Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.

Comparison of Testability Verification Test Sample Size Determination Methods Based on Binomial Distribution

Abstract: The classical sample size determination methods in the testability verification test are introduced, including single, double, multiple sampling methods and sequential probability ratio test (SPRT) method. The sampling characteristics of the methods and the expressions of the average sampling times are analyzed and compared. The results show that the SPRT method has similar sampling characteristics to the single sampling method under the same requirements of bilateral testability indexes and risks, and the SPRT method has the smaller average sampling times. It is recommended to use single sampling method and SPRT method in testability verification test. Considering that these four classical methods do not use prior information, the sample size of the testability verification test is often large. Under consideration of the testability prior information, the Bayesian theory is used to improve the SPRT method to obtain the Sequential Posterior Odds Test (SPOT) method. The sampling characteristics and average sampling times of the single sampling method, SPRT method and SPOT method are compared and analyzed under the same constraint parameters in the test. The results indicate that the average sampling times of SPOT method is less than single sampling method and SPRT method with the premise of approximate sampling characteristics. It is recommended to scientifically use priori information reasonably to reduce the sample size.

Detection of system failure by human operator — mathematical model and experiments

Abstract: This paper proposes a model of human operators' failure detection behavior in actively controlling a linear system and passively monitoring signals on the display screen. Estimation and signal detection theories were appliied to the development of this model. Its mechanism of failure detection is expressed by Wald's Sequential Probability Ratio Test, and two autoregressive models are used to predict the values at one step ahead of signals - signals on the display screen and a displacement of the manipulator - from their current values as perceived by the human operator. One of these autoregressive models is for hypothesis H0 where the system is in normal working order, and the other is for hypothesis H1 where the system is out of order. A major feature of the proposed model is that the information accessible to the controller includes proprioceptive information associated with control manipulation in addition to visual information. The detection time and accuracy predicted by this model corresponded well with the data obtained from experiments over a wide range for the controller and monitor.

Decision fusion for parallel sequential sensors

Abstract: Lee and Thomas (1984) have introduced a modified version of Wald's sequential probability ratio test. The modified version retains most of the features of Wald's procedure but is easier to analyze and offers efficient truncation procedures. In this study, we use the Lee-Thomas design to analyze the performance of a bank of M parallel sequential sensors whose decisions are fused. We evaluate the performance of the sensor bank by two criteria: (1) the probability of error; (2) average sample number (ASN) needed to achieve it. Three rules are studied: (1) first-to-decide rule (Niu and Varshney, 1984): once at least one sensor has stopped sampling, we adopt the decision of one of the stopped sensors; (2) all-that-decided rule: once at least one sensor has stopped sampling, we integrate all the decisions of stopped sensors through the 1986 Chair-Varshney decision fusion rule; and (3) all-sensors rule: once at least one sensor has stopped sampling, we combine the available decisions of the stopped sensor and the implied decisions of the remaining sensors. Performance of the three rules is calculated and gains with respect to the performance of a single sensor are quantified.

An Information Theoretic Methodology for Kansei Engineering: Kansei Channel and Subjective Probability

Abstract: This paper proposes an application of the notions in Information Theory to Kansei Engineering toward a mathematical methodology for the analysis in the Kansei Engineering field. First, we propose a new definition of correlation using the mutual information in Information Theory. Second, we present a relation between the Bayes' Updating using the notion of binary channel and Sequential Probability Ratio Test (SPRT). Third, we show a possibility that the computation of optimal input probability distribution (OIPD) of channel capacity can be used as a tool of Clustering Analysis.

A note on weak admissibility of the sequential probability eatio test

Abstract: The sequential probability ratio test (SPRT) is shown to be weakly admissible in ease of continuous time and arbitrary simple alternatives. This property of the SPRT generalizes a corresponding one proved for discrete time by EISENBERG,GHOSH and SIMONS [3]