International Journal of Computer Applications (0975 – 8887) Volume 70– No.17, May 2013 1 Posterior Analysis of Sequential Normal Testing Procedure Birjesh kumar J.P Institute of Engg &Technology,Meerut A-115 ganga sagar colony Ganganagar,Meerut Abha Chandra, PhD Deptt.of Statistics Meerut college,Meerut K.K.Sharma, PhD Retd Prof&Head Deptt.of Statistics C.C.S University,Meerut ABSTRACT Several studies deals with the non- robust character of various types of acceptance plans. Many such studies also analyze the robust character of sequential testing procedures when the underlying failure time distribution has a monotone failure rate. A vast literature on the life testing plans in the Bayesian framework is also available where updating prior with experimental data has been the main concern. Highlighting the point that the basic normal lifetime distribution can also be updated in respect of prior variations in the involve parameters. The present study deals with the analysis of the robust character of sequential normal testing procedures when the mean of the basic normal distribution is considered as a random variable. The robust character of the consistency of the random variable n, in view of prior variations, is also analyzed Keywords Robustness, SNTP, OC, ASN and Coefficient of variation function(C.V). 1. INTRODUCTION An important contribution in the area of sequential test of statistical hypothesis is due to A. Wald (1947), who developed sequential probability ratio test (SPRT) for testing a simple hypothesis against a simple alternative. He obtained the expressions for operating characteristic (O.C.) and average sample numbers (ASN) function of the SPRT. The robustness of the SPRT, when the distribution under consideration has undergone a change, has been studied by various authors while dealing with various probability models, like Montagne and Singapurwala (1985), Sharma K.K. and Rana (1990), Sharma K.K. and Bhutani (1992) and others. The robustness of these procedures has been investigated in respect of producer's and consumer's risk and the ASN. Further on using different life time models, the studies in [2A] include a vast literature on the life testing plans in Bayesian framework in which updating the prior with experimental data has been the main concern. However, in the Bayesian framework, it should be recognized that priors do have an impact on the basic distribution and therefore the basic distribution can be updated in view of prior variations. This updated basic distribution be used in the analysis. In the present paper we consider SPRT for testing the 0 : H     v/s 1 1 : H    when samples are sequentially recorded from   2 , N     being known. Further, when we consider  to be a random variable we use the prior of  to update the basic distribution,   N    and use this basic updated distribution to study the robust character of SPRT when  is considered to be a random variable. The concept has been highlighted in the present study. Further, it was also noted that the basic distribution can be further updated in respect of the posterior distribution. This further updated distribution is also named as predictive basic distribution. In view of above, the present paper considers the robust character of SPRT, when predictive distribution is used in the analysis. A comparison of OC , ASN curve and C.V curve in the corresponding situation has been used as the basis of analysis. 2. NOTATIONS N(, 2) : Normal distribution with mean  and variance 2 p.d.f. : Probability density function SPRT : Sequential probability ratio test SNTP : Sequential normal testing procedure L() : The OC function, the probability of accepting H0 when  is the true parametric value n : The sample size needed to terminate the sequential testing. Thus n is a random variable. E(n) : ASN functions for fixed . V(n) : Variance of the random variable n for fixed  CV(n) : Co-efficient of variation of the random variable n for fixed   : Size of the type I error, also called producer's risk in quality control terminology.  MTSF : ; Size of the type II error, also called consumer's risk in quality control terminology. Mean Time to system failure 3. STATISTICAL BACKGROUND For developing the procedure we assume that (i)The failure time distribution of X is   2 1 N   with,p.d