• Home
  • Submit Paper
  • Check Paper Status
  • Download Certificate/Paper
  • FAQs
  • Feedback
  • Contact Us
Email: ijraset@gmail.com
IJRASET Logo
Journal Statistics & Approval Details
Recent Published Paper
Our Author's Feedback
 •  ISRA Impact Factor 7.894       •  SJIF Impact Factor: 7.538       •  Hard Copy of Certificates to All Authors       •  DOI by Crossref for all Published Papers       •  Soft Copy of Certificates- Within 04 Hours       •  Authors helpline No: +91-8813907089(Whatsapp)       •  No Publication Fee for Paper Submission       •  Hard Copy of Certificates to all Authors       •  UGC Approved Journal: IJRASET- Click here to Check     
  • About Us
    • About Us
    • Aim & Scope
  • Editorial Board
  • Impact Factor
  • Call For Papers
    • Submit Paper Online
    • Current Issue
    • Special Issue
  • For Authors
    • Instructions for Authors
    • Submit Paper
    • Download Certificates
    • Check Paper Status
    • Paper Format
    • Copyright Form
    • Membership
    • Peer Review
  • Past Issue
    • Monthly Issue
    • Special Issue
  • Pay Fee
    • Indian Authors
    • International Authors
  • Topics
ISSN: 2321-9653
Estd : 2013
IJRASET - Logo
  • Home
  • About Us
    • About Us
    • Aim & Scope
  • Editorial Board
  • Impact Factor
  • Call For Papers
    • Submit Paper Online
    • Current Issue
    • Special Issue
  • For Authors
    • Instructions for Authors
    • Submit Paper
    • Download Certificates
    • Check Paper Status
    • Paper Format
    • Copyright Form
    • Membership
    • Peer Review
  • Past Issue
    • Monthly Issue
    • Special Issue
  • Pay Fee
    • Indian Authors
    • International Authors
  • Topics

Ijraset Journal For Research in Applied Science and Engineering Technology

  • Home / Ijraset
  • On This Page
  • Abstract
  • Introduction
  • References
  • Copyright

A note on Variance-Sum Third Order Slope Rotatable Designs

Authors: R. Md. Mastan Shareef, B. Guravaiah, G. V. S. R. Anjaneyulu

DOI Link: https://doi.org/10.22214/ijraset.2021.38512

Certificate: View Certificate

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 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 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.

Introduction

  1.  Introduction

Box and Hunter (1957) proved that a necessary and sufficient condition for a design of order d (d=1, 2…) to be rotatable.  Gardiner, Grandage and Hader (1959) constructed some third order rotatable designs for two and three factors. Das and Narasimham(1962) constructed TORDs both sequential and non-sequential, uptofifteen factors, using doubly balanced incomplete block designs and complementary BIB designs. Hader and Park (1978) introduced slope rotatability for central composite second order designs analogous to Box and Hunter (1957) central composite second order rotatable designs several authors gave various methods to construct second order slope rotatable designs. Anajaneyulu et al (1993; 1998) have introduced embedded type SOSRDs, Group-Divisible SOSRDs respectively. Anjaneyulu (1995, 2000) introduced Third Order Slope Rotatable Designs over an axial direction analogous to Third Order Rotatable Designs and constructed TOSRDs using Central Composite type Design points and Doubly Balanced Incomplete Block Designs.

Park (1987) studied the necessary and sufficient conditions for Second Order Slope RotatabilityOver All Directions.Anjaneyulu et al (2004) introduced TOSRD (OAD).Slope rotatability in axial directions introduced by Hader and Park (1978) requires that the variance of the estimated slope in every axial direction be constant at points equidistant from the design origin. Sloperotatability over all directions requires that the variance of the estimated slope averaged over all directions through a uniforms distribution be constant at points equidistant from the origin.

Anjaneyulu et al (1997) established that SOSRD (OAD) has the additional interesting property that the sum of the variances 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 an attempt is made to introduce Variance – Sum Third Order Slope Rotatable Designs.

References

[1] ANJANEYULU G. V. S. R., DATTATREYA RAO, A.V and NARASIMHAM, V. L. (1993): Embeeding in Second-Order-Slope-Rotatable Designs, Reports of Statistical Application Research, JUCE, Vol.40, Issue 4, pp:1-11. [2] ANJANEYULU G. V. S. R., DATTATREYA RAO, A.V and NARASIMHAM, V. L. (1995): Construction of Third Order Slope Rotatable Designs through Doubly Balanced Incomplete Block Designs, Gujarat Statistical Review, Vol.(21-22), pp:49-54. [3] ANJANEYULU G. V. S. R., DATTATREYA RAO, A.V and NARASIMHAM, V. L. (1997): A note On Second Order Slope Rotatable Designs Over All Directions, Communications in Statistics: Theory and Methods , Vol.(26), Issue 6, pp:1477-1479. [4] ANJANEYULU G. V. S. R., DATTATREYA RAO, A.V and NARASIMHAM, V. L. (1998): Group-Divisible Second Order Slope Rotatable Designs, Gujarat Statistical Review,Vol.(25), pp:1-2, 3-8. [5] ANJANEYULU G. V. S. R., DATTATREYA RAO, A.V and NARASIMHAM, V. L. (2000): Third Order Slope Rotatable Designs, J. Ind. Soc. For Probablity And Statistics, Vol. (5), pp: 65-74. [6] ANJANEYULU G. V. S. R.,NAGABHUSHANAM. P.,and NARASIMHAM. V. L.(2004): On Third Order Slope Rotatable Design (OAD), Journal of ISPS, Vol.8, pp:92-102. [7] BOX.G.E.P,and HUNTER, J.S. (1957): Multi-Factor Experimental Designs for Exploring Response Surfaces, Ann. Math. Statist. Vol.28,Issue 1, pp: 195-241. [8] DAS,M. N. and NARASIMHAM, V. L.(1962): Construction of Rotatable Designs Through Balanced Incomplete Block Designs, Ann. Math. Statist. Vol.33, Issue 4, pp: 1421-1439. [9] GARDINER, D. A. . GRANDAGE, A. H. E and HADER, R. J.(1959): Third OrderRotatable Designs for Exploring Response Surfaces,Ann. Math. Statist. Vol.30,Issue 4, pp: 1082-1096. [10] HADER, R.J. and PARK, S.H. (1978): Slope-Rotatable central composite designs, Technometrics, Vol.20, pp:413-417. [11] PARK.SUNG H (1987): A class of multi factor designs for estimating the slope of response surfaces, Technometrics, Nov.1987.

Copyright

Copyright © 2021 R. Md. Mastan Shareef, B. Guravaiah, G. V. S. R. Anjaneyulu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ijraset38512Mastan

Download Paper

Authors : B. GURAVAIAH

Paper Id : IJRASET38512

Publish Date : 2021-10-13

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here

About Us

International Journal for Research in Applied Science and Engineering Technology (IJRASET) is an international peer reviewed, online journal published for the enhancement of research in various disciplines of Applied Science & Engineering Technologies.

Quick links
  • Privacy Policy
  • Refund & Cancellation Policy
  • Shipping Policy
  • Terms & Conditions
Quick links
  • Home
  • About us
  • Editorial Board
  • Impact Factor
  • Submit Paper
  • Current Issue
  • Special Issue
  • Pay Fee
  • Topics
Journals for publication of research paper | Research paper publishers | Paper publication sites | Best journal to publish research paper | Research paper publication sites | Journals for paper publication | Best international journal for paper publication | Best journals to publish papers in India | Journal paper publishing sites | International journal to publish research paper | Online paper publishing journal

© 2022, International Journal for Research in Applied Science and Engineering Technology All rights reserved. | Designed by EVG Software Solutions