Optimal Two Stage Procedures for Estimating Functions of Parameters in Reliability and Queueing Models
Abstract
In this dissertation, we consider the problem of estimating functions of parameters found in reliability and queueing models. The problem is to allocate a fixed sampling budget among the populations with the goal of minimizing the mean squared error (MSF) of the estimator. We consider the reliability model with three components such that the probability the system works is f(u1,u2,u3) = u1(u2+u3), and the mean waiting time of the M/G/I queue. For each of these models, we consider a set of sample sizes referred to as a first-allocation procedure which minimizes the first-order approximation to the MSE. Since the first-order allocation procedure depends on the unknown parameters in the model, we propose a two-stage procedure in which we first use a fraction of the sampling budget to estimate the unknown parameters and then allocate the remaining budget based on the initial sample. We show that the difference between the MSE for the two-stage procedure and the minimum MSE obtained using the optimal set of sample sizes from the first-allocation procedure goes to zero as the budget goes to infinity. Simulations are used to demonstrate the asymptotic optimality results for the two stage procedures. The empirical studies show that the two stage estimation procedures work well for reasonable sample sizes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1998
- Accession Number
- ADA348622
Entities
People
- Kevin E. Burns
Organizations
- University of North Carolina at Chapel Hill