The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Identification of the out-of-control variable based on Hotelling's T2 statistic

호텔링 T2의 이상신호 원인 식별

  • Lee, Sungim (Department of Applied Statistics, Dankook University)
  • Received : 2018.10.30
  • Accepted : 2018.11.01
  • Published : 2018.12.31
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Abstract

Multivariate control chart based on Hotelling's $T^2$ statistic is a powerful tool in statistical process control for identifying an out-of-control process. It is used to monitor multiple process characteristics simultaneously. Detection of the out-of-control signal with the $T^2$ chart indicates mean vector shifts. However, these multivariate signals make it difficult to interpret the cause of the out-of-control signal. In this paper, we review methods of signal interpretation based on the Mason, Young, and Tracy (MYT) decomposition of the $T^2$ statistic. We also provide an example on how to implement it using R software and demonstrate simulation studies for comparing the performance of these methods.

호텔링 $T^2$ 통계량에 근거한 다변량 관리도는 공정의 이상상태를 식별하는 통계적 공정관리의 강력한 도구 중 하나이다. 다수의 품질 특성치를 동시에 모니터링하는데 사용된다. $T^2$ 관리도를 통해 이상신호가 탐지된다는 것은 평균 벡터의 변화가 있다는 것을 의미하게 된다. 그러나, 이러한 다변량 통계량의 신호는 이상신호에 대한 원인을 식별하기 어렵게 한다. 이 논문에서는 $T^2$ 통계량을 서로 독립인 항으로 분해한 Mason, Young, Tracy (MYT) 분해에 기반한 원인 식별 방법들을 살펴본다. 또한, R 소프트웨어를 사용하여 사례분석을 하고, 모의실험을 통해 각 절차의 성능을 비교 평가해보고자 한다.

Keywords

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Figure 3.1. R code for a phase II control chart based on the T2 statistic.

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Figure 3.2. Output for the mult.chart function: the MYT decomposition of the T2 statistic for an out-of-control observation.

Table 3.1. All possible MYT decompositions for an 18th observation which falls outside the upper control limit

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Table 3.2. Summary of the individual T2 statistics

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Table 3.3. Summary of all $T^{2}_{ij}$

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Table 4.1. Comparison of the percentages of correct identification of the cause for out-of-control signals

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