Open Access   Article Go Back

Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population

J.R. Singh1 , A. Sanvalia2

  1. School of Studies in Statistics,Vikram University, Ujjain, India.
  2. School of Studies in Statistics,Vikram University, Ujjain, India.

Correspondence should be addressed to: arvindsanvalia@gmail.com.

Section:Research Paper, Product Type: Journal Paper
Volume-5 , Issue-10 , Page no. 153-169, Oct-2017

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v5i10.153169

Online published on Oct 30, 2017

Copyright © J.R. Singh, A. Sanvalia . 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.

View this paper at   Google Scholar | DPI Digital Library

XML View
PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: J.R. Singh, A. Sanvalia, “Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population,” International Journal of Computer Sciences and Engineering, Vol.5, Issue.10, pp.153-169, 2017.

MLA Style Citation: J.R. Singh, A. Sanvalia "Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population." International Journal of Computer Sciences and Engineering 5.10 (2017): 153-169.

APA Style Citation: J.R. Singh, A. Sanvalia, (2017). Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population. International Journal of Computer Sciences and Engineering, 5(10), 153-169.

BibTex Style Citation:
@article{Singh_2017,
author = {J.R. Singh, A. Sanvalia},
title = {Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {10 2017},
volume = {5},
Issue = {10},
month = {10},
year = {2017},
issn = {2347-2693},
pages = {153-169},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=1492},
doi = {https://doi.org/10.26438/ijcse/v5i10.153169}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i10.153169}
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=1492
TI - Effect of AR (2) Model on the Economic Design Mean Chart with Known Coefficient of Variation Under Non Normal Population
T2 - International Journal of Computer Sciences and Engineering
AU - J.R. Singh, A. Sanvalia
PY - 2017
DA - 2017/10/30
PB - IJCSE, Indore, INDIA
SP - 153-169
IS - 10
VL - 5
SN - 2347-2693
ER -

VIEWS PDF XML
620 320 downloads 312 downloads
  
  
           

Abstract

In this paper, we have studied the effect of AR (2) model and non-normality on the economic design of mean chart with known coefficient of variation under non normal population. We use the first four terms of an Edgeworth series for the production cycle time and cost parts. In AR (2) model three different situations arise as (i) Roots are real and distinct (ii) Roots are real and equal (iii) Roots are complex conjugate. The significant effects are seen on mean chart for the above three situation. We also develop the formula for the sample size (n) and sampling interval (h) for different combination of the skewness and kurtosis under AR (2) model.

Key-Words / Index Term

AR (2) Model, Mean Chart, Autocorrelation, Non-Normality, coefficient of variation (CV), Sample Size, Sampling Interval

References

[1] G.E.P. Box, G.M. Jenkins, “Time Series Analysis Forecasting and Control", San-Francisco, Holden-Day, 1976.
[2] Y.K. Chen, K.L. Hsieh, C.C. Chang, “Economic Design of the VSSI X Control Charts for Correlated Data”, Int. J. Prod. Econ., Vol. 107, pp. 528–539, 2007.
[3] C.Y. Chou, H.R. Liu, C.H. Chen, “Economic Design of Averages Control Charts for Monitoring a Process with Correlated Samples”, Int. J. Manuf. Technol, Vol. 18, pp. 49-53, 2001.
[4] A.J. Duncan, “The economic design of X ̅ charts used to maintain current control of a process”, J. Am. Stat. Assoc., Vol. 51, pp. 228–242, 1956.
[5] B.C. Franco, P. Castagliola, G. Celano, A.F.B. Cost, “New Sampling Strategy to Reduce the Effect of Autocorrelation on a Control Chart”,. J. Appl. Stat., http://dx. doi.org/10.1080/02664763.2013.871507 (in press), 2012.
[6] S.N. Lin, C.Y. Chou, S.L. Wang, H. R. Liu, “Economic design of autoregressive moving average control chart using genetic algorithms”, Expert Syst. Appl., Vol. 39, pp. 173–179, 2012.
[7] H.R.. Liu, C.Y. Chou, C.H. Chen, “Minimum Loss Design of x bar Charts for Correlated Data”, J. LossPrev. ProcessInd, Vol. 15, pp. 405–411, 2002.
[8 E.M. Saniga, “Economic Statistical Control Chart Design with an Application to X ̅ and R Charts”, Technometrics, Vol. 31, pp. 313-320, 1981.
[9] E.M. Saniga, D.J. Davis, T.P. McWilliams, “Economic Statistical Design of Attribute Charts, J. Qual. Technol., Vol. 27, pp. 56-73, 1995.
[10] W.A. Shewhart, “Quality Control Charts”, BellSyst. Tech. J., pp. 593–603, 1926.
[11] H.R. Singh, J.R. Singh, “Variable Sampling Plan under Second Order Autoregressive Model”, Indian Association of Products Quality and Reliability Transaction, Vol. 7, pp. 97-104, 1982.
[12] C.C. Trong, P.H. Lee, N.Y. Liao, “An Economic Statistical Design of Double Sampling X ̅ Control Chart”, Int. J. Prod. Econ., Vol. 120, pp. 495-500, 2009.
[13] W.H. Woodall, “The Statistic Design of Quality Control Charts”, Technometrics, Vol. 28, pp. 408-410, 1985.