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Journal articles on the topic 'Third Order Rotatable Designs'

Author: Grafiati

Published: 8 September 2023

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1

Draper, Norman R., Berthold Heiligers, and Friedrich Pukelsheim. "On optimal third order rotatable designs." Annals of the Institute of Statistical Mathematics 48, no. 2 (June 1996): 395–402. http://dx.doi.org/10.1007/bf00054798.

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2

Shareef, R. Md Mastan. "A note on Variance-Sum Third Order Slope Rotatable Designs." International Journal for Research in Applied Science and Engineering Technology 9, no. 10 (October 31, 2021): 760–66. http://dx.doi.org/10.22214/ijraset.2021.38512.

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Abstract: Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for analyzing experiments where the yield is believed to be influenced by one or more controllable factors. Box and Hunter (1957) introduced rotatable designs in order to explore the response surfaces. The analogue of Box-Hunter rotatability criterion is a requirement that the variance of i yˆ(x)/ x be constant on circles (v=2), spheres (v=3) or hyperspheres (v 4) at the design origin. These estimates of the derivatives would then be equally reliable for all points (x , x ,...,x ) 1 2 v equidistant from the design origin. This property is called as slope rotatability (Hader and Park (1978)).Anjaneyulu et al (1995 &2000) introduced Third Order Slope Rotatable Designs. Anjaneyulu et al(2004) introduced and established that TOSRD(OAD) has the additional interesting property that the sum of the variance of estimates of slopes in all axial directions at any point is a function of the distance of the point from the design origin. In this paper we made an attempt to construct Variance-Sum Third Order Slope Rotatable in four levels. Keywords: Response Surface Methodology. Third Order Slope Rotatable Design; TOSRD (OAD), Variance-Sum Third Order Slope Rotatable Design.

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3

Babu, P. Seshu, and A. V. Dattatreya Rao. "ON THIRD ORDER SLOPE ROTATABLE DESIGNS USING PAIRWISE BALANCED DESIGNS." Far East Journal of Theoretical Statistics 63, no. 1 (November 10, 2021): 29–37. http://dx.doi.org/10.17654/ts063010029.

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4

Guravaiah, B. "Construction of Variance-Sum Third Order Slope Rotatable Designs." International Journal for Research in Applied Science and Engineering Technology 9, no. 3 (March 31, 2021): 1075–83. http://dx.doi.org/10.22214/ijraset.2021.33422.

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5

Rotich, Jeremy, Mathew Kosgei, and Gregory Kerich. "Optimal Third Order Rotatable Designs Constructed from Balanced Incomplete Block Design (BIBD)." Current Journal of Applied Science and Technology 22, no. 3 (July 14, 2017): 1–5. http://dx.doi.org/10.9734/cjast/2017/34937.

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6

Omwando Cornelious, Nyakundi, and Evans Mbuthi Kilonzo. "Optimal Sequential Third Order Rotatable Designs in Three, Four and Five Dimensions." International Journal of Systems Science and Applied Mathematics 6, no. 2 (2021): 35. http://dx.doi.org/10.11648/j.ijssam.20210602.11.

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7

Moore, Ronald W., K. M. Eskridge, P. E. Read, and T. P. Riordan. "OPTIMIZING CALLUS INITIATION USING STOLON NODAL SEGMENTS OF BUFFALOGRASS NE84-609 AND A RESPONSE SURFACE DESIGN." HortScience 26, no. 6 (June 1991): 766C—766. http://dx.doi.org/10.21273/hortsci.26.6.766c.

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The concept that greater callus mass will induce competence was investigated. The second most immature nodal segments were removed from heavily fertigatcd greenhouse grown plants. Shoots initiated from those nodes were only cut back to one-third their total length. They were subjected to the following treatments: (1) dicamba from 1μM to 5μM in increments of 1.0; (2) B5 medium salt concentrations from 1/3x to 5/3x in increments of 1/3; (3) sucrose levels from 2% to 10% in increments of 2; (4) casein hydrolysate from 0 to 200mg/l in increments of 50. The experiment consisted of twenty-five different treatment combinations in a central composite rotatable second order design. Explants were placed in continuous cool white fluorescent light at 26°C. Dicamba, B5 salts, and sucrose had significant effects on callus mass (p<.12), while casein hydrolysate had no notable effects on callus mass (p ≥ .57). It was determined that optimum response occurred at 5/3x concentration of B5 salts, 10% sucrose, and 5.0μM dicamba. White, compact calli were observed in treatment combinations that yielded callus fresh weights of two-hundred milligrams or higher.

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8

H. sulaymon, Abbas, Abdul-Rezzak H.A l-Karaghouli, and Sattar I. Ghulam. "Concentration of Hydrogen Peroxide by Batch Distillation Column." Iraqi Journal of Chemical and Petroleum Engineering 8, no. 3 (September 30, 2007): 13–18. http://dx.doi.org/10.31699/ijcpe.2007.3.3.

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An investigation was conducted to study the concentration of hydrogen peroxide by vacuum distillation. The effect of the process variables (such as vacuum pressure, reflux ratio, time of distillation, and packing height of the column used in the distillation process) on the concentration of hydrogen peroxide were investigated. During the third stage of distillation (95 wt.%) concentration was obtained. Box-Wilson central composite rotatable design is used to design the experimental work for the mentioned variables. It was found that the concentration of hydrogen peroxide increases with Increasing vacuum pressure, decreasing reflux ratio, increasing the time of distillation and increasing the packing height. The second order polynomial regression analysis of the objective response (concentration of hydrogen peroxide). with respect to the four variable, using statistical program gave the following equations: Y1 = 54.87 - 0.27 P - 81.45 R .+ 16.36 t + 0.69 H + 55.67 R2 - 0.0035 H2 Y2 = 104.04 - 0.44 P - 140.62 R + 19.8 t + 0.211 H + 0.0018 P+ 105.25 R2-3.33 r Y3 = 83.79 - 0.18 P - I 9.04 R + I J.14 t - 0.094 H - 0.0047 P 2 - 26.78 R2 - 2.78 t2

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9

Mukerjee, Rahul. "On fourth order rotatable designs." Communications in Statistics - Theory and Methods 16, no. 6 (January 1987): 1697–702. http://dx.doi.org/10.1080/03610928708829463.

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10

Das, Rabindra Nath. "Robust Second Order Rotatable Designs : Part I." Calcutta Statistical Association Bulletin 47, no. 3-4 (September 1997): 199–214. http://dx.doi.org/10.1177/0008068319970306.

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In Panda and Das ( Cal. Statist. Assoc. Bull., 44, 1994, 83-101) a study of rotatable designs with correlated errors was initiated and a systematic study of first order rotatable designs was attempted. Various correlated structures of the errors were considered. This two-part article relates to a thorough study on robust second order rotatable designs (SORD's) under violation of the usual homoscedasticity assumption of the distribution of errors. Under a suitable autocorrelated structure of the dispersion matrix of the error components, we examine existence and construction of robust rotatable designs. In part I, general conditions for rotatability have been derived and special cases have been examined under autocorrelated structure of the errors. Starting with the usual SORD's (under the uncorrelated error setup), we have discussed a method of construction of SORD's with correlated errors under the autocorrelated structure. An illustrative example is given at the end. In part II,we propose to examine robustness of the usual SORD's with emphasis on properties such as weak rotatability, with due consideration as to the cost involved.

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11

Emily, Otieno-Roche. "Construction of Second Order Rotatable Simplex Designs." American Journal of Theoretical and Applied Statistics 6, no. 6 (2017): 297. http://dx.doi.org/10.11648/j.ajtas.20170606.16.

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12

Das, Rabindra Nath, Partha Pal, and Sung H. Park. "Modified Robust Second-Order Slope-Rotatable Designs." Communications in Statistics - Theory and Methods 44, no. 1 (December 2014): 80–94. http://dx.doi.org/10.1080/03610926.2012.732183.

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13

Mukerjee, Rahul, and S. Huda. "Fourth-order rotatable designs: A-optimal measures." Statistics & Probability Letters 10, no. 2 (July 1990): 111–17. http://dx.doi.org/10.1016/0167-7152(90)90005-r.

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14

Das, Rabindra Nath. "Slope Rotatability with Correlated Errors." Calcutta Statistical Association Bulletin 54, no. 1-2 (March 2003): 57–70. http://dx.doi.org/10.1177/0008068320030105.

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In Das (Cal. Statist. Assoc. Bull. 47, 1997. 199 -214) a study of second order rotatable designs with correlated errors was initiated. Robust second order rotatable designs under autocorrelated structures was developed. In this paper, general conditions for second order slope rotatability have been derived assuming errors have a general correlated error structure. Further, these conditions have been simplified under the intra-class structure of errors and verified with uncorrelated case.

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15

Bhatra Charyulu, N. Ch, A. Saheb Shaik, and G. Jayasree. "New Series for Construction of Second Order Rotatable Designs." European Journal of Mathematics and Statistics 3, no. 2 (March 8, 2022): 17–20. http://dx.doi.org/10.24018/ejmath.2022.3.2.46.

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Second order Rotatable designs have good significance in response surface methodology. In this paper, two new seriesfor the construction the same using Binary Ternary Designs were presented with illustrated examples.

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16

Panda, Rajendra Nath, and Rabindra Nath Das. "First Order Rotatable Designs with Correlated Errors (Fordwce)." Calcutta Statistical Association Bulletin 44, no. 1-2 (March 1994): 83–102. http://dx.doi.org/10.1177/0008068319940107.

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Rotatability as a desirable condition for fitting a responss surface was formally introduced by Box and Hunter (1957) who also derived the rotatability conditions (on the design matrix), assuming the errors to be homoscedastic. However, it is not uncommon to come across practical situations where tho errors are correlated, violating the usual assumptions. In this paper we confine to a first order (linear) regression model with correlated errors. We examine the concept of rotatability of this model and emphasize on properties such as weak rotatability of underlying designs. Various FORDs are examined and their robustness studied. Cost consideration also leads to interesting comparisons.

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17

Das, Rabindra Nath. "Robust Second Order Rotatable Designs Part II (RSORD)." Calcutta Statistical Association Bulletin 49, no. 1-2 (March 1999): 65–78. http://dx.doi.org/10.1177/0008068319990106.

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18

Huda, S., and Rahul Mukerjee. "D-optimal measures for fourth-order rotatable designs." Statistics 20, no. 3 (January 1989): 353–56. http://dx.doi.org/10.1080/02331888908802180.

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19

Das, Rabindra Nath, Jinseog Kim, and Youngjo Lee. "Robust first-order rotatable lifetime improvement experimental designs." Journal of Applied Statistics 42, no. 9 (March 23, 2015): 1911–30. http://dx.doi.org/10.1080/02664763.2015.1014888.

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20

Victor Babu, B. Re, and V. L. Narasimhant. "Construction of second order slope rotatable designs through balanced incomplete block designs." Communications in Statistics - Theory and Methods 20, no. 8 (January 1991): 2467–78. http://dx.doi.org/10.1080/03610929108830644.

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21

Emily, Otieno-Roche. "Construction of Weighted Second Order Rotatable Simplex Designs (Wrsd)." American Journal of Theoretical and Applied Statistics 6, no. 6 (2017): 303. http://dx.doi.org/10.11648/j.ajtas.20170606.17.

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22

Nath Das, Rabindra, Sung H. Park, and Manohar Aggarwal. "On D-optimal robust second order slope-rotatable designs." Journal of Statistical Planning and Inference 140, no. 5 (May 2010): 1269–79. http://dx.doi.org/10.1016/j.jspi.2009.11.012.

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23

Das, Rabindra Nath, Sung H. Park, and Manohar Aggarwal. "Robust Second-Order Slope-Rotatable Designs with Maximum Directional Variance." Communications in Statistics - Theory and Methods 39, no. 5 (February 25, 2010): 803–14. http://dx.doi.org/10.1080/03610920902796064.

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24

Das, Rabindra Nath, and Sung Hyun Park. "On efficient robust first order rotatable designs with autocorrelated error." Journal of the Korean Statistical Society 37, no. 2 (June 2008): 95–106. http://dx.doi.org/10.1016/j.jkss.2007.08.003.

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25

Victorbabu, B. Re. "Modified second-order slope rotatable designs with equi-spaced levels." Journal of the Korean Statistical Society 38, no. 1 (March 2009): 59–63. http://dx.doi.org/10.1016/j.jkss.2008.07.001.

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26

Victorbabu, B. Re. "Modified Second Order Slope Rotatable Designs using Symmetrical Unequal Block Arrangements with two Unequal Block Sizes." Mapana - Journal of Sciences 5, no. 1 (June 21, 2006): 21–29. http://dx.doi.org/10.12723/mjs.8.3.

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27

Kim, Jinseog, Rabindra Nath Das, Poonam Singh, and Youngjo Lee. "Robust second-order rotatable designs invariably applicable for some lifetime distributions." Communications for Statistical Applications and Methods 28, no. 6 (November 30, 2021): 595–610. http://dx.doi.org/10.29220/csam.2021.28.6.595.

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28

Anjaneyulu, G. V. S. R., D. N. Varma, and V. L. Narasimham. "A note on second order slope rotatable designs over all directions." Communications in Statistics - Theory and Methods 26, no. 6 (January 1997): 1477–79. http://dx.doi.org/10.1080/03610929708831994.

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29

Koukouvinos, C., K. Mylona, A. Skountzou, and P. Goos. "A General Construction Method for Five-Level Second-Order Rotatable Designs." Communications in Statistics - Simulation and Computation 42, no. 9 (October 2013): 1961–69. http://dx.doi.org/10.1080/03610918.2012.687062.

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30

Isaac Kipkosgei, Tum. "Construction of twenty-six points specific optimum second order rotatable designs in three dimensions with a practical example." International Journal of Advanced Statistics and Probability 8, no. 1 (February 18, 2020): 1. http://dx.doi.org/10.14419/ijasp.v8i1.30122.

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This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural levels. The experiment starts from some best guess or “control” combination of the predictor variables (usually coded to x = 0 for this case x1u=30, x2u=25 and x3u =40) and experiment is performed varying them in a region around this center point.We go further to construct a specific optimum second order rotatable design of three factors in twenty-six points. The achievement of this is done with estimation of the free parameters using calculus in an existing second order rotatable design of twenty-six points. Such a design permits a response surface to be fitted easily and provides spherical information contours besides the realizations of optimum combination of ingredients in Agriculture, horticulture and allied sciences which results in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving Phosphate (x1u), Nitrogen (x2u) and Potassium (x3u) is used to represent the three factors in the coded level and converted into natural levels.

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31

Guravaiah, B. "On Construction of Three Level Variance-Sum Second Order Slope Rotatable Designs." International Journal for Research in Applied Science and Engineering Technology 9, no. 3 (March 31, 2021): 651–55. http://dx.doi.org/10.22214/ijraset.2021.33299.

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32

Arap Koske, J. K., and M. S. Patel. "Construction of fourth order rotatable designs with estimation of corresponding response surface." Communications in Statistics - Theory and Methods 16, no. 5 (January 1987): 1361–76. http://dx.doi.org/10.1080/03610928708829444.

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33

Mutiso, J. M., G. K. Kerich, and H. M. Ng’eno. "CONSTRUCTION OF FIVE LEVEL SECOND ORDER ROTATABLE DESIGNS USING SUPPLEMENTARY DIFFERENCE SETS." Advances and Applications in Statistics 49, no. 1 (September 6, 2016): 21–30. http://dx.doi.org/10.17654/as049010021.

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34

Huda, Shahariar. "On a Problem of Increasing the Efficiency of Second-order Rotatable Designs." Biometrical Journal 32, no. 4 (January 19, 2007): 427–33. http://dx.doi.org/10.1002/bimj.4710320405.

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35

Victorbabu, B. Re, and K. Rajyalakshmi. "A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs." Open Journal of Statistics 02, no. 01 (2012): 39–47. http://dx.doi.org/10.4236/ojs.2012.21005.

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36

Victorbabu, B. Re, and K. Rajyalakshmi. "A New Method of Construction of Robust Second Order Slope Rotatable Designs Using Pairwise Balanced Designs." Open Journal of Statistics 02, no. 03 (2012): 319–27. http://dx.doi.org/10.4236/ojs.2012.23040.

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37

Yamamoto, Hirotaka, Masatake Hirao, and Masanori Sawa. "A construction of the fourth order rotatable designs invariant under the hyperoctahedral group." Journal of Statistical Planning and Inference 200 (May 2019): 63–73. http://dx.doi.org/10.1016/j.jspi.2018.09.005.

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38

Mutiso, J. M., G. K. Kerich, and H. M. Ng’eno. "CONSTRUCTION OF FIVE LEVEL MODIFIED SECOND ORDER ROTATABLE DESIGNS USING SUPPLEMENTARY DIFFERENCE SETS." Far East Journal of Theoretical Statistics 52, no. 5 (November 12, 2016): 333–43. http://dx.doi.org/10.17654/ts052050333.

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39

Park, Sung H., and Hyo T. Kwon. "Slope-rotatable designs with equal maximum directional variance for second order response surface models." Communications in Statistics - Theory and Methods 27, no. 11 (January 1998): 2837–51. http://dx.doi.org/10.1080/03610929808832258.

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40

Mwan, D., M. Kosgei, and S. Rambaei. "DT- optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design." British Journal of Mathematics & Computer Science 22, no. 6 (January 10, 2017): 1–7. http://dx.doi.org/10.9734/bjmcs/2017/34288.

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41

Rajyalakshmi, K., and B. Re Victorbabu. "An Empirical Study of Second Order Rotatable Designs under Tri-Diagonal Correlated Structure of Errors using Incomplete Block Designs." Sri Lankan Journal of Applied Statistics 17, no. 1 (April 28, 2016): 1. http://dx.doi.org/10.4038/sljastats.v17i1.7842.

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42

Arshad, Hafiz Muhammad, Tanvir Ahmad, and Munir Akhtar. "Some sequential third order response surface designs." Communications in Statistics - Simulation and Computation 49, no. 7 (November 11, 2018): 1872–85. http://dx.doi.org/10.1080/03610918.2018.1508700.

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43

Kumar, Jitendra, Seema Jaggi, Eldho Varghese, Arpan Bhowmik, and Cini Varghese. "First order rotatable designs incorporating differential neighbour effects from experimental units up to distance 2." Metrika 83, no. 8 (February 15, 2020): 923–35. http://dx.doi.org/10.1007/s00184-020-00762-6.

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44

Chiranjeevi, P. "Second Order Rotatable Designs of Second Type using Symmetrical Unequal Block Arrangements with Two Unequal Block Sizes." International Journal for Research in Applied Science and Engineering Technology 9, no. 2 (February 28, 2021): 515–25. http://dx.doi.org/10.22214/ijraset.2021.33139.

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45

M. P., Iwundu, and Agadaga G. O. "Five-level Non-Sequential Third-Order Response Surface Designs and their Efficiencies." African Journal of Mathematics and Statistics Studies 5, no. 1 (February 3, 2022): 14–32. http://dx.doi.org/10.52589/ajmss-ijyzjb2c.

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New non-sequential third-order response surface designs are proposed with good optical properties. They are suitable as one-stage experimental designs for use in modeling third-order effects. The new designs are presented for cuboidal region in k dimensions and the technique employed in the construction of the non-sequential designs on the cuboidal region is flexible for use in regions that may be non-cuboidal. The new non-sequential designs lay importance on the use of axial points and two or three other blocks of points selected from a discrete design region such that the design is non-singular. For a continuous design region, uniform grids are formed over the entire design region. Five grid levels are utilized in this work thus resulting in 5^k grid points from which blocks of points are selected to form the desired non-sequential designs. The goodness of the designs is assessed via optimality and efficiency criteria and the new designs possess good optimality properties and are very high by G-efficiency.

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46

Adhikary, Basudev, and Rajendranath Panda. "Group Divisible Response Surface (GDRS) Designs of Third Order." Calcutta Statistical Association Bulletin 34, no. 1-2 (March 1985): 75–88. http://dx.doi.org/10.1177/0008068319850107.

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47

Sulochana, B., and B. Re Victor Babu. "A STUDY ON SECOND ORDER SLOPE ROTATABLE DESIGNS UNDER TRI-DIAGONAL CORRELATED STRUCTURE OF ERRORS USING A PAIR OF BALANCED INCOMPLETE BLOCK DESIGNS." Advances and Applications in Statistics 65, no. 2 (December 10, 2020): 189–208. http://dx.doi.org/10.17654/as065020189.

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48

Arshad, Hafiz Muhammad, Munir Akhtar, and Steven G. Gilmour. "Augmented Box-Behnken Designs for Fitting Third-Order Response Surfaces." Communications in Statistics - Theory and Methods 41, no. 23 (October 10, 2012): 4225–39. http://dx.doi.org/10.1080/03610926.2011.568154.

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49

Duckett, George. "Simple designs to correct all third- and fifth-order aberrations." Applied Optics 52, no. 13 (April 22, 2013): 2960. http://dx.doi.org/10.1364/ao.52.002960.

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50

Rashid, Fareeha, Atif Akbar, and Zahra Zafar. "Some new third order designs robust to one missing observation." Communications in Statistics - Theory and Methods 48, no. 24 (January 22, 2019): 6054–62. http://dx.doi.org/10.1080/03610926.2018.1528362.

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