Fitting Models to Data: Residual Analysis, a Primer

Martín, Julia; Adana, David Daffos Ruiz de; Asuero, Agustín G.

doi:10.5772/68049

Cited by 36 publications

(30 citation statements)

References 120 publications

(166 reference statements)

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“…Three parts were considered: the requirements that the residues must have a normal distribution and, in considering the normal distribution of the residuals, the normal probability plot and the histogram were further considered. The final test of the residuals of the trial versus the prediction value (versus fits) was considered to be the residual from the trial order (versus order) [18,19].…”

Section: Methodsmentioning

confidence: 99%

Model Analyzing for Reusing Gold Wire Capillary in the Gold Wire Bonding Process

Phimpha¹,

Sindhuchao²

2021

IIUMEJ

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Manufacturing process improvement is necessary for manufacturers to gain business advantages. Re-using or increasing the useful lives of machine parts is considered to be a process of performance improvement. To re-use parts, the manufacturers must know the effects of the factors related to workpieces' qualities to prevent defects. This research study aims at presenting the results of analysing the effects of the factors and mathematical models for bond shear strength when reusing gold wire bonding capillary in the gold wire bonding process of integrated circuit (IC) products using design experiment. The operation factors in the reference experiment, including bond force, bond time, USG current, EFO current and EFO gap, are investigated. The Fractional Factorial Design was used to determine five factors that affect the bond shear strength. The analysis of the results show that the bond force is a significant factor where increasing bond force factors leads to increasing bond shear strength. In the end, a Regression model of bond shear strength is obtained to show the result between the bond shear strength and effect of factors. ABSTRAK: Proses pembaharuan pengilangan adalah penting untuk para pengilang bagi memperoleh keuntungan bisnes. Guna-semula atau menambah jangka hayat pada bahagian-bahagian tertentu pada mesin adalah dianggar sebahagian proses penambahbaikan prestasi mesin. Bagi mengguna semula bahagian-bahagian ini, pengilang mesti mengetahui akibat sesuatu faktor berkaitan kualiti bahan bagi mengelak kecacatan. Kajian ini bertujuan menyampaikan dapatan kajian melalui kesan faktor dan model matematik pada kekuatan ricihan ikatan apabila mengguna semula wayar emas melalui proses kapilari ikatan wayar emas pada produk litar bersepadu melalui rekaan eksperimen. Faktor operasi melalui rujukan eksperimen dari daya ikatan, masa ikatan, arus USG, arus EFO dan jarak EFO dikaji. Rekaan Faktorial Pecahan digunakan bagi mendapatkan lima faktor yang mempengaruhi kekuatan ricihan ikatan. Dapatan kajian menunjukkan daya ikatan merupakan faktor penting di mana, pertambahan faktor daya ikatan menguatkan ricihan ikatan. Akhirnya, model Regression kekuatan ricihan ikatan diperoleh bagi menjelaskan dapatan kajian antara kekuatan ricihan ikatan dan kesan faktor.

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Section: Methodsmentioning

confidence: 99%

Model Analyzing for Reusing Gold Wire Capillary in the Gold Wire Bonding Process

Phimpha¹,

Sindhuchao²

2021

IIUMEJ

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“…Ignoring the fact that nonconstant variance might result in suboptimal calibration and invalid uncertainty estimates [ 41 , 42 ], instead, weighted least square (WLS) could be used as it may not be reasonable to assume that every calibration concentration should be treated equally. One disadvantage of using WLS is the weighting is often unknown, but an appropriate weighting factor (

) for WLS may well be the reciprocal of the variance (

) for each calibration concentration.…”

Section: Methodsmentioning

confidence: 99%

Uncertainty Analysis of Fluorescence-Based Oil-In-Water Monitors for Oil and Gas Produced Water

Hansen

Jespersen

Bram

et al. 2020

Sensors

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Offshore oil and gas facilities are currently measuring the oil-in-water (OiW) concentration in the produced water manually before discharging it into the ocean, which in most cases fulfills the government regulations. However, as stricter regulations and environmental concerns are increasing over time, the importance of measuring OiW in real-time intensifies. The significant amount of uncertainties associated with manual samplings, that is currently not taken into consideration, could potentially affect the acceptance of OiW monitors and lower the reputation of all online OiW measurement techniques. This work presents the performance of four fluorescence-based monitors on an in-house testing facility. Previous studies of a fluorescence-based monitor have raised concerns about the measurement of OiW concentration being flow-dependent. The proposed results show that the measurements from the fluorescence-based monitors are not or insignificantly flow-dependent. However, other parameters, such as gas bubbles and droplet sizes, do affect the measurement. Testing the monitors’ calibration method revealed that the weighted least square is preferred to achieve high reproducibility. Due to the high sensitivity to different compositions of atomic structures, other than aromatic hydrocarbons, the fluorescence-based monitor might not be feasible for measuring OiW concentrations in dynamic separation facilities with consistent changes. Nevertheless, they are still of interest for measuring the separation efficiency of a deoiling hydrocyclone to enhance its deoiling performance, as the separation efficiency is not dependent on OiW trueness but rather the OiW concentration before and after the hydrocyclone.

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“…The data distribution for a study of the signal (μA) that is detected by an immunoassay ( [26], Ex.1) is shown in Figure 11. [24]. However, this equation cannot be used for the blank test (x = 0).…”

Section: Evaluation Of Other Data Setsmentioning

confidence: 99%

“…A partial F-test is used to select the order of the polynomial equation. Martin et al used residual analysis to verify the fitting-agreement for calibration equations and a constant variance [24]. Several studies involve nonlinear calibration curves but polynomial equations are only used to represent the data distribution [25].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

Chen

2022

Sensors

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A calibration curve is used to express the relationship between the response of the measuring technique and the standard concentration of the target analyst. The calibration equation verifies the response of a chemical instrument to the known properties of materials and is established using regression analysis. An adequate calibration equation ensures the performance of these instruments. Most studies use linear and polynomial equations. This study uses data sets from previous studies. Four types of calibration equations are proposed: linear, higher-order polynomial, exponential rise to maximum and power equations. A constant variance test was performed to assess the suitability of calibration equations for this dataset. Suspected outliers in the data sets are verified. The standard error of the estimate errors, s, was used as criteria to determine the fitting performance. The Prediction Sum of Squares (PRESS) statistic is used to compare the prediction ability. Residual plots are used as quantitative criteria. Suspected outliers in the data sets are checked. The results of this study show that linear and higher order polynomial equations do not allow accurate calibration equations for many data sets. Nonlinear equations are suited to most of the data sets. Different forms of calibration equations are proposed. The logarithmic transformation of the response is used to stabilize non-constant variance in the response data. When outliers are removed, this calibration equation’s fit and prediction ability is significantly increased. The adequate calibration equations with the data sets obtained with the same equipment and laboratory indicated that the adequate calibration equations differed. No universe calibration equation could be found for these data sets. The method for this study can be used for other chemical instruments to establish an adequate calibration equation and ensure the best performance.

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Fitting Models to Data: Residual Analysis, a Primer

Cited by 36 publications

References 120 publications

Model Analyzing for Reusing Gold Wire Capillary in the Gold Wire Bonding Process

Model Analyzing for Reusing Gold Wire Capillary in the Gold Wire Bonding Process

Uncertainty Analysis of Fluorescence-Based Oil-In-Water Monitors for Oil and Gas Produced Water

Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

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