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

Year 2019, , 251 - 262, 01.04.2019

Burcu Aytaçoğlu , Özlem Türker Bayrak

https://doi.org/10.19113/sdufenbed.506918

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

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