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Journal articles on the topic 'Rotatable designs'

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Published: 8 September 2023

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1

Khuri, A. I. "Blocking with Rotatable Designs." Calcutta Statistical Association Bulletin 41, no. 1-4 (March 1991): 81–98. http://dx.doi.org/10.1177/0008068319910105.

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2

Kiwu, Lawrence Chizoba, Desmond Chekwube Bartholomew, Fidelia Chinenye Kiwu-Lawrence, Chukwudi Paul Obite, and Okafor Ikechukwu Boniface. "Evaluating Percentage Rotatability For The Small Box – Behnken Design." Journal of Mathematics and Statistics Studies 2, no. 2 (August 13, 2021): 16–24. http://dx.doi.org/10.32996/jmss.2021.2.2.3.

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Rotatability property for the Small Box-Behnken design is discussed in this paper. This paper aimed at applying a measure of obtaining percentage rotatability on the Small Box-Behnken designs to determine if the Small Box-behnken designs are rotatable or not and investigated the extent of rotatability in terms of percentage. The factors, q, considered range from 3 to 11. The results showed that for factors q, the Small Box-Behnken design is rotatable for q = 3 factors, near rotatable for q = 4, 7 factors and not rotatable for q = 5, 6, 8, 9, 10 and 11 factors.
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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

Streit, D. A., and B. J. Gilmore. "‘Perfect’ Spring Equilibrators for Rotatable Bodies." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 4 (December 1, 1989): 451–58. http://dx.doi.org/10.1115/1.3259020.

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A new equilibrator design approach based on system potential energy functions is presented. This approach was used to discover a group of spring equilibrators which perfectly balance a rotatable rigid link at every orientation angle through 360 deg of link rotation. Springs are connected between a rotatable link and ground, where one end of each spring is connected to the rigid link and the other end of each spring is connected to ground. The rigid link is connected to ground by a pin joint and is free to rotate about that joint. The conditions for existence and the design equations for all equilibrators which fall into this category are developed and presented. Three designs appear to offer unique advantages over the infinite number of design options available.
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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

Angelopoulos, P., H. Evangelaras, and C. Koukouvinos. "Small, balanced, efficient and near rotatable central composite designs." Journal of Statistical Planning and Inference 139, no. 6 (June 2009): 2010–13. http://dx.doi.org/10.1016/j.jspi.2008.09.001.

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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

Sawa, Masanori, and Masatake Hirao. "Characterizing D-optimal Rotatable Designs with Finite Reflection Groups." Sankhya A 79, no. 1 (October 24, 2016): 101–32. http://dx.doi.org/10.1007/s13171-016-0091-1.

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24

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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25

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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26

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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27

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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28

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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29

Hirao, Masatake, Masanori Sawa, and Masakazu Jimbo. "Constructions of Φ p -Optimal Rotatable Designs on the Ball." Sankhya A 77, no. 1 (June 12, 2014): 211–36. http://dx.doi.org/10.1007/s13171-014-0053-4.

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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

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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32

Mukhopadhyay, Anis Chandra, Srijib Bhusan Bagchi, and Rabindra Nath Das. "Improvement of Quality of a System Using Regression Designs." Calcutta Statistical Association Bulletin 53, no. 3-4 (September 2002): 225–32. http://dx.doi.org/10.1177/0008068320020305.

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Improvement of performance of a system plays an important role in reliability theory. In this article an attempt has been made to use response surface designs incorporating correlated errors for improving the performance of a system by increasing the reliability for a given mission time or increasing the mean life. Robust rotatable designs are used in estimating regression parameters by Least Squares method assuming life distribution to follow exponential distribution and experimental error following a known correlated structure.
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33

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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34

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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35

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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36

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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37

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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38

Cornelious, Nyakundi Omwando, and Evans Mbuthi Kilonzo. "Robustness of Higher Levels Rotatable Designs for Two Factors against Missing Data." International Journal of Advances in Scientific Research and Engineering 07, no. 04 (2021): 80–83. http://dx.doi.org/10.31695/ijasre.2021.34003.

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39

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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40

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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41

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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42

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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43

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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44

E.I., Jaja, Iwundu M.P., and Etuk E.H. "The Comparative Study of CCD and MCCD in the Presence of a Missing Design Point." African Journal of Mathematics and Statistics Studies 4, no. 2 (May 11, 2021): 10–24. http://dx.doi.org/10.52589/ajmss-jf1a1dza.

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The work constructed a modified central composite design from a rotatable central composite design augmented with seven center points adapted from the work of Wu and Li (2002). The comparison of the robustness of the CCD and MCCD to missing observation was investigated at various design points of factorial, axial and center points’ when the model is non-standard, using A-efficiency and the Losses associated. The results of the evaluations of the designs to missing observations are presented, and the MCCD is shown to be more A-optimal while the CCD is more robust and relatively A-efficient to a missing observation.
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45

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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46

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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47

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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48

Ukaegbu, et al., Eugene C. "of Prediction Variance Properties of Rotatable Central Composite Designs for 3 to 10 Factors." International Journal of Computational and Theoretical Statistics 2, no. 2 (November 1, 2015): 87–97. http://dx.doi.org/10.12785/ijcts/020203.

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49

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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50

Varghese, Eldho, Seema Jaggi, and V. K. Sharma. "Rotatable Response Surface Designs in the Presence of Differential Neighbour Effects from Adjoining Experimental Units." Calcutta Statistical Association Bulletin 67, no. 3-4 (September 2015): 163–86. http://dx.doi.org/10.1177/0008068320150305.

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