Operating Characteristic and Average Sample Number of Binary and Multi-Hypothesis Sequential Probability Ratio Test

Abstract

The operating characteristic (OC) and average sample number (ASN) of the sequential probability ratio test (SPRT) and multi-hypothesis SPRT (MSPRT) are studied. We consider the case where the observation sequence is independent but not necessarily identically distributed. Also, the thresholds for the test can be time varying. Based on the governing equations for OC and ASN of the SPRT developed in our previous work, a solution for the general case is proposed. The governing equations for OC and ASN of the MSPRT are also obtained. Numerical solutions for MSPRT are developed. Basically, the solutions rely on approximating the original test by truncation, that is, truncating the test at some finite time $K$ . We show that under some mild conditions, the approximation error diminishes as $K$ increases, at the cost of increased computation. Numerical examples are provided to demonstrate our solutions by comparing with Monte Carlo simulations, Simon’s lower bound, and Dragalin’s method (if available) for ASN.