Fuzzy Xbar and S Control Charts Based on Confidence Intervals

Year 2021, , 114 - 131, 20.03.2021

Nilufer Pekin Alakoc

https://doi.org/10.28979/jarnas.890356

Cited By: 1

Abstract

There have been changes since the companies have realized the important role of quality improvement in their success. If they are able to produce high quality products and satisfy demands, then they can survive in competitive global markets. Quality improvement applications aim to decrease variability, which leads to less cost, production time, number of defects, scrap, rework and more customer satisfaction. Quality can be improved by reducing product variability. On the other hand, uncertainty or subjectivity is a part of many engineering and real life problems. However, these problems cannot be solved by traditional methods. This study focuses on constructing Xbar and S control charts in fuzzy environment. The approach is developed by considering the theoretical structure of the Shewhart control charts. The core of the approach depends on the combination of parametric interval estimation and fuzzy statistics. Control limits and samples are presented by fuzzy numbers which ensures to maintain fuzziness in control charts. An important property of the approach is that the fuzzy charts can be reduced to Shewhart control charts. A simulation study was conducted for the performance evaluation of fuzzy Xbar and S control charts. The proposed fuzzy control chart is sensitive to process mean shifts and variance changes, and outperforms the traditional control charts under the changes of variance. In addition, an example from the literature shows that the approach is an effective way of presenting fuzziness in the quality characteristics, which enables the approach to have high applicability to the real life problems.

Keywords

Confidence intervals, Fuzzy numbers, Fuzzy set theory, Fuzzy statistics, Quality control charts

Thanks

Dear Editor, Please find attached my manuscript entitled “Fuzzy X bar and S control Charts Based on Confidence Intervals” for your kind review. The paper demonstrates a new approach for monitoring fuzzy quality control charts and should be of interest to a broad readership including those interested in fuzzy theory and statistical quality control. The manuscript has never been published, or under the consideration for any other journal. Thank you for receiving the manuscript and considering it for review. I appreciate your time and look forward to your response. Most sincerely, Nilüfer PEKİN ALAKOÇ

Güven Aralıklarına Dayalı Bulanık Xbar ve S Kontrol Grafikleri

Abstract

Şirketler, başarılarında kalite iyileştirmenin önemli rolünü fark ettiklerinden beri değişiklikler olmuştur. Yüksek kaliteli ürünler üretebilir ve talepleri karşılayabilirlerse, rekabetçi küresel pazarlarda hayatta kalabilirler. Ürün değişkenliği azaltılarak kalite artırılabilir. Sonuç olarak, kalite iyileştirme uygulamaları, daha az maliyet, üretim süresi, hata sayısı, hurda, yeniden işleme ve daha fazla müşteri memnuniyetine yol açan değişkenliği azaltmayı amaçlamaktadır. Öte yandan, belirsizlik veya öznellik birçok mühendislik ve gerçek yaşam probleminin bir parçasıdır. Ancak, bu sorunlar geleneksel yöntemlerle çözülemez. Bu çalışma bulanık ortamda Xbar ve S kontrol grafiklerinin oluşturulmasına odaklanmıştır. Yaklaşım, Shewhart kontrol grafiklerinin teorik yapısı dikkate alınarak geliştirilmiştir. Yaklaşımın özü, parametrik aralık tahmini ve bulanık istatistiklerin kombinasyonuna bağlıdır. Kontrol limitleri ve örneklemler, kontrol grafiklerinde bulanıklığın korunmasını sağlayan bulanık sayılarla gösterilir. Yaklaşımın önemli bir özelliği, bulanık grafiklerin Shewhart kontrol grafiklerine indirgenebilmesidir. Bulanık Xbar ve S kontrol grafiklerinin performans değerlendirmesi için bir simülasyon çalışması yapılmıştır. Önerilen bulanık kontrol grafiği, süreç ortalaması kaymaları ve varyans değişikliklerine duyarlıdır ve varyans değişiklikleri altında geleneksel kontrol grafiklerinden daha iyi sonuç verir. Ek olarak, literatürden bir örnek, yaklaşımın kalite özelliklerinde bulanıklığı sunmanın etkili bir yolu olduğunu ve gerçek yaşam problemlerinde yüksek uygulanabilirliğe sahip olduğunu göstermektedir.

Keywords

Bulanık sayılar, Bulanık küme teorisi, Bulanık istatistik, Kalite kontrol şemaları, İstatistiksel aralıklar

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