Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2 , pp. 129--136

A NOTE ON CONFIDENCE BOUNDS FOR $P(X>Y)$ IN BIVARIATE NORMAL SAMPLES

By

S. B. NANDI, *Gauhati University*

and

A. B. AICH, *Presidency College, Calcutta*

SUMMARY. In the context of reliability under a stress-strength (SS) model, the problem of constructing confidence bounds for P(X > Y) frequently arises. Many authors have considered the problem both under parametric and non-parametric frameworks. While most of the authors have taken X and Y to be independent, we, in this study, assume that the random vector (X, Y) follows a bivariate normal distribution. The problem of obtaining the sample size for specified confidence length and confidence coefficient is then considered.

*AMS (1980) subject classification.* 62N05, 62J99.

*Key words and phrases.* Reliability, confidence bounds, confidence coefficient, correlation coefficient.