Purely Sequential Fixed Accuracy Confidence Intervals for P(X < Y) under Bivariate Exponential Models

SYNOPTIC ABSTRACT

This article deals with the estimation of the reliability or the availability parameter θ = P(X < Y) in a stress-strength model. We consider separate cases where (X, Y) has a bivariate exponential distribution due to Marshall and Olkin (1976) and Freund (1961). We construct a purely sequential estimation methodology to find a fixed accuracy confidence interval for the unknown θ in each case. First-order asymptotic efficiency and consistency properties are also established of our proposed procedures. We then supplement extensive sets of simulation studies and real data analysis to show encouraging performances of our proposed stopping strategies.

KEYWORDS AND PHRASES:

• Diabetic retinopathy
• laser photocoagulation
• stress-strength model
• bivariate exponential
• scale parameter
• first-order asymptotic efficiency
• first-order asymptotic consistency
• purely sequential
• simulations