Multivariate Statistical Quality Control Based on Ranked Set Sampling

Abstract

The sample of the study was formed using simple random sampling, ranked set sampling, extreme ranked set sampling and median ranked set sampling. At the end of this process, the researcher created Hotelling's T 2 control charts, a multivariate statistical process control method. The performances of SRS, RSS, ERSS and MRSS sampling methods were compared to one another using these control charts. A simulation was performed to see the average run-length values for Hotelling's T 2 control charts, and these findings were also used for the comparison of the sampling performances.At the end of the study, the researcher formed a sample using median ranked set sampling and created the Hotelling's T 2 control chart. As a result of this operation, the researcher found that there was an out-of-control signal in the process, while there was no such signal in other sampling methods. When the average run-length values obtained from Hotelling's T 2 control charts were compared, it was seen that a shift in the process was detected by the ranked set sampling earlier, when compared to other sampling methods. This paper it can be said that the methods used are unique to the literature because they are applied to multivariate data.

Jackknife ve Bootstrap Yöntemlerine İlişkin Bir Uygulama

“…Ayrıca örnek hacmini artırmadan ana kütle parametresi ile tahmin edici arasındaki sapmanın azalacağından bahsetmiştir. Bu bağlamda örnek hacminin farklı örnekleme yöntemleriyle de araştırıldığında örnek hacminin belli bir sayıdan sonra anakütle parametresi ile tahmin edici arasındaki sapmanın azalacağı belirlenmiştir [32]. [33]; tahmin edicinin, parametre için doğru bilgi taşıyıp taşımadığına cevap aramak üzere, standart sapmanın bootstrap tahminini ele almışlardır.…”

Generalized Hotelling T2 control chart based on bivariate ranked set techniques with runs rules

“…Eygü and Özçomak (2017) initiated the multivariate control chart procedure for ranked set schemes. Later, Mehmood et al (2019) suggested the Hotelling T 2 control chart under BVRST with the classical runs rule.…”

“…Their results revealed that the Hotelling T 2 control chart under BVRST has extraordinary performance relative to the existing control chart under SRS (Hotelling, 1947). Since the studies by Eygü and Özçomak (2017) and Mehmood et al (2019) are dependent on the classical runs rule, they cannot be considered effective for detection of small and moderate shifts. The disadvantage of the classical runs rule with theoretical justification is described above in detail.…”

“…This study aims to resolve the limitations and also enhance the functionality of existing control charts (Eygü and Özçomak, 2017; Hotelling, 1947; Mehmood et al, 2019) by considering the above elaborated motivations. In this regard, we will propose a generalized Hotelling T 2 control chart under BVRST with runs rules.…”