On the reliability of Shewhart-type control charts for multivariate process variability

Djauhari, Maman A.; Salleh, Rohayu Mohd; Zolkeply, Zunnaaim; Lee, Siaw Li

doi:10.1063/1.4982866

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…Dengan mengadopsi paradigma 3 sigma bahwa dari sejuta produk yang dihasilkan hanya 2700 produk yang cacat [1], konstanta K bernilai 3 jika distribusi dari statistik mutu tersebut adalah normal berdasarkan fakta bahwa jika variabel acak X~N(μ,σ 2 ) maka P(X<μ-3σ atau X> μ+3σ) ≅ 0.002700 atau P(X<μ-3σ) = P(X>μ+3σ) ≅ 0.00135 Konstanta K tidak sama dengan 3 jika statistik mutu tidak berdistribusi normal, namun dekat dengan 3 jika statistik mutu berdistribusi normal asimtotis -berdistribusi normal jika ukuran sampel menuju tak hingga. Sebagai contoh untuk statistik mutu generalized variance dan vector variance, [2] memperlihatkan bahwa ketika K = 3 maka nilai PFA (probability of a false alarm) jauh dari angka 0.002700 meskipun untuk n = 100. Untuk mencari nilai K yang lebih baik, [2] melakukan simulasi untuk ukuran sampel n = 5, 20, dan 100 dan banyaknya variabel p = 3.…”

Section: Pendahuluanunclassified

“…Sebagai contoh untuk statistik mutu generalized variance dan vector variance, [2] memperlihatkan bahwa ketika K = 3 maka nilai PFA (probability of a false alarm) jauh dari angka 0.002700 meskipun untuk n = 100. Untuk mencari nilai K yang lebih baik, [2] melakukan simulasi untuk ukuran sampel n = 5, 20, dan 100 dan banyaknya variabel p = 3. Dengan menggunakan metode simulasi serupa, pada artikel ini akan dibahas pencarian konstanta K p yang diekspresikan sebagai sebuah fungsi K p = f(n) untuk statistik mutu generalized variance.…”

Section: Pendahuluanunclassified

“…Misalkan pula S adalah matriks kovariansi sampelnya. Maka (lihat [3]) distribusi eksak dari generalized variance S sama dengan distribusi dari statistik dimana variabel acak Z 1 , Z 2 ,  , Z p saling bebas dan masing-masing berdistribusi 2 ÷ dengan derajat kebebasan n-1, n-2,  , n-p. Dengan demikian, (lihat [4]), didapatkan bahwa…”

Section: Metode Penelitianunclassified

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Pengembangan Bagan Kendali 3 Sigma Berbasis Simulasi Untuk Pengawasan Variabilitas Proses Multivariat

Sagara

Umam

2020

Kalbiscientia

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This article describes a method in developing control charts for generalized variance as a quality statistics in terms of process variability through simulation. Mathematical equation that maps sample size n and number of quality variables p onto constant multiplier of standard deviation K is obtained thorough least square method using simulated data. The constant K for a certain n and p is used for control charts with the upper control limits of UCL=μ+Kσ where μ and σ are the mean and the standard deviation of the generalized variance, respectively. The simulation of finding the constant K is used with the constraint of 3 sigma paradigm.

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Section: Pendahuluanunclassified

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Pengembangan Bagan Kendali 3 Sigma Berbasis Simulasi Untuk Pengawasan Variabilitas Proses Multivariat

Sagara

Umam

2020

Kalbiscientia

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“…Hence,considering the special requirement of the semiconductor chip's quality analysis, the method of color-spectrum is developed. By combining the theory of Shewhart-type control chart (Tong et al 2004;Djauhari et al 2017;Iglesias et al 2016) and scientific data visualization (Montgomery 2005;Chu and Wu 2016), a new method named quality-spectrum is proposed. As we know, the chip's data set is a huge, nonlinear and multivariate series that contains all information of the chip's quality.…”

Section: Introductionmentioning

confidence: 99%

Semiconductor chip’s quality analysis based on its high dimensional test data

Sun

2019

Ann Oper Res

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A semiconductor chip usually has thousands test parameters in order to guaranteed its quality. Hence, a batch of chips' test data set include thousands of float data. The primary goal of dealing with this test data is to obtain the fault parameter distribution and judge the chip's quality. It is a challenge due to the large scale and complex relationship of the test data set. This paper presents a novel method to analyze the test data set by meshing the quality theory and scientific data visualization. First, transfer the test data set to a quality classifier matrix Q: a series of quality region is defined based on quality theory, which is the baseline to classify the test data set into different group and mark them with various number. Second, form a qualityspectrum: define a color rule based on the RGB color model and color the quality classifier matrix Q. Hence chip's quality distribution could be observed through the quality-spectrum. Furthermore, by analyzing the quality-spectrum, the chip's quality could be quantitative and fault diagnose has a data basic. One case is included to illustrate appropriateness of the proposed method.

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Control Charts for Correlated Process Parameters

Volodarskyi,

Kozyr

2024

Sist. dosl. energ. (Online)

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An urgent practical task is to ensure the serviceability and safety of complex technical and information systems by monitoring their current states. Additionally, an important task is to use control charts to automatically detect the moment when certain limit states are exceeded by the characteristic features (parameters) of the technological process. In practice, it is quite common for characteristic features to be correlated. The presence of correlation affects the effectiveness of control charts in determining the moment of process disruption. The study objective is to compare the effectiveness of using different control chart types to control a correlated parameter process. The following control charts were studied: Shewhart, Hotelling, and modified Shewhart charts − principal component charts. Numerical modeling of a two-parameter process was conducted with the introduction of a non-random change in one of them at two control points, i.e., the process disorder was modeled at the appropriate time points. Subsequently, statistical studies of the modeled process were conducted using three types of control charts. The results revealed that the Shewhart charts did not reveal any process disruption, which is explained by the correlation of the parameters. Hotelling charts revealed a processing disorder at two points, but they do not indicate the cause of the disorder. The calculated partial Hotelling criterion did not indicate the cause of the disorder. The principal component charts revealed both the presence of a process disorder in two points and identified which parameter caused the disorder. This result demonstrates the effectiveness of principal component charts in detecting process disorder with correlated parameters, as well as their superiority over other charts that were studied. In addition, with an increase in the number of parameters, this method becomes even more effective, as it allows to reduce the number of parameters studied while maintaining their statistical significance. Keywords: effectiveness of control charts, Shewhart charts, Hotelling charts, principal components, statistical quality control, correlation of parameters.

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On the reliability of Shewhart-type control charts for multivariate process variability

Cited by 3 publications

References 9 publications

Pengembangan Bagan Kendali 3 Sigma Berbasis Simulasi Untuk Pengawasan Variabilitas Proses Multivariat

Pengembangan Bagan Kendali 3 Sigma Berbasis Simulasi Untuk Pengawasan Variabilitas Proses Multivariat

Semiconductor chip’s quality analysis based on its high dimensional test data

Control Charts for Correlated Process Parameters

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