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.

In this paper, we develop purely sequential, two-stage, three-stage, and “accelerated” sequential procedures for the point estimation of the location of negative exponential distribution having an unknown scale parameter. We do minimum risk point estimation by using all four sequential procedures mentioned above. In addition, we do bounded risk point estimation by using three-stage and “accelerated” sequential procedures. Consideration is given to a modified LINEX loss function. We aim at controlling the associated risk functions for all the procedures. Second-order approximations are obtained for the proposed procedures. We also discuss first-order properties for purely sequential procedure.

In this paper, we develop testing procedures for hypotheses regarding the difference of location parameters from two independent two-parameter exponential populations with unknown but proportional scale parameters. We design appropriate two-stage and purely sequential procedures to determine the appropriate sample sizes while controlling both type-I and type-II error probabilities at or below the preassigned levels α, β respectively. We prove that both two-stage and purely sequential testing strategies enjoy a number of practically appealing properties. Extensive sets of computer simulations validate our theoretical findings. We illustrate the testing methodologies along with sampling procedures on a cancer studies data.

In this article, we develop two-stage, three-stage, and accelerated sequential procedures for the point estimation of the mean μ of an inverse Gaussian distribution when the scale parameter λ is unknown. Both minimum risk and bounded risk estimation problems are considered subject to a weighted squared error loss function. We aim at controlling the associated risk functions for all three procedures. Second-order approximations are obtained for the proposed procedures.