Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Abstract
Process capability indices are considered as an important concept in statistical quality control. They have been widely used in the manufacturing industry to provide numerical measures on process performance. Moreover, some incapability indices have been introduced to account the process performance. In this paper, we focus on the one proposed by Chen ~\cite{Che:Stat}. In today's modern world, accurate and flexible information is needed. So, we apply fuzzy logic to measure the process incapability. Buckley's approach is used to fuzzify this index and to make a decision on process incapability, we utilize fuzzy critical value. Numerical examples are presented to demonstrate the performance and effectiveness of the proposed index.
[1] R. A. Boyles, The Taguchi capability index, Journal of Quality Technology, 23 (1991), 17–26. [2] J. J. Buckley, Fuzzy statistics: Hypothesis testing, Soft Computing, 9 (2005a), 512–518. [3] J. J. Buckley, Fuzzy statistics: Hypothesis testing, Soft Computing, 9 (2005b), 757–760. [4] L. K. Chan, S. W. Cheng and F. A. Spiring, A new measure of process capability Cpm, Quality Technology, 20 (1988), 162–175. [5] K. S. Chen, Incapability index with asymmetric tolerances, Statistica Sinica, 8 (1998), 253– 262. [6] M. Greenwich and B. L. Jahr-Schaffrath, A process incapability index, International Journal of Quality Reliability Management, 12 (1995), 58–71. [7] T. C. Hsiang and G. Taguchi, Tutorial on quality control and assurance the Taguchi methods, Joint Meeting of the American Statistical Association, Las Vegas, Nevada, 188 (1985). [8] B. M. Hsu and M. H. Shu, Fuzzy inference to assess manufacturing process capability with imprecise data, European Journal of Operational Research, (2008), 652–670. [9] J. M. Juran, Juran;s Quality Control Handbook, 3rd edition, McGrawHill, New York, 1974. [10] C. Kahraman and I. Kaya, Fuzzy process capability indices for quality control of irrigation water, Stochastic Environmental Research and Risk Assessment, 23(4) (2009a), 451–462. [11] C. Kahraman and I. Kaya, Fuzzy process accuracy index to evaluate risk assessment of drought effects in Turkey, Human and Ecological Risk Assessment: An International Journal, 15(4) (2009b), 789–810. [12] V. E. Kane, Process capability indices, Quality Technology, 18 (1986), 41–52. [13] I. Kaya, The process incapability index under fuzziness with an application for decision making, International Journal of Computational Intelligence Systems, 7(1) (2014), 114–128. [14] I. Kaya and H. Baracli, Fuzzy process incapability index with asymmetric tolerances, Multiple- Valued Logic and Soft Computing, 18(5-6) (2012), 493–511. [15] I. Kaya and C. Kahraman, Fuzzy process capability analyses: An application to teaching processes, Journal of Intelligent and Fuzzy Systems, 19(45) (2008), 259–272. [16] I. Kaya and C. Kahraman, Fuzzy robust process capability indices for risk assessment of air pollution, Stochastic Environmental Research and Risk Assessment, 23(4) (2009a), 529–541. [17] I. Kaya and C. Kahraman, Air pollution control using fuzzy process capability indices in sixsigma approach, Human and Ecological Risk Assessment: An International Journal, 15(4) (2009b), 689–713. [18] I. Kaya and C. Kahraman, Development of fuzzy process accuracy index for decision making problems, Information Sciences, 180(6) (2010a), 861–872. [19] I. Kaya and C. Kahraman, A new perspective on fuzzy process capability indices: Robustness, Expert Systems with Applications, 37(6) (2010b), 4593–4600. [20] I. Kaya and C. Kahraman, Fuzzy process capability analyses with fuzzy normal distribution, Expert Systems with Applications, 37(7) (2010c), 5390–5403.
[21] I. Kaya and C. Kahraman, Process capability analyses with fuzzy parameters, Expert Systems with Applications, 38(9) (2011a), 11918–11927. [22] I. Kaya and C. Kahraman, Process capability analyses based on fuzzy measurements and fuzzy control charts, Expert Systems with Applications, 38(4) (2011b), 3172–3184. [23] I. Kaya and C. Kahraman, Fuzzy process capability indices with asymmetric tolerances, Expert Systems with Applications, 38 (2011c), 14882–14890. [24] Y. H. Lee, C. C. Wei and C. L. Chang, Fuzzy design of process tolerances to maximize process capability, International Journal of Advanced Manufacturing Technology, 15 (1999), 655–659. [25] H. T. Lee, Cpk index estimation using fuzzy numbers, European Journal of Operational Research, 129 (2001), 683–688. [26] A. Parchami, M. Mashinchi, A. R. Yavari and H. R. Maleki, Process capability indices as fuzzy numbers, Austrian Journal of Statisics, 34(4) (2005), 391–402. [27] A. Parchami, M. Mashinchi and H. R. Maleki, Fuzzy confidence interval for fuzzy process capability index, Journal of Intelligent and Fuzzy Systems, 17 (2006), 287–295. [28] A. Parchami and M. Mashinchi, Fuzzy estimation for process capability indices, Information Sciences, 177 (2007), 1452–1462. [29] A. Parchami and M. Mashinchi, A new generation of process capability indices, Journal of Applied Statistics, 37(1) (2010), 77–89. [30] Z. Ramezani, A. Parchami and M. Mashinchi, Fuzzy confidence regions for the Taguchi capability index, International Journal of Systems Science, 42(6) (2011), 977–987. [31] B. Sadeghpour-Gildeh, Comparison of and process capability indices in the case of measurement error occurrence, IFSA World Congress, Istanbul, Turkey, (2003), 563–567. [32] B. Sadeghpour-Gildeh and T. Angoshtari, Monitoring fuzzy capability index ˜ Cpk by using the EWMA control chart with imprecise data, Iranian Journal of Fuzzy Systems, 10(2) (2013), 111–132. [33] K. Vannman, A unified approach to capability indices, Statistica Sinica, (5) (1995), 805–820. [34] C. Yongting, Fuzzy quality and analysis on fuzzy probability, Fuzzy Sets and Systems, 83 (1996), 283–290. [35] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353. [36] H. J. Zimmermann, Fuzzy set theory, John Wiley & Sons, Inc., 2 (2010), 317–332.
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