SPC and Order Statistics: Burr Type XII Model

SPC and Order Statistics: Burr Type XII Model

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2017 by IJETT Journal
Volume-49 Number-1
Year of Publication : 2017
Authors : Dr.R.Satya Prasad, M.Anuradha, Dr.G.Sridevi
DOI :  10.14445/22315381/IJETT-V49P205

Citation 

Dr.R.Satya Prasad, M.Anuradha, Dr.G.Sridevi "SPC and Order Statistics: Burr Type XII Model", International Journal of Engineering Trends and Technology (IJETT), V49(1),33-40 July 2017. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

Abstract
This paper presents a simple SRGM, the Burr Type XII Non Homogeneous Poisson Process (NHPP) model is used as a control mechanism based on order statistics of the cumulative quantity between observations of time domain failure data. This model has the ability of modeling both reliability improving and deteriorating systems and has gained wide acceptance. The Maximum Likelihood Estimation (MLE) method is used to derive the point estimators. We have applied the model to sets of existing software failure datasets to assess the failure process using SPC.

 References

[1] Balakrishnan. N., Clifford Cohen. A., (1991), “Order Statistics: Theory and Methods, Hand Book of Statistics”, Vol. 16, Elsevier.
[2] Arak M Mathai, (2003), “On the distribution of order statistics from generalized logistic samples”.
[3] Crow. L. H. (1974). “Reliability for Complex Systems, Reliability and Biometry”, Society for Industrial and Applied Mathematics (SIAM), pp.379-410.
[4] Duane, J.T., (1964). “Learning curve approach to reliability monitoring”, IEEE Trans. Aerospace, AS-2, pp.[563-566].
[5] M. Horigome, N. D. Singpurwalla, and R. Soyer. (1984). “A Bayes Empirical Bayes Approach for Software Reliability growth”. In Computer Science and Statistics, (16th Symp. Interface, Atlanta, GA), NorthHolland, pp.47-55.
[6] Khoshgoftaar, T.M. and Woodstock, T.G. (1991). “Software reliability model selection: a case study”, Proc. Int. Symp. On software reliability engineering, may 18-19, Austin, Texas, pp.[183-191].
[7] Lyu, M.R. and Nikora, A. (1991). “A Heuristic approach for software reliability prediction: the equally weighted linear combination model. Proc. Int. Symp. On software reliability engineering, may 18-19, Austin, Texas, pp.[172-181].
[8] Gutta Sridevi, R.Satya Prasad and K.V.Murali Mohan, “Monitoring Burr Type XII Software Quality Using SPC”,International Journal of Applied Engineering Research (IJAER), Vol. 9, No. 22 (2014), pp:16651-16660, ISSN:0973-4562.
[9] Xie, M and Zhao, M, “On some reliability growth models with simple graphical interpretations”, to appear in Microelectronics and reliability.
[10] Lyu, M. R., (1996). “Handbook of Software Reliability Engineering”. McGraw-Hill publishing, ISBN 0-07-039400-8.
[11] Pham. H., 2006. “System software reliability”, Springer.
[12] Xie. M, T.N Goh and P.Ranjan. (2002). “Some effective control chart procedures for reliability monitoring”, Reliability Engineering and System Safety. 77, 143-150.
[13] Gokhale, S.S and Trivedi, K.S., 1998. “Log-Logistic Software Reliability Growth Model”. The 3rd IEEE International Symposium on HighAssurance Systems Engineering. IEEE Computer Society.
[14] Lyu, M. R., (1996). “Handbook of Software Reliability Engineering”. McGraw-Hill publishing, ISBN 0-07-039400-8.
[15] Burr (1942), “Cumulative Frequency Functions”, Analysis of Mathematical Statistics, 13, pp. 215-232.

Keywords
Burr type XII model, NHPP, MLE, Statistical Process Control, Order Statistics.