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Rayleigh based SPRT: Order Statistics

Dr. R. Satya Prasad, Syed Khasim, T.Anuradha, ,
Affiliations
Associate Professor, Dept. of CS&E, Acharya Nagarjuna University, Guntur, A.P., India.
Research Scholar, Rayalaseema University, Kurnool, A.P.,India.
Lecutrer in P.G.Dept.of Mathematics, P.B. Siddhartha College of Arts & Science, Vijayawada, A.P. India.
:NOT ASSIGNED


Abstract
Noise is integral in the software failure data. A conversion of data is needed to smooth out the noise. Smoothing enhances quality at first as the size increments and turns out to be more regrettable as the gathering size is vast. Order statistics deals with applications of ordered random variables and functions of these variables. When failures are frequent or inter failure time is less, the use of order statistics is significant. Classical Hypothesis testing needs more time to draw conclusions by collecting volumes of data. But, to decide upon the reliability or unreliability of the developed software very quickly Sequential Analysis of Statistical science could be adopted. The method embraced for this is, Sequential Probability Ratio Test (SPRT), which is designed for continuous monitoring. The likelihood based SPRT proposed by Wald is very general and it can be used for many different probability distributions. The method used to derive the unknown parameters is Maximum Likelihood Estimation (MLE). In this paper, a control mechanism based on Order statistics and Sequential Probability Ratio Test is applied using mean value function of Rayleigh distribution and analysed the results.


Citation
Dr. R. Satya Prasad,Syed Khasim,T.Anuradha."Rayleigh based SPRT: Order Statistics". International Journal of Computer Engineering In Research Trends (IJCERT) ,ISSN:2349-7084 ,Vol.2, Issue 08,pp.523-529, August - 2015, URL :https://ijcert.org/ems/ijcert_papers/V2I811.pdf,


Keywords : Rayleigh, Maximum Likelihood Estimation, Order statistics, SPRT, Reliability

References
[1] Balakrishnan, N. and Cohen, A.C., (1991). “Order statistics and inference: estimation methods”, Academic Press. 
[2] Krishna Mohan. G and Satya Prasad. R. “Detection of Reliable Software using SPRT on Time Domain data”, International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol. 1, No. 4, August 2011, pp[92-99].
[3] Krishna Mohan. G, Satya Prasad. R and Prof. Kantam. R.R.L. “Software Reliability Using SPC and Weibull Order Statistics”, International Journal of Engineering Research and Applications (IJERA). Vol 1. Issue 4. pp[1486-1493], Nov-Dec, 2011.  
[4] Lyu. M.R., (1996). “Handbook of software reliability engineering”, Data Dictionary IEEE Computer Society and MCGraw-Hill, New York. 
[5] Pham. H., (2006). “System software reliability”, Springer.
 [6] Reckase, M. D. (1983). “A procedure for decision making using tailored testing”, In D. J. Weiss (Ed.), New horizons in testing: Latent trait theory and computerized adaptive testing (pp. 237-254). New York: Academic Press. 
[7] Satyaprasad, R. (2007). “Half Logistic Software Reliability Growth Model”, Ph.D Thesis, Acharya Nagarjuna University, India. 
[8] Wald. A., (1945). “Sequential tests of statistical hypotheses”. Annals of Mathematical Statistics, 16:117– 186. 
[9] Wald. A., (1947). “Sequential Analysis”, John Wiley and Son, Inc, New York. 
[10]Weibull, W. (1951). “A Statistical distribution function of wide Applicability”, Journal of Applied Mechanics, 18, 293-297.


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