous foods that are contaminated with aflatoxins. The International Agency for Research on Cancer puts aflatoxins in the list of primary causes of tumors, Riyadh Magazine, June 15, 2010, Issue 15331
- - Montgomery, D. C. (2005). Introduction to Statistical Quality Control (5th ed.). New York: John Wiley & Sons. 732p .
- - Nelson, P. R. (1979). Control charts for Weibull processes with standards given. IEEE Transactions on Reliability, Knoxville, 28(3), 383387 .
- - Quesenberry, C. P. (1991). SPC Q charts for a Binomial parameter p: short and long runs. Journal of Quality Technology, Milwaukee, 23(3), 239246
- - Schader, M., & Schmid, F. (1989). Two rules of thumb for the approximation of the binomial distribution by normal distribution. The American Statistician, Alexandria, 43(1), 2324
- - Sim, C. H., & Lim, M. H. (2008). Attribute charts for zero-inflated process, communications in statistics simulations and computation. Hamilton, 37(7), 14401452 .
- - Schwertman, N. C., & Ryan, T. P. (1997). Optimal limits for attributes control charts. Journal of Quality Technology, Milwaukee, 29(1), 86
- - Aebtarm, S., & Bouguila, N. (2011). An empirical evaluation of attribute control charts for monitoring defects. Expert Systems with Applications, 38, 78697880
- - Bayer , Fabio , Tondalob , Catia and Mulle , Fernanda ,(2018 ) Beta regression control chart for monitoring fractions and proportions, Computers & Industrial Engineering 2018 1 23 April .
- - Bourke, P. D. (2008). Performance comparisons for the Synthetic control chart for detecting increases in fraction nonconforming. Journal of Quality Technology, Milwaukee, 40(4), 461475.
- - Chen, G. (1998). An improved p Chart through simple adjustments. Journal of Quality Technology, Milwaukee, 30(2), 142151
- - Fleiss, J. L., Levin, B., & Paik, M. C. (2003). Statistical methods for rates and proportions (3rd ed.). New Jersey: John Wiley & Sons, p. 760 .
- - - Gupta, A. K., Nadarajah, S., 2004. Handbook of Beta Distribution and Its Applications. CRC Press LLC.
- - Heimann, P. A. (1996). Attribute control charts with large sample sizes. Journal of Quality Technology, Milwaukee, 28(4), 451459
- - Lin, S. N., Chou, C. Y., Wang, S. L., & Liu, H. R. (2012). Economic design of autoregressive moving average control chart using genetic algorithms. Expert Systems with Applications, 39, 17931798 .
