Application of a Mathematical Programming Model to Solve the Confidence Interval of Process Capability Index S_(pk)

10.6186/IJIMS.2016.28.1.2

Ching-Hsin Wang；Ming-Lang Tseng；Kim-Hua Tan；Kun-Tzu Yu

Mathematical programming ； process capability index ； Monte Carlo simulation ； coverage rate

International Journal of Information and Management Sciences

28卷1期（2017 / 03 / 01）

11 - 23

英文

This study developed a mathematical programming model to determine confidence intervals of S_(pk) by converting index S_(pk) into a function of μ_y = (μ - T ) and σ_y =σ/d, constructing the feasible region of joint confidence interval with μ_y and σ_y, and then regarding S_(pk)(μ_y, σ_y) as an objective function, to overcome the shortage of point-estimate and interval-estimate calculations of the past process capability index. Then, Monte Carlo simulation was used to analyze the coverage rate in order to validate the accuracy of the proposed method. Our results demonstrate the efficacy of the proposed evaluation model using quartz crystal oscillators, a passive component commonly used in communication devices. The proposed method eliminates the complex complexity of statistical methods, and the results are optimal values largely robust to errors. The proposed model can also be applied to other complex process evaluation indices, thereby presenting manufacturers with an efficient and convenient method for the assessment of process capability.

1. Boyles, R. A.(1991).The Taguchi capability index.Journal of Quality Technology,23,17-26.
2. Boyles, R. A.(1994).Process capability with asymmetric tolerances.Communications in Statistic: Computer and Simulation,23,615-643.
3. Buck, D. L.(2002).Digital design for a self-temperature compensating oscillator.IEEE International Frequency Control and PDA Exhibition
4. Chan, L. K.,Cheng, S. W.,Spring, F. A.(1998).A new measure of process capability Cpm.Journal of Quality Technology,20,162-175.
5. Chang, T. C.,Wang, K. J.,Chen, K.-S.(2014).Capability performance analysis for processes with multiple characteristics using accuracy and precision.Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture,228,766-776.
6. Chen, J. P.,Chen, K. S.(2004).Comparison the capabilities of two process using Cpm.Journal of Quality Technology,36,329-335.
7. Chen, K. S.,Pearn, W. L.(1997).An application of non-normal process capability indices.Quality and Reliability Engineering International,13,355-360.
8. Chen, K. S.,Pearn, W. L.,Lin, P. C.(2003).Capability measures for processes with multiple characteristics.Quality and Reliability Engineering International,19,101-110.
9. Chen, K. S.,Wang, C. H.,Chen, H. T.(2006).A MAIC approach to TFT-LCD panel quality improvement.Microelectronics Reliability,46,1189-1198.
10. Chen, K. S.,Yang, S. L.,Chen, H. T.(2015).Process improvement capability index with cost -a modeling method of mathematical programming.Source of the Document Applied Mathematical Modelling,39,1577-1586.
11. Cheng, F. T.,Chen, K. S.,Sung, W. P.(2005).Evaluation model for the performance of multi-manufacturing schedule.International Journal of Advanced Manufacturing Technology,27,345-350.
12. Chou, Y. M.,Owen, D. B.(1989).On the distribution of the estimated process capability Indices.Communication in statistic - Theory and Method,18,4549-4560.
13. Juran, J. M.(1974).Juran's Quality Control Handbook.New York:McGraw Hill.
14. Kane, V. E.(1986).Process capability indices.Journal of Quality Technology,18,41-52.
15. Kunikiyo, T.,Takenaka, M.,Kamakura, Y.,Yamaji, M.,Mizuno, H.,Morifuji, M.,Taniguchi, K.,Hamaguchi, C.(2009).A Monte Carlo simulation of anisotropic electron transport in silicon including full band structure and anisotropic impact-ionization model.Journal of Applied Physics,75,297-312.
16. Lin, C. J.,Pearn, W. L.(2010).Process selection for higher production yield based on capability index Spk.Quality and Reliability Engineering International,26,247-258.
17. Pearn, W. L.,Chen, K. S.(1998).New generalization of the process capability index Cpk.Journal of Applied Statistics,25,801-810.
18. Pearn, W. L.,Cheng, Y. C.(2007).Estimating process yield based on Spk for multiple samples.International Journal of Production Research,45,49-64.
19. Pearn, W. L.,Chuang, C. C.(2004).Accuracy analysis of the estimated process yield based on Spk.Quality and Reliability Engineering International,20,305-316.
20. Taguchi, G.(1991).Introduction to Quality Engineering, Asian Productivity Organization.White Plains, New York:UNIPUB.
21. Wang, C. C.,Chen, K. S.,Wang, C. H.,Chang, P. H.(2011).Application of 6-sigma Design System to Developing an improvement model for multi-process multi-characteristic product quality.Proceedings of the Institution of Mechanical Engineers, Part B, Journal of Engineering Manufacture,225,1205-1216.
22. Wu, C. W.,Liao, M. Y.(2014).Fuzzy nonlinear programming approach for evaluating and ranking process yields with imprecise data.Fuzzy Sets and Systems,246,142-155.
23. Wu, C. W.,Liu, S. W.,Lee, A. H. I.(2015).Design and construction of a variables multiple dependent state sampling plan based on process yield.European Journal of Industrial Engineering,9,819-838.