Multivariate Statistical Quality Control Based on Ranked Set Sampling

Hakan Eygü,M. Suphi Özçomak

doi:10.5539/ass.v14n1p1

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 T2 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 T2 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 T2 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 T2 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.

Highlights

Statistical process control can be defined as a procedure that uses statistical methods to check whether or not a manufacturing and service process is working normally, and that detects an abnormal incident and eliminates it by determining the reasons for it (Burnak, 1997:61)
In the event that the process is in control – in other words if the magnitude value d is equal to zero – it is clear that the number of out-of-control signals does not increase when Ranked set sampling (RSS), SRS, Extreme ranked set sampling (ERSS) and Median ranked set sampling (MRSS) methods are used
Data may be generated from standard multivariate normal distribution by simulation

Summary

Introduction

Statistical process control can be defined as a procedure that uses statistical methods to check whether or not a manufacturing and service process is working normally, and that detects an abnormal incident and eliminates it by determining the reasons for it (Burnak, 1997:61). The number of variables included is a significant difference between the methods, but there are much more important differences One of these differences is the fact that the variables obtained from the multivariate processes are often related to one another. Aparisi et al (2004) suggested that Hotelling’s T2 method can be used to determine whether or not a process is out-of-control with sample data randomly obtained from the process. They compared the average-run-length values of chi-square control charts using certain assumptions

Hotelling’s T 2 quality control chart

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Application

Conclusions