Statistical Quality Control Based on the Process Capability Index and Control Charts with Fuzzy Approach (Case Study: Water and Wastewater Company of West Azerbaijan Province)

Document Type : Research Article


1 MSc student, Faculty of Industrial Engineering, Urmia University of Technology, Urmia, Iran

2 Urmia University of technology faculty member

3 Assistant Professor, Faculty of Civil Engineering, Urmia University of Technology


Statistical quality control is a method for monitoring the process to identify the underlying causes of changes and carrying out corrective actions. Process and capability control charts are two important applied tools for statistical quality control. In many actual systems in which accurate and certain information is not always available and the information is vague and fuzzy, fuzzy based methods can survey production process more precisely using appropriate linguistic terms and fuzzy numbers. In this study, fuzzy control charts were developed using fuzzy rules, and then the fuzzy actual capability index of process (Cpm) was investigated in order to evaluate the precision, accuracy and performance of production process in the fuzzy state. The results of the studies performed on the quality of water flowmeters in the urban water and wastewater company of West Azerbaijan province showed that using fuzzy rules provides more decision-making options to decision- makers compared to the crisp data and provided more precise division about the product quality. Also, the fuzzy actual capability index of process could propose a more precise analysis of the process taking into account the average, target value and process variance, simultaneously. The values of the fuzzy actual capability index of process in the studied case were less than one, showing that the conditions of the production process are unfavorable.


Main Subjects

[1]  Rodriguez, M., Montgomery, D. C., & Borror, C. M. (2009). Generating experimental designs involving control and noise variables using genetic algorithms. Quality and Reliability Engineering International, 25(8), 1045-1065.
[2]  Kaya, İ., & Kahraman, C. (2011). Process capability analyses based on fuzzy measurements and fuzzy control charts. Expert Systems with Applications, 38(4), 3172-3184.
[3]  Lundkvist, P. (2015). Application of Statistical Methods: Challenges Related to Continuous Industrial Processes. Luleå tekniska universitet.
[4]  Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
[5]  Bradshaw Jr, C. W. (1983). A fuzzy set theoretic interpretation of economic control limits. European Journal of Operational Research, 13(4), 403-408.
[6]  Raz, T., & Wang, J.-H. (1990). Probabilistic and membership approaches in the construction of control charts for linguistic data. Production Planning & Control, 1(3), 147-157.
[7]  Gülbay, M., & Kahraman, C. (2007). An alternative approach to fuzzy control charts: Direct fuzzy approach. Information Sciences, 177(6), 1463-1480.
[8]  Senturk, S., & Erginel, N. (2009). Development of fuzzy x~-r~ and x~-s~ control charts using α-cuts. Information Sciences, 179(10), 1542-1551.
[9]  Carot Sánchez, M. T., Sagbas, A., Juan,  S.,  &  María, J. (2013). A new approach for measurement  of the efficiency of Cpm and Cpmk control charts. International journal for quality research, 7(4), 605- 622.
[10]  Wooluru, Y., Swamy, D., & Nagesh, P. (2014). The Process Capability Analysis-A Tool For Process Performnce Measures and Metrics-A Case Study. International journal for quality research, 8(3).
[11]  Dabbagh, R., & Ahmadi, S. (2019). Evaluation of Water and Wastewater Company Performance by Using Balanced Scorecard Model. Journal of Water and Wastewater, 30(1).
[12]  S. nazif, M., Gholami Mayani, B. Roghani,  .  (2017). Development of performance indicators for evaluation of wastewater treatment plant’s units. Amirkabir Journal of Civil Engineering, Available Online from (in persian)
[13]  Shah, S., Shridhar, P., & Gohil, D. (2014). Control chart: A statistical process control tool in pharmacy. Asian Journal of Pharmaceutics (AJP): Free full text articles from Asian J Pharm, 4(3).
[14]  A.Pandurajan, R. V. (2011). Construction of α - cut fuzzy and Xbar-R and Xbar-S Control Charts Using Fuzzy Trapezoidal Number. International Journal of Research and Reviews in Applied Sciences, 9(1), 100–111.
[15]  Kane, V. E. (1986). Process capability indices. Journal of quality technology, 18(1), 41-52.
[16]  Boyles, R. A. (1991). The Taguchi capability index. Journal of quality technology, 23(1), 17-26.
[17]  N. A. Z. Ahmad Basri, M. S. R., R. Roslan, M. Mohamad, K. Khalid. (2016). Application of Fuzzy Charts for Solder Paste Thickness, Global Journal of Pure and Applied Mathematics. Global Journal of Pure and Applied Mathematics, 12(5), 4299-4315.