The Sequential Tests for Success Ratio and the Confidence Limits of Success Ratio after Testing

Let X_i，i≥1 be a sequence of i.i. d. r.v.’s satisfying q＝P（X_i＝0）＝1-P（X_i＝1）,q is unknown. Suppose that A_n：1≤n≤n₀ and R_n：1≤n≤n₀ are any two sets of numbers satisfying A₁≤A₂≤…≤A_n0，0＜R₁≤R₂≤…≤R_n0,A_i＜R_i（i＝1，…，n_o-1） and A_n0＝RnoR_n0.
For the hypothesis H₀：q≥q₀（0＜q₀＜1）, We consider the sequential test △＝（r，d） in which r＝min｛n：n₁，D_n≤A_norD_n≥R_n, d＝I_{（Dr≥Rr）}, where D_n=\sum_i=1^n X_i(n \geq 1).I_A is the indicator of set A, “d =1” means rejecting H₀ and “d = 0” means accepting H₀. In the present paper, we find out the optimal lower （upper） confidence limits for q based on data （r，D_r） in some sence