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1

Aparisi, Francisco, Eugenio Epprecht, Andrés Carrión, and Omar Ruiz. "The variable sample size variable dimensionT2control chart." International Journal of Production Research 52, no. 2 (2013): 368–83. http://dx.doi.org/10.1080/00207543.2013.826832.

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2

Costa, Antonio F. B. "X̄Charts with Variable Sample Size." Journal of Quality Technology 26, no. 3 (1994): 155–63. http://dx.doi.org/10.1080/00224065.1994.11979523.

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3

Wu, Jianrong. "Sample size calculation – continuous outcome variable." Southwest Respiratory and Critical Care Chronicles 6, no. 25 (2018): 60–62. http://dx.doi.org/10.12746/swrccc.v6i25.487.

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4

Park, Changsoon, and Marion R. Reynolds. "Economic design of a variable sample size -chart." Communications in Statistics - Simulation and Computation 23, no. 2 (1994): 467–83. http://dx.doi.org/10.1080/03610919408813182.

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5

Chan, Lai K., and H. J. Xiao. "Weighted attribute control charts for variable sample size." Total Quality Management 1, no. 3 (1990): 345–54. http://dx.doi.org/10.1080/09544129000000043.

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6

Costa, Antonio F. B. "X̄Chart with Variable Sample Size and Sampling Intervals." Journal of Quality Technology 29, no. 2 (1997): 197–204. http://dx.doi.org/10.1080/00224065.1997.11979750.

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7

Krejić, Nataša, and Nataša Krklec Jerinkić. "Nonmonotone line search methods with variable sample size." Numerical Algorithms 68, no. 4 (2014): 711–39. http://dx.doi.org/10.1007/s11075-014-9869-1.

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8

Shiffler, Ronald E., and Arthur J. Adams. "A Correction for Biasing Effects of Pilot Sample Size on Sample Size Determination." Journal of Marketing Research 24, no. 3 (1987): 319–21. http://dx.doi.org/10.1177/002224378702400309.

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When a pilot study variance is used to estimate σ2 in the sample size formula, the resulting [Formula: see text] is a random variable. The authors investigate the theoretical behavior of [Formula: see text]. Though [Formula: see text] is more likely to underachieve than overachieve the unbiased n, correction factors to balance the bias are provided.
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9

Kretzschmar, André, and Gilles E. Gignac. "At what sample size do latent variable correlations stabilize?" Journal of Research in Personality 80 (June 2019): 17–22. http://dx.doi.org/10.1016/j.jrp.2019.03.007.

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10

Mahadik, Shashibhushan B., and Digambar T. Shirke. "A Special Variable Sample Size and Sampling Interval Chart." Communications in Statistics - Theory and Methods 38, no. 8 (2009): 1284–99. http://dx.doi.org/10.1080/03610920802404108.

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11

Castagliola, Philippe, Ying Zhang, Antonio Costa, and Petros Maravelakis. "The Variable Sample Size X¯ Chart with Estimated Parameters." Quality and Reliability Engineering International 28, no. 7 (2011): 687–99. http://dx.doi.org/10.1002/qre.1261.

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12

Kazemzadeh, Reza Baradaran, Amirhossein Amiri, and Behnoush Kouhestani. "Monitoring simple linear profiles using variable sample size schemes." Journal of Statistical Computation and Simulation 86, no. 15 (2016): 2923–45. http://dx.doi.org/10.1080/00949655.2016.1138115.

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13

Krejić, Nataša, Nataša Krklec Jerinkić, and Andrea Rožnjik. "Variable sample size method for equality constrained optimization problems." Optimization Letters 12, no. 3 (2017): 485–97. http://dx.doi.org/10.1007/s11590-017-1143-8.

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14

Lee, Ming Ha, and Michael B. C. Khoo. "Double sampling |S| control chart with variable sample size and variable sampling interval." Communications in Statistics - Simulation and Computation 47, no. 2 (2017): 615–28. http://dx.doi.org/10.1080/03610918.2017.1288246.

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15

Zhou, Maoyuan. "Variable sample size and variable sampling interval Shewhart control chart with estimated parameters." Operational Research 17, no. 1 (2015): 17–37. http://dx.doi.org/10.1007/s12351-015-0214-9.

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16

You, Zhiying, O. Dale Williams, Inmaculada Aban, Edmond Kato Kabagambe, Hemant K. Tiwari, and Gary Cutter. "Relative efficiency and sample size for cluster randomized trials with variable cluster sizes." Clinical Trials: Journal of the Society for Clinical Trials 8, no. 1 (2010): 27–36. http://dx.doi.org/10.1177/1740774510391492.

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17

Yang, Su-Fen, and Hui-Chun Su. "Controlling-dependent process steps using variable sample size control charts." Applied Stochastic Models in Business and Industry 22, no. 5-6 (2006): 503–17. http://dx.doi.org/10.1002/asmb.657.

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18

Bittner, Alvah C., Frank J. Winn, and Stephen J. Morrissey. "Proportionally Reducing Sample-Size Requirements by Increasing Dependent-Variable Reliability." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 47, no. 18 (2003): 2000–2004. http://dx.doi.org/10.1177/154193120304701811.

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19

Aslam, Muhammad, Osama H. Arif, and Chi-Hyuck Jun. "A new variable sample size control chart using MDS sampling." Journal of Statistical Computation and Simulation 86, no. 18 (2016): 3620–28. http://dx.doi.org/10.1080/00949655.2016.1178263.

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20

Krejić, Nataša, and Nataša Krklec. "Line search methods with variable sample size for unconstrained optimization." Journal of Computational and Applied Mathematics 245 (June 2013): 213–31. http://dx.doi.org/10.1016/j.cam.2012.12.020.

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21

Chen, Yan-Kwang, and Kun-Lin Hsieh. "Hotelling’s T2 charts with variable sample size and control limit." European Journal of Operational Research 182, no. 3 (2007): 1251–62. http://dx.doi.org/10.1016/j.ejor.2006.09.046.

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22

Nanni, Marcos Rafael, Fabrício Pinheiro Povh, José Alexandre Melo Demattê, Roney Berti de Oliveira, Marcelo Luiz Chicati, and Everson Cezar. "Optimum size in grid soil sampling for variable rate application in site-specific management." Scientia Agricola 68, no. 3 (2011): 386–92. http://dx.doi.org/10.1590/s0103-90162011000300017.

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The importance of understanding spatial variability of soils is connected to crop management planning. This understanding makes it possible to treat soil not as a uniform, but a variable entity, and it enables site-specific management to increase production efficiency, which is the target of precision agriculture. Questions remain as the optimum soil sampling interval needed to make site-specific fertilizer recommendations in Brazil. The objectives of this study were: i) to evaluate the spatial variability of the main attributes that influence fertilization recommendations, using georeferenced soil samples arranged in grid patterns of different resolutions; ii) to compare the spatial maps generated with those obtained with the standard sampling of 1 sample ha-1, in order to verify the appropriateness of the spatial resolution. The attributes evaluated were phosphorus (P), potassium (K), organic matter (OM), base saturation (V%) and clay. Soil samples were collected in a 100 × 100 m georeferenced grid. Thinning was performed in order to create a grid with one sample every 2.07, 2.88, 3.75 and 7.20 ha. Geostatistical techniques, such as semivariogram and interpolation using kriging, were used to analyze the attributes at the different grid resolutions. This analysis was performed with the Vesper software package. The maps created by this method were compared using the kappa statistics. Additionally, correlation graphs were drawn by plotting the observed values against the estimated values using cross-validation. P, K and V%, a finer sampling resolution than the one using 1 sample ha-1 is required, while for OM and clay coarser resolutions of one sample every two and three hectares, respectively, may be acceptable.
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23

Hu, Naiyi, and Christopher J. Martinez. "Statistical Project of Control Chart with Variable Sample Size and Interval." Advances in Computing 2, no. 2 (2012): 9–15. http://dx.doi.org/10.5923/j.ac.20120202.02.

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24

Leoni, R. C., N. A. S. Sampaio, R. C. M. Tavora, J. W. J. Silva, and R. B. Ribeiro. "Statistical Project of Control Chart with Variable Sample Size and Interval." American Journal of Mathematics and Statistics 4, no. 4 (2014): 195–203. http://dx.doi.org/10.5923/j.ajms.20140404.04.

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25

Mahadik, Shashibhushan B. "X¯ Charts with Variable Sample Size, Sampling Interval, and Warning Limits." Quality and Reliability Engineering International 29, no. 4 (2012): 535–44. http://dx.doi.org/10.1002/qre.1403.

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26

Hu, XueLong, Philippe Castagliola, Jinsheng Sun, and Michael B. C. Khoo. "The Performance of Variable Sample Size X̄ Chart with Measurement Errors." Quality and Reliability Engineering International 32, no. 3 (2015): 969–83. http://dx.doi.org/10.1002/qre.1807.

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27

Khoo, Michael B. C., May Yen See, Nger Ling Chong, and Wei Lin Teoh. "An improved variable sample size and sampling interval S control chart." Quality and Reliability Engineering International 35, no. 1 (2018): 392–404. http://dx.doi.org/10.1002/qre.2407.

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28

Yang, Chih-Ching, and Su-Fen Yang. "Optimal variable sample size and sampling interval ‘mean squared error’ chart." Service Industries Journal 33, no. 6 (2013): 652–65. http://dx.doi.org/10.1080/02642069.2011.614345.

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29

Amiri, Amirhossein, Ali Nedaie, and Mahdi Alikhani. "A New Adaptive Variable Sample Size Approach in EWMA Control Chart." Communications in Statistics - Simulation and Computation 43, no. 4 (2013): 804–12. http://dx.doi.org/10.1080/03610918.2012.718834.

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30

Kooli, I., and M. Limam. "Economic Design of an AttributenpControl Chart Using a Variable Sample Size." Sequential Analysis 30, no. 2 (2011): 145–59. http://dx.doi.org/10.1080/07474946.2011.563703.

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31

Khaw, Khai Wah, XinYing Chew, Sin Yin Teh, and Wai Chung Yeong. "Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal." International Journal of Machine Learning and Computing 9, no. 6 (2019): 880–85. http://dx.doi.org/10.18178/ijmlc.2019.9.6.887.

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32

Ali, Sabz, Amjad Ali, Sajjad Ahmad Khan, and Sundas Hussain. "Sufficient Sample Size and Power in Multilevel Ordinal Logistic Regression Models." Computational and Mathematical Methods in Medicine 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7329158.

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For most of the time, biomedical researchers have been dealing with ordinal outcome variable in multilevel models where patients are nested in doctors. We can justifiably apply multilevel cumulative logit model, where the outcome variable represents the mild, severe, and extremely severe intensity of diseases like malaria and typhoid in the form of ordered categories. Based on our simulation conditions, Maximum Likelihood (ML) method is better than Penalized Quasilikelihood (PQL) method in three-category ordinal outcome variable. PQL method, however, performs equally well as ML method where five-category ordinal outcome variable is used. Further, to achieve power more than 0.80, at least 50 groups are required for both ML and PQL methods of estimation. It may be pointed out that, for five-category ordinal response variable model, the power of PQL method is slightly higher than the power of ML method.
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33

van Smeden, Maarten, Karel GM Moons, Joris AH de Groot, et al. "Sample size for binary logistic prediction models: Beyond events per variable criteria." Statistical Methods in Medical Research 28, no. 8 (2018): 2455–74. http://dx.doi.org/10.1177/0962280218784726.

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Binary logistic regression is one of the most frequently applied statistical approaches for developing clinical prediction models. Developers of such models often rely on an Events Per Variable criterion (EPV), notably EPV ≥10, to determine the minimal sample size required and the maximum number of candidate predictors that can be examined. We present an extensive simulation study in which we studied the influence of EPV, events fraction, number of candidate predictors, the correlations and distributions of candidate predictor variables, area under the ROC curve, and predictor effects on out-of-sample predictive performance of prediction models. The out-of-sample performance (calibration, discrimination and probability prediction error) of developed prediction models was studied before and after regression shrinkage and variable selection. The results indicate that EPV does not have a strong relation with metrics of predictive performance, and is not an appropriate criterion for (binary) prediction model development studies. We show that out-of-sample predictive performance can better be approximated by considering the number of predictors, the total sample size and the events fraction. We propose that the development of new sample size criteria for prediction models should be based on these three parameters, and provide suggestions for improving sample size determination.
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34

Mahadik, Shashibhushan B. "Variable Sample Size and Sampling Interval X¯ Charts with Runs Rules for Switching Between Sample Sizes and Sampling Interval Lengths." Quality and Reliability Engineering International 29, no. 1 (2012): 63–76. http://dx.doi.org/10.1002/qre.1293.

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35

Kim, Hajin, Myeong-Seon Gil, Yang-Sae Moon, and Mi-Jung Choi. "Variable size sampling to support high uniformity confidence in sensor data streams." International Journal of Distributed Sensor Networks 14, no. 4 (2018): 155014771877399. http://dx.doi.org/10.1177/1550147718773999.

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In order to rapidly process large amounts of sensor stream data, it is effective to extract and use samples that reflect the characteristics and patterns of the data stream well. In this article, we focus on improving the uniformity confidence of KSample, which has the characteristics of random sampling in the stream environment. For this, we first analyze the uniformity confidence of KSample and then derive two uniformity confidence degradation problems: (1) initial degradation, which rapidly decreases the uniformity confidence in the initial stage, and (2) continuous degradation, which gradually decreases the uniformity confidence in the later stages. We note that the initial degradation is caused by the sample range limitation and the past sample invariance, and the continuous degradation by the sampling range increase. For each problem, we present a corresponding solution, that is, we provide the sample range extension for sample range limitation, the past sample change for past sample invariance, and the use of UC-window for sampling range increase. By reflecting these solutions, we then propose a novel sampling method, named UC-KSample, which largely improves the uniformity confidence. Experimental results show that UC-KSample improves the uniformity confidence over KSample by 2.2 times on average, and it always keeps the uniformity confidence higher than the user-specified threshold. We also note that the sampling accuracy of UC-KSample is higher than that of KSample in both numeric sensor data and text data. The uniformity confidence is an important sampling metric in sensor data streams, and this is the first attempt to apply uniformity confidence to KSample. We believe that the proposed UC-KSample is an excellent approach that adopts an advantage of KSample, dynamic sampling over a fixed sampling ratio, while improving the uniformity confidence.
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36

Eriksson, A., B. Mehlig, M. Rafajlovic, and S. Sagitov. "The Total Branch Length of Sample Genealogies in Populations of Variable Size." Genetics 186, no. 2 (2010): 601–11. http://dx.doi.org/10.1534/genetics.110.117135.

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37

Hemel, Jan B., Frans R. Hindriks, Willem van der Slik, and Hilko van der Voet. "Influence of variable selection and sample size on classification results with classy." Analytica Chimica Acta 220 (1989): 119–34. http://dx.doi.org/10.1016/s0003-2670(00)80256-1.

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38

Krejić, Nataša, Nataša Krklec Jerinkić, and Sanja Rapajić. "Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems." Optimization 65, no. 2 (2015): 479–99. http://dx.doi.org/10.1080/02331934.2015.1062008.

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39

Tavaré, C. J., E. L. Sobel, and F. H. Gilles. "Misclassification of a prognostic dichotomous variable: Sample size and parameter estimate adjustment." Statistics in Medicine 14, no. 12 (1995): 1307–14. http://dx.doi.org/10.1002/sim.4780141204.

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40

Chang, S. M., J. Y. Tzeng, and R. B. Chen. "Fast Bayesian variable screenings for binary response regressions with small sample size." Journal of Statistical Computation and Simulation 87, no. 14 (2017): 2708–23. http://dx.doi.org/10.1080/00949655.2017.1341887.

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41

Ershadi, Mohammad Javad, Rassoul Noorossana, and Seyed Taghi Akhavan Niaki. "Economic design of phase 2 simple linear profiles with variable sample size." International Journal of Productivity and Quality Management 18, no. 4 (2016): 537. http://dx.doi.org/10.1504/ijpqm.2016.077781.

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42

Mahadik, Shashibhushan B., and Digambar T. Shirke. "A special variable sample size and sampling interval Hotelling’s T 2 chart." International Journal of Advanced Manufacturing Technology 53, no. 1-4 (2010): 379–84. http://dx.doi.org/10.1007/s00170-010-2819-8.

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43

Castagliola, Philippe, Ali Achouri, Hassen Taleb, Giovanni Celano, and Stelios Psarakis. "Monitoring the coefficient of variation using a variable sample size control chart." International Journal of Advanced Manufacturing Technology 80, no. 9-12 (2015): 1561–76. http://dx.doi.org/10.1007/s00170-015-6985-6.

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44

Kosztyán, Zsolt Tibor, and Attila Imre Katona. "Risk-Based X-bar chart with variable sample size and sampling interval." Computers & Industrial Engineering 120 (June 2018): 308–19. http://dx.doi.org/10.1016/j.cie.2018.04.052.

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45

Muhammad, Anis Nabila Binti, Wai Chung Yeong, Zhi Lin Chong, Sok Li Lim, and Michael Boon Chong Khoo. "Monitoring the coefficient of variation using a variable sample size EWMA chart." Computers & Industrial Engineering 126 (December 2018): 378–98. http://dx.doi.org/10.1016/j.cie.2018.09.045.

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46

Gnedin, Alexander V. "Sequential selection of an increasing subsequence from a sample of random size." Journal of Applied Probability 36, no. 04 (1999): 1074–85. http://dx.doi.org/10.1017/s0021900200017873.

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A random number of independent identically distributed random variables is inspected in strict succession. As a variable is inspected, it can either be selected or rejected and this decision becomes final at once. The selected sequence must increase. The problem is to maximize the expected length of the selected sequence. We demonstrate decision policies which approach optimality when the number of observations becomes in a sense large and show that the maximum expected length is close to an easily computable value.
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47

Gnedin, Alexander V. "Sequential selection of an increasing subsequence from a sample of random size." Journal of Applied Probability 36, no. 4 (1999): 1074–85. http://dx.doi.org/10.1239/jap/1032374756.

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A random number of independent identically distributed random variables is inspected in strict succession. As a variable is inspected, it can either be selected or rejected and this decision becomes final at once. The selected sequence must increase. The problem is to maximize the expected length of the selected sequence.We demonstrate decision policies which approach optimality when the number of observations becomes in a sense large and show that the maximum expected length is close to an easily computable value.
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48

Zhao, Hui Zhen, Ju Tao Zhang, and Zhong Shan Li. "Selection of Sample Size in R&R Analysis of Variable Measuring System." Advanced Materials Research 422 (December 2011): 282–85. http://dx.doi.org/10.4028/www.scientific.net/amr.422.282.

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Measurement System Analysis is of vital importance in a Six Sigma project. Variable measurement system takes the advantage of being practical and efficient. This paper focuses on the effect of sample size selection on error estimation of repeatability and reproducibility(R&R). After the discussion about the interval estimation of relevant statistics of R&R, this paper continues to analyze how the confidence interval is influenced by the number of operators, the number of samples and times of repeating measurements and a reasonable sample size in assessing the R&R of a measuring system is established for more effectiveness and efficiency.
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49

Abbas, Hussain, and Huang Hai. "Weight Size Determined Variable Step Size LMS Method for Identifying under Damped Systems." Applied Mechanics and Materials 511-512 (February 2014): 238–41. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.238.

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This paper presents a novel improvement to the LMS method which seeks to set different step sizes to different weights depending on their relative sizes. Sample numerical simulations carried out to identify different plant configurations shows that the proposed method provides an early convergence and thus identifies the plant earlier.
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50

Endrenyi, Laszlo, and Laszlo Tothfalusi. "Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs." Journal of Pharmacy & Pharmaceutical Sciences 15, no. 1 (2011): 73. http://dx.doi.org/10.18433/j3z88f.

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Purpose. To provide tables of sample sizes which are required, by the European Medicines Agency (EMA) and the U.S. Food and Drug Administration (FDA), for the design of bioequivalence (BE) studies involving highly variable drugs. To elucidate the complicated features of the relationship between sample size and within-subject variation. Methods. 3- and 4-period studies were simulated with various sample sizes. They were evaluated, at various variations and various true ratios of the two geometric means (GMR), by the approaches of scaled average BE and by average BE with expanding limits. The sample sizes required for yielding 80% and 90% statistical powers were determined. Results. Because of the complicated regulatory expectations, the features of the required sample sizes are also complicated. When the true GMR = 1.0 then, without additional constraints, the sample size is independent of the intrasubject variation. When the true GMR is increased or decreased from 1.0 then the required sample sizes rise at above but close to 30% variation. An additional regulatory constraint on the point estimate of GMR and a cap on the use of expanding limits further increase the required sample size at high variations. Fewer subjects are required by the FDA than by the EMA procedures. Conclusions. The methods proposed by EMA and FDA lower the required sample sizes in comparison with unscaled average BE. However, each additional regulatory requirement (applying the mixed procedure, imposing a constraint on the point estimate of GMR, and using a cap on the application of expanding limits) raises the required number of subjects. 
 
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