Effect of Estimation on Simple Linear Profile Monitoring under Non-normality

Abstract

In recent years, many control charts have been proposed to monitor profiles where the quality of a process/product is expressed as function of response and explanatory variable(s). The methods mostly assume that the in control parameter values are known in Phase II analysis and innovations are normally distributed. However, in practice, the parameters are estimated in Phase I analysis and innovations may be non-normal. In this study, the performance of T², EWMA-R and EWMA-3 methods for monitoring simple linear profiles is examined via simulation where the parameters are estimated and innovations have Student’s t-distribution. As a performance measure, both the average and standard deviation of the run length is considered. Finally, some recommendations for practitioners are summarized in a table.    

Keywords

• Control chart,Run length,Exponentially weighted moving average,Profile monitoring,Statistical process control

Normal Olmayan Dağılımlar Altında Tahminin Basit Doğrusal Profil İzleme Üzerine Etkisi

Abstract

Son yıllarda, bir ürün veya sürecin kalitesinin tepki ve açıklayıcı değişken(ler) arasındaki ilişkinin fonksiyonu ile ifade edildiği profillerin izlenmesi için pek çok kalite şeması önerilmiştir. Bu yöntemlerin çoğu Faz II analizlerinde kontrol parametre değerlerinin bilindiğini ve artıkların normal dağıldığını varsaymaktadır. Oysaki uygulamada parametreler Faz I analizlerinde tahmin edilir ve artıklar normal olmayabilir. Bu çalışmada simülasyon ile artıkların t dağıldığı ve parametrelerin tahmin edildiği durumlarda basit doğrusal profillerin izlenmesi için önerilen T², EWMA-R ve EWMA-3 yöntemlerinin performansları değerlendirilmiştir. Performans ölçüsü olarak hem ortalama koşu uzunluğu hem de koşu uzunluğu standart sapması dikkate alınmıştır. En sonunda uygulayıcılar için bazı öneriler tablo halinde özetlenmiştir.    

Keywords

• Kontrol şeması,Koşu uzunluğu,Üstel ağırlıklı hareketli ortalama,Profil izleme,İstatistiksel süreç kontrol

References

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