Fundamentals of Multivariate Analysis Part II. Inference About Two Treatments

Kramer, Clyde Young; Jensen, D. R.

doi:10.1080/00224065.1969.11980372

Cited by 26 publications

(11 citation statements)

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“…Kramer and Jensen showed that G statistic follows a chi‐square distribution with p ( p + 1 )/ 2 degrees of freedom asymptotically. Therefore, one can use the following control limits for this chart:

LCL = χ_{\frac{α}{2}, \frac{p ((), p + 1)}{2}}^{2} and UCL = χ_{1 - \frac{α}{2}, \frac{p ((), p + 1)}{2}}^{2} .

…”

Section: Multivariate Control Charts For Process Variabilitymentioning

confidence: 99%

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Mostajeran

Iranpanah

Noorossana

2017

Appl Stoch Models Bus & Ind

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Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.

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LCL = χ_{\frac{α}{2}, \frac{p ((), p + 1)}{2}}^{2} and UCL = χ_{1 - \frac{α}{2}, \frac{p ((), p + 1)}{2}}^{2} .

…”

Section: Multivariate Control Charts For Process Variabilitymentioning

confidence: 99%

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Mostajeran

Iranpanah

Noorossana

2017

Appl Stoch Models Bus & Ind

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“…Dalam mengkontruksi diagram kontrol G, Levinson, dkk memperluas konsep statistik G yang diusulkan oleh Kramer dan Jensen [6]. Kramer dan Jensen mengusulkan statistik G untuk menguji kesamaan dua matriks kovarian sampel (S1 dan S2).…”

Section: Diagram Kontrol Gunclassified

“…Menurut Kramer dan Jensen[6] statistik G berdistribusi chi-square dengan derajat kebebasan adalah taraf kepercayaan yang diinginkan. Menurut Levinson, dkk [4].…”

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Efektivitas Kinerja Diagram Kontrol G

Delsen

2015

BAREKENG: J. Mat. & Ter.

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AbstrakStatistical Proses Control (SPC) merupakan metode dalam ilmu statistika yang bertujuan untuk mengontrol suatu proses. Dalam mencapai tujuan SPC maka metode yang dapat digunakan adalah Diagram Kontrol (Control Chart). Diagram kontrol merupakan sebuah grafik yang memberi gambaran tentang perilaku sebuah proses. Diagram kontrol dapat dibagi menjadi dua berdasarkan banyaknya karakterisrtik kualitas yang diamati, yaitu diagram kontrol univariat dan diagram kontrol multivariat. Dalam memonitor proses membutuhkan dua hal penting, yaitu memonitor mean proses dan memonitor variabilitas proses [1]. Kinerja dari suatu diagram kontrol dapat dilihat dari seberapa cepat suatu diagram kontrol dapat mengidentifikasi sinyal out of control. Salah satu metode untuk melihat kinerja diagram kontrol adalah Average Run Length (ARL). Noya Van Delsen dan Mashuri dalam [2], membandingkan kinerja diagram kontrol G dan diagram kontrol yang berdasar pada ARL. Namun penelitian tersebut dibatasi pada jumlah karakteristik kualitas yang digunakan. Sehingga penelitian ini bertujuan untuk meninjau kinerja diagram kontrol G yang berdasar pada ARL, dengan jumlah karakteristik kualitas yang bervariasi. Hasil simulasi ARL menunjukkan bahwa kinerja diagram kontrol G sangat efisien walaupun menggunakan jumlah karakteristik karakteristik yang bervariasi. Ini dibuktikan dengan interval nilai ARL yang saling mendekati. AbstractStatistical Proces Control (SPC) is a statistical method that useful for monitoring process. In achieving the goals of the SPC, the method of control chart is used. Control chart is a chart that gives an overview of the behavior of a process. Based on the number of quality characteristics which observed, control chart is divided into univariate control chart and multivariate control chart. In monitoring process, it requires two important things, which are monitoring mean process and variability process [1]. The performance of a control chart can be seen from how fast a control chart can identify the signal out of control. A method to see performance of control chart is called the Average Run Length (ARL). Noya Van Delsen and Mashuri in [2] compared the performance of G control chart with control chart that based on the ARL. But their research is limited to the number of quality characteristic. So this research aims to look at the performance of G control chart with a varied of quality characteristics. The results of ARL show that the performance of G control chart is efficient even only use a varied of quality characteristics. This is proved by interval of ARL values which are approaching each other.

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“…The proposed test is derived from the work described in Kramer and Jensen (1969), which is as follows: The test we are proposing overcomes this deficiency.…”

Section: Modelmentioning

confidence: 99%

A Multivariate Subgroup Rationality Test

Holmes¹,

Mergen

2004

Quality Engineering

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In one of our recent articles (Holmes, D. S., Mergen, A. E. (2003). Testing rationality of subgroups in multivariate control charts. In: The 2003 Northeast Decision Sciences Institute Meeting Proceedings. Providence, Rhode Island, March 27-29, Fariborz Partovi, 286-288.) we proposed an aggregate measure for checking rationality of the subgroups in multivariate control charts, such as T 2 charts. The purpose of this article is to build on that measure and propose a similar multivariate test to check the rationality of each subgroup used in the chart. The proposed test uses the statistical process control (SPC) approach; i.e., maintains the time sequence of the data. The method is based on a test for equality of two covariance matrices (Kramer, C. Y., Jensen, D. R. (1969). Fundamentals of multivariate analysis-part II: inference about two treatments. Journal of Quality Technology 1(3):189-204.). The first covariance matrix is the one normally described in statistical literature (for example Johnson and Wichern (Johnson, R. A., Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. New Jersey: Prentice Hall 92-122.) The second matrix used in the test is the multivariate mean square successive difference (MSSD) covariance matrix (Holmes, D. S., Mergen, A. E. (1993). Improving the performance of T-square control chart. Quality Engineering 5(4):619-625.). If the test indicates a significant difference of these two matrices, this is an indication of the lack of rationality of the corresponding subgroup(s) being used on the multivariate control chart. The test result for each subgroup can then be plotted on a control chart to explore which subgroup(s) may be the cause of the nonrationality. Two examples of the use of the proposed method are given.

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Fundamentals of Multivariate Analysis Part II. Inference About Two Treatments

Cited by 26 publications

References 0 publications

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Efektivitas Kinerja Diagram Kontrol G

A Multivariate Subgroup Rationality Test

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