Performance Analysis of Sequential Probability Ratio Test

Abstract

The sequential probability ratio test (SPRT) is a fundamental tool for sequential analysis. It forms the basis of numerous sequential techniques for different applications; for example, the truncated SPRT and Page's cumulative sum test (CUSUM). The performance of SPRT is characterized by two important functions—operating characteristic (OC) and average sample number (ASN), and CUSUM's performance is revealed by the average run length (ARL) function. These functions have been studied extensively under the assumption of independent and identically distributed log-likelihood ratios (LLRs) with constant bounds, which is too stringent for many applications. In this article, inductive integral equations governing these functions are developed under very general settings—the bounds can be time-varying and the LLRs are assumed independent but nonstationary. These inductive equations provide a theoretical foundation for performance analysis. Unfortunately, they have nonunique solutions in the general case except for the truncated SPRT. Numerical solutions for some frequently encountered special cases are developed and are compared with the results of Monte Carlo simulations.

Keywords:

• Average run length
• Average sample number
• CUSUM
• Operating characteristic
• SPRT

Subject Classifications:

• 62L10

ACKNOWLEDGMENTS

The authors thank the associate editor, Dr. Solanky, and the anonymous referees for their valuable comments and suggestions on the improvement of this article.

This research was supported in part by NASA/LEQSF(2013-15)-Phase3-06 through grant NNX13AD29A and ONR-DEPSCoR through grant N00014-09-1-1169.

Notes

Recommended by T. K. S. Solanky