Shewhart CUSUM ve EWMA Kontrol Grafiklerinin Makine Sanayine Uygulanması

Öz

Bu çalışmada, süreç içerisinde hedeflenen ortalamada meydana gelebilecek büyük veya küçük çaplı kaymaların tespiti amacıyla Shewhart (Değişken nicelikler için kontrol grafikleri), CUSUM (Birikimli toplam kontrol grafikleri), EWMA (Üstel ağırlıklı hareketli ortalama kontrol grafikleri) kontrol grafikleri ve Gebze-Organize sanayi bölgesinden alınan kablolara ait veriler kullanılmıştır. Düzenlenen veri setine önce Shewhart, daha sonra CUSUM ve EWMA kontrol grafikleri uygulanarak süreç hakkında bilgi edinilmiş, geçici kontrol sınırları belirlenmiş, genel ortalamadan sapmalar tespit edilmiş ve üretim süreci için ileriye dönük tahminleryapılmıştır. Uygulama sonucunda ortalama kontrol grafiğinde 2 nokta, değişim aralığı ve standart sapma kontrol grafiklerinde ise 1 nokta, belirlenen kontrol sınırlarını aşarak “kontrol dışı” sinyali vermiştir. 3σ’lık ayrılışlar dikkate alındığında, CUSUM kontrol grafiğinde 11 ve EWMA kontrol grafiğinde de 1 noktanın kontrol sınırlarını aşması ile sürecin kontrol dışı olduğugörülmüştür. Sonuç olarak, zirai üretim süreci, gıda ve makine sanayi gibi birçok farklı alanda kalite kontrol grafikleri kullanılmakta ve çalışmalarda Shewhart, CUSUM veya EWMA grafiklerinden birinin kullanılması, süreç hakkında fikir verme açısından yanıltıcı olabileceğinden, bunlardan en az ikisine göre karar verilmesinin daha uygun olacağıönerilebilir.

The Application of Shewhart CUSUM and EWMA Control Graphics on Machine Industry

Abstract

In this study, Shewhart (control charts for variable quantities), CUSUM (cumulative sum control charts ), EWMA (exponential weighted moving average control charts) control graphics and data belonging to cable taken from Gebze Organized Industrial Zone is used with the purpose of determination of big or small drifts occurring in targeted average within the process. Respectively, by applying Shewhart, CUSUM and EWMA control graphics to the coordinated data set, information about the process has been obtained, temporary control limits have been determined, deviation from general average has been identified, and prospective predictions have been made for production process. In application result, 2 points in the mean control graphic and 1 point in range and standard deviation control graphics signaled to be "out of control" exceeding designated control limits. Considering 3σ deviation, having exceeded the control limits, 11 points in the CUSUM control graphic and also 1 point in the EWMA control graphic have shown that the process was "out of control" As a result, quality control graphics are being used in many different areas such as agricultural production process, food and machine industry and as using one of the following graphics; Shewhart, CUSUM and EWMA could be misleading in terms of giving an idea about the process, it could be suggested that it will be more proper if decisions are made based on two of above mentioned graphics at least.

References

1. Başar A, Oktay E (1999). Üretimde Kalite Kontrolü, 12. Bölüm. Uygulamalı İstatistik 1, 2. Baskı. Aktif Yayınevi, Erzurum.
2. Başer G (1972). Kalite Kontrolu. İlk baskı. Çağlayan Kitapevi, İstanbul.
3. Burliskowska MD (2005). Quality estimation of process with usage control charts type X-R and quality capability of process Cp, Cpk. Journal of Materials Processing Technology, 162-163: 736-743.
4. Cavill I, Ricketts C (1974). Automated quality control for the haematology laboratory. J. Clin. Path., 27: 757-759.
5. Champ CW, Jones LA (2004). Designing phase I charts with small sample sizes. Quality and Reliability Engineering International, 20: 497-510.
6. Chang SI, Samuel TR (1998). A control point methodology for cusum control charts. Computers ind. Engng, 34(3): 565-572.
7. Coleman EP (1962). Statistical decision procedures in industry I control charts by variables. Mathematics Magazine, 35(3): 129-143.
8. Çınar A, Undey C (1999). Statistical process and controller performance monitoring. A tutorial on current methods and future directions. Proceedings of the American Control Conference, 4: 2625-2639.

9. De Vargas VCC, Lopes LFD, Souza AM (2004). Comparative study of the performance of the CuSum and EWMA control charts. Computers & Industrial Engineering, 46(4): 707-724.
10. Goel AL, Wu SM (1973). Economically optimum design of cusum charts. Management Science, 19(11): 1271-1282.
11. Huertas C, Morillo J, Usero J, Gracia-Manarillo I (2007). Validation of stir bar sorptive extraction for the determination of 24 priority substances from the european water framework directive in estuarine and sea water. Elsevier B.V. All rights reserved, 72: 1149-1156.
12. İpek H, Ankara H, Özdağ H (1999). Technical note the application of statistical process control. Minerals Engineering, 12(7): 827-835.
13. Kartal M (1999). İstatistiksel Kalite Kontrolu, Şafak Yayınevi, Sivas.
14. Ledolter J, Burrill CV (1999). Statistical Quality Control Strategies and Tools for Continval Improvement, John Wiley & Sons, New York.
15. Maravelakis PE, Panaretos J, Psarakis S (2004). EWMA chart and measurement error. Journal of Applied Statistics, 31(4): 445-455.
16. May GS, Spanos CJ (2006). Fundamentals of Semiconductor Manufacturing and Process Control. Wiley-Interscience, New Jersey.
17. Ncube MM, Woodall WH (1984). A combined Shewhart-Cumulative score quality control chart. Applied Statistics, 33(3): 259-265.
18. Neubauer AS (1997). The EWMA control chart: properties and comparison with other quality-control procedures by computer simulation. Clinical Chemistry, 43(4): 594- 601.
19. Oktay E (1998). Kalite Kontrol Grafikleri, Şafak Yayınevi, Yayın No:86, Erzurum.
20. Osanaiye PA, Talabi CO (1989). On some non-manufacturing applications of counted data cumulative sum (CUSUM) control chart schemes. The Statistician, 38(4): 251-257.
21. Park Y (2005). A Statistical Procces Control Approach for Network Intrusion Detection (Basılmamış Doktora Tezi). Georgia Institute of Technology, Georgia.
22. Stapenhurst T (2005). Mastering Statistical Process Control, 1. Edition. Elsevier Butterworth Heinemann, Jordan Hill, Oxford.
23. Svolba G, Bauer P (1999). Statistical quality control in clinical trials. Controlled Clinical Trials, 20: 519-530.