Functional process capability indices for a simple linear profile in fuzzy environment

Document Type : Research Paper

Authors

1 Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

In some practical applications, the quality of a process or a product is characterized by a relationship, namely a profile between a response variable and one or more explanatory variables. Assuring the capability of a profile to meet the process requirements is particularly important. Process capability indices (PCIs) are widely used to measure whether a process is capable of reproducing product items within the specification limits (SLs). Background literature on the PCIs for profiles mostly take crisp values for process data. However, in practice, the outcomes of a measurement are often imprecise. So, the basic assumption of crisp data for process capability analysis (PCA) in profiles is not valid. Hence, fuzzy methods are developed to analyze the capability of a fuzzy profile with fuzzy response data. To this end, we extend the functional approach based on fuzzy set theory for the situations in which the SLs and target values of the response variable are imprecise. The performance of the proposed indices is investigated through simulation studies. The simulation results confirm that the proposed method performs well regarding -distance between the estimated value and the true value of fuzzy PCIs. Furthermore, a case study shows the applicability of the proposed method.

Keywords

Main Subjects


Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2016a). Assessing process performance with incapability index based on fuzzy critical value. Iranian Journal of Fuzzy Systems, 13(5), 21–34.
Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2016b). Fuzzy multivariate process capability vector. Journal of Intelligent & Fuzzy Systems, 30, 1007–1017.
Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2016c). On the Multivariate Process Capabiity Vector in Fuzzy Enviorement. Iranian Journal of Fuzzy Systems, 13(5), 147–159.
Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2019). Fuzzy process capability indices for simple linear profile. Journal of Applied Statistics, 47, 2136-2158.
Abdolshah, M., Yusuff, R. M., Hong, T. S., Ismail, M. Y. B., & Sadigh, A. N. (2011). Measuring process capability index Cpmk with fuzzy data and compare it with other fuzzy process capability indices. Expert Systems with Applications, 38(6), 6452–6457.
Alevizakos, V., Koukouvinos, C., & Castagliola, P. (2018). Process capability index for Poisson regression profile based on the Spmk index. Quality Engineering, 1–9.
Alevizakos, V., Koukouvinos, C., & Lappa, A. (2019). Comparative study of the Cp and Spmk indices for logistic regression profile using different link functions. Quality Engineering, 31(3),  453–462.
Bradshaw, C. W. (1983). A fuzzy set theoretic interpretation of economic control limits. European Journal of Operational Research, 13(4), 403–408.
Buckley, J. J. (2004). Fuzzy statistics, studies in fuzziness and soft computing. New York: Springer Book.
Chen, C. C., Lai, C. M., & Nien, H. Y. (2010). Measuring process capability index Cpm with fuzzy data. Quality and Quantity, 44(3), 529–535.
Chiang, J. Y., Lio, Y. L., & Tsai, T. R. (2017). MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within-profile Autocorrelation. Quality and Reliability Engineering International, 33(5), 1083–1094.
Ebadi, M., & Amiri, A. (2012). Evaluation of process capability in multivariate simple linear profiles. Scientia Iranica, 19(6), 1960–1968.
Ebadi, M., & Shahriari, H. (2013). A process capability index for simple linear profile. International Journal of Advanced Manufacturing Technology, 64(5–8), 857–865.
Fortemps, P., & Roubens, M. (1996). Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems, 82(3), 319–330.
Ghobadi, Sh., Noghondarian, K., Noorossana, R., & Sadegh Mirhosseini, S. M. (2014). Developing a multivariate approach to monitor fuzzy quality profile. Quality and Quantity, 48(2), 817–836.
Guevara, R. D., & Vargas, J. A. (2015a). Process capability analysis for nonlinear profiles using depth functions. Quality and Reliability Engineering International, 31, 465–487.
Guevara, R. D., & Vargas, J. A. (2015b). Evaluation of process capability in multivariate nonlinear profiles. Journal of Statistical Computation and Simulation, 86(12), 2411–2428.
Guevara, R. D., Vargas, J. A., & Castagliola, P. (2016). Evaluation of process capability in non-linear profiles using Hausdorff distance. Quality Technology & Quantitative Management, 13(1), 1–15.
Hassanpour, H., Maleki, H. R., & Yaghoobi, M. A. (2009). A Goal Programming Approach to Fuzzy Liner Regression with Non-Fuzzy Input and Fuzzy Output Data. Asia-Pacific Journal of Operational Research, 26(5), 587–604.
Hong, D. H. (2004). A note on Cpk index estimation using fuzzy numbers. European Journal of Operational Research, 158, 529–532.
Hosseinifard, S. Z., & Abbasi, B. (2012a). Evaluation of process capability indices of linear profiles. International Journal of Quality and Reliability Management, 29(2), 162–176.
Hosseinifard, S. Z., & Abbasi, B. (2012b). Process capability analysis in non normal linear regression profiles. Communications in Statistics: Simulation and Computation, 41(10), 1761–1784.
Hsu, B. M., & Shu, M. H. (2008). Fuzzy inference to assess manufacturing process capability with imprecise data. European Journal of Operational Research, 186(2), 652–670.
Kahraman, C., & Kaya, İ. (2009). Fuzzy Process Accuracy Index to Evaluate Risk Assessment of Drought Effects in Turkey. Human and Ecological Risk Assessment: An International Journal, 15(4), 789–810.
Kang, L., & Albin, S. L. (2000). On-line Monitoring When the Process Yields a Linear Profile. Journal of Quality Technology, 32(4), 418–426.
Karimi Ghartemani, M., Noorossana, R., & Niaki, S. T. A. (2016). A New Approach in Capability Analysis of Processes Monitored by a Simple Linear Regression Profile. Quality and Reliability Engineering International, 32(2), 209–221.
Kaya, I., & Kahraman, C. (2010). Fuzzy process capability analyses with fuzzy normal distribution. Expert Systems with Applications, 37(7), 5390–5403.
Kaya, I., & Kahraman, C. (2011a). Process capability analyses based on fuzzy measurements and fuzzy control charts. Expert Systems with Applications, 38(4), 3172–3184.
Kaya, I., & Kahraman, C. (2011b). Process capability analyses with fuzzy parameters. Expert Systems with Applications, 38, 11918–11927.
Kwakernaak, H. (1978). Fuzzy Random Variable- I. Definations and theorems. Information Sciences, 15, 1–29.
Kwakernaak, H. (1979). Fuzzy Random Variable- II. Algorithm and Examples for the Discrete Case. Information Sciences, 17, 253–278.
Lee, H. T. (2001). Cpk index estimation using fuzzy numbers. European Journal of Operational Research, 129(3), 683–688.
Lee, K. H. (2005). First course on fuzzy theory and applications. Berlin: Springer-Verlag Berlin Heidelberg.
Maleki, M. R., Amiri, A., & Castagliola, P. (2018). An overview on recent profile monitoring papers (2008-2018) based on conceptual classification scheme. Computers & Industrial Engineering, 126, 705–728.
Moeti, M. T., Parchami, A., & Mashinchi, M. (2006). A Note on Fuzzy Process Capability Indices. Scientia Iranica, 13(4), 379–385.
Moghadam, G., Ardali, G. A. R., & Amirzadeh, V. (2015). Developing New Methods to Monitor Phase II Fuzzy Linear Profiles. Iranian Journal of Fuzzy Systems, 12(4), 59–77.
Moghadam, G., Ardali, G. A. R., & Amirzadeh, V. (2018). A novel phase I fuzzy profile monitoring approach based on fuzzy change point analysis. Applied Soft Computing Journal, 71, 488–504.
Monov, V., Sokolov, B., & Stoenchev, S. (2012). Grinding in ball mill: modeling and process control. Cybernetics andnformation Technologies, 12, 1–68.
Moradi, V., & Sadeghpour Gildeh, B. (2013). Fuzzy process capability plots for families of one-sided specification limits. International Journal of Advanced Manufacturing Technology, 64(1–4), 357–367.
Nemati Keshteli, R., Kazemzadeh, R. B., Amiri, A., & Noorossana, R. (2014a) ‘Developing functional process capability indices for simple linear profile. Scientia Iranica, 21(3), 1044–1050.
Nemati Keshteli, R., Kazemzadeh, R. B., Amiri, A., & Noorossana, R. (2014b). Functional process capability indices for circular profile. Quality and Reliability Engineering International, 30(5), 633–644.
Noghondarian, K., & Ghobadi, S. (2012). Developing a univariate approach to phase-I monitoring of fuzzy quality profiles. International Journal of Industrial Engineering Computations, 3, 829–842.
Noorossana, R., Saghaei, A., & Amiri, A. (2011). Statistical Analysis of Profile Monitoring, Wiley, New York.
Parchami, A., Mashinchi, M., Yavari, A. R., & Maleki, H. R. (2005). Process Capability Indices as Fuzzy Numbers. Austrian Journal of Statistics, 34(4), 391–402.
Parchami, A., Sadeghpour Gildeh, B., Nourbakhsh, M., & Mashinchi, M. (2013). A new generation of process capability indices based on fuzzy measurements. Journal of Applied Statistics, 41(5), 1122–1136.
Parchami, A., & Mashinchi, M. (2007). Fuzzy estimation for process capability indices. Information Sciences, 177(6), 1452–1462.
Parchami, A., & Mashinchi, M. (2010). A new generation of process capability indices. Journal of Applied Statistics, 37(1), 77–89.
Pour Larimi, A. M., Nemati Keshteli, R., & Safaei, A. S. (2019). Functional process capability indices for nonlinear profile. Journal of Industrial and Systems Engineering, 12, 1–14.
Rezaye Abbasi Charkhi, M., Aminnayeri, M., & Amiri, A. (2015). Process Capability Index for Logistic Regression Profile Based on Spmk Index. International Journal of Engineering, 28(8), 1186–1192.
Rezaye Abbasi Charkhi, M., Aminnayeri, M., & Amiri, A. (2016). Process Capability Indices for Logistic Regression Profile. Quality and Reliability Engineering International, 32(5), 1655–1661.
Sadeghpour Gildeh, B. (2011). Measurement error effects on the performance of the process capability index based on fuzzy tolerance interval. Annals of Fuzzy Mathematica and Informatics, 1(2), 17–32.
Sadeghpour Gildeh, B., & Moradi, V. (2012). Fuzzy Tolerance Region and Process Capability. Advances in Intelligent and Soft Computing, 157, 183–193.
Shahriari, H., & Sarrafian, M. (2009). Assessment of process capability in linear profiles. in 6th International Industrial Engineering Conference, Tehran, Iran. Tehran.
Shu, M. H., & Wu, H. C. (2009). Quality-based supplier selection and evaluation using fuzzy data. Computers and Industrial Engineering, 57(3), 1072–1079.
Shu, M. H., & Wu, H. C. (2012). Manufacturing process performance evaluation for fuzzy data based on loss-based capability index. Soft Computing, 16(1), 89–99.
Tsai, C. C., & Chen, C. C. (2006a). Making decision to evaluate process capability index Cp with fuzzy numbers. International Journal of Advanced Manufacturing Technology, 30(3–4), 334–339.
Tsai, C. C., & Chen, C. C. (2006b). Measuring process capability index Cpk with fuzzy data. Journal of information & optimization science, 27(3), 733–746.
Viertl, R. (2011). Statistical Methods for Fuzzy Data. First. Austria: John Wiley and Sons, Inc.
 
Wang, F. K. (2014a). A process yield for simple linear profiles. Quality Engineering, 26(3), 311–318.
Wang, F. K. (2014b). Measuring the process yield for simple linear profiles with one-sided specification. Quality and Reliability Engineering International, 30(8), 1145–1151.
Wang, F. K. (2015). Measuring the process yield for circular profiles. Quality and Reliability Engineering International, 31(4), 579–588.
Wang, F. K. (2016). Process yield analysis for multivariate linear profiles. Quality Technology and Quantitative Management, 13(2), 124–138.
Wang, F. K., & Guo, Y. C. (2014). Measuring process yield for nonlinear profiles. Quality and Reliability Engineering International, 30(8), 1333–1339.
Wang, F. K., & Tamirat, Y. (2014). Process yield analysis for autocorrelation between linear profiles. Computers and Industrial Engineering, 71(1), 50–56.
Wang, F. K., & Tamirat, Y. (2015). Process Yield Analysis for Linear Within-Profile Autocorrelation. Quality and Reliability Engineering International, 31(6), 1053–1061.
Wang, F. K., & Tamirat, Y. (2016). Process yield for multivariate linear profiles with one-sided specification limits. Quality and Reliability Engineering International, 32(4), 1281–1293.
Woodall, W. H. (2007). Current research on profile monitoring. Production, 17(3), 420–425.
Yongting, C. (1996). Fuzzy quality and analysis on fuzzy probability. Fuzzy Sets and Systems, 83, 283–290.
Zadeh, L. A. (1965). Fuzzy Sets. information and control, 8, 338–353.