scholarly journals Second Order Slope Rotatable Designs under Tri-diagonal Correlation Structure of Errors Using a Pair of Incomplete Block Designs

2020 ◽  
pp. 1-11
Author(s):  
B. Sulochana ◽  
B. Re. Victorbabu
Keyword(s):  
Response Surface ◽  
Design Criterion ◽  
Second Order ◽  
Correlation Structure ◽  
Block Designs ◽  
Response Surface Design ◽  
Surface Design ◽  
Response Surface Designs ◽  
Block Sizes ◽  
Important Design

Box and Hunter [1] introduced the concept of rotatability for response surface designs. The concept of slope-rotatability was introduced by Hader and Park [2] as an analogous to rotatability property, which is an important design criterion for response surface design. Slope-rotatable design is that of which the variance of partial derivative is a function of distance from the design (d). Recently, a few measures of slope-rotatability for a given response surface design was introduced. In this paper, a new method of slope rotatability for second order response surface designs under tri-diagonal correlation structure of errors using a pair of symmetrical unequal block arrangements with two unequal block sizes is studied. Further, a study on the dependence of variance function of the second order response surface at different design points for different values of tri-diagonal correlation coefficient ρ which lies between -0.9 to 0.9 and the distance from centre (d) is suggested.

scholarly journals A Measure for Evaluating the Degree of Slope Rotatability in Three Level Second Order Slope Rotatable Designs

2019 ◽  
pp. 1-12
Author(s):  
Chepkemoi Ednah ◽  
John Muindi Mutiso ◽  
Fredrick Oluoch Nyamwala
Keyword(s):  
Response Surface ◽  
Block Design ◽  
Design Criterion ◽  
Second Order ◽  
Response Surface Design ◽  
Surface Design ◽  
Incomplete Block Design ◽  
Exact Slope ◽  
Balanced Incomplete Block ◽  
Rotatable Design

Response surface methodology (RSM) often deals with a natural and desirable property rotatability, which requires that, the variance of the predicted response at a point remains constant at all such points that are equidistant from the design center. To achieve stability in prediction variance, this important property of rotatability was developed. Analogous to rotatability, the concept of slope-rotatability has been progressed. The idea of slope - rotatability is an important design criterion for response surface design. Recently, in the design of experiments for response surface analysis, attention has been focused on the estimation of dierences in response rather than absolute value of the response mean itself. The slope-rotatable design is that of which the variance of partial derivative is only a functions of : distance from the design center. If circumstances are such that exact slope rotatability is unattainable because of more cost and time, and more important restrictions such as orthogonal blocking it is still a good idea to make the design as slope rotatable as possible. Thus, it is important to measure the extent of deviation from slope rotatability. In this study, a new measure of the degree of slope-rotatability for three level second-order slope rotatable designs using a pair of a partially balanced incomplete block design is suggested that enables us to assess the degree of slope-rotatability for a given response surface design. This determines the degree slope rotatability for the design when subjected to existing conditions of measure. The measure takes the value zero when the design is exact slope-rotatable, and becomes larger as the design deviates from being slope-rotatable design.

scholarly journals Evaluating Measure of Reformed Rotatability for Second Degree Polynomial Using a Pair of Incomplete Block Designs with Two Unequal Block Sizes

2021 ◽  
pp. 59-70
Author(s):  
P. Jyostna ◽  
B. Re Victorbabu
Keyword(s):  
Response Surface ◽  
Block Designs ◽  
Incomplete Block ◽  
Response Surface Design ◽  
Degree Polynomial ◽  
Surface Design ◽  
Block Sizes ◽  
Second Degree

In this paper, a study on evaluating measure of reformed rotatability for second degree polynomial using a pair of incomplete block designs with two unequal block sizes (like symmetrical unequal block arrangements with two unequal block sizes) is suggested which enables us to assess the degree of reformed (modified) rotatability for a given response surface design.

scholarly journals Lab-Scale Fiber Spinning Experimental Design Cost Comparison

2010 ◽  
Vol 5 (1) ◽  
pp. 155892501000500 ◽  
Author(s):  
Jeffrey C. Moreland ◽  
Julia L. Sharp ◽  
Philip J. Brown
Keyword(s):  
Factorial Design ◽  
Response Surface ◽  
Second Order ◽  
Fiber Spinning ◽  
Raw Material ◽  
Time Cost ◽  
Response Surface Design ◽  
Surface Design ◽  
Split Plot ◽  
Plot Design

Many statistical experimental designs are too costly or require too much raw material to be feasible for lab-scale fiber spinning experiments. In this study a four-factor response surface design is presented to study the fiber spinning process in detail at the lab scale. The time, cost, and amount of raw material required to execute the proposed design are compared to the typical completely randomized 24 factorial design used in fiber spinning experiments and also to a standard four-factor response surface design. Sample fiber data as well as analysis from a typical statistical software package is provided to further demonstrate the differences between each design. By designating some treatment factors in the design as hard-to-change, split-plotting is used to reduce the time, cost, and amount of raw material required to complete the experiment. The proposed split-plot design is faster and less expensive than a typical factorial design and has the advantage of fitting a more complex second-order model to the system. When compared to a standard response surface design, the proposed split-plot design provides the same second-order modeling capabilities but reduces the cost of the experiment by 53%, the total time by 36%, and the amount of polymer required by 24%. Thus, a split-plot response surface design based on hard-to-change factors is recommended in lab-scale spinning.

scholarly journals Evaluating Measure of Modified Rotatability for Second Degree Polynomial Design Using Balanced Incomplete Block Designs

2021 ◽  
pp. 47-59
Author(s):  
P. Jyostna ◽  
B. Re. Victor Babu
Keyword(s):  
Response Surface ◽  
Design Criterion ◽  
Block Designs ◽  
Incomplete Block ◽  
Degree Polynomial ◽  
Balanced Incomplete Block Designs ◽  
Number Of Factors ◽  
Response Surface Designs ◽  
Balanced Incomplete Block ◽  
Second Degree

Box and Hunter (1957) introduced the concept of rotatability. It is an important design criterion for response surface methodology (RSM). In this paper, evaluating measure of modified rotatability for second degree polynomial design using balanced incomplete block designs (3 ≤ V ≤ 11 : v-number of factors) which enables us to assess the degree of modified rotatability for a given response surface designs at different values of rotatability is recommended.

scholarly journals Measure of Slope Rotatability for Second Order Response Surface Designs Under Tri-Diagonal Correlation Error Structure Using Symmetrical Unequal Block Arrangements with Two Unequal Block Sizes

2021 ◽  
Vol 9 (VII) ◽  
pp. 2409-2424
Author(s):  
Sulochana B
Keyword(s):  
Response Surface ◽  
Second Order ◽  
Error Structure ◽  
Response Surface Designs ◽  
Block Sizes

In this paper, measure of slope rotatability for second order response surface designs using symmetrical unequal block arrangements with two unequal block sizes under tri-diagonal correlation error structure is suggested and illustrated with examples.

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