Showing papers on "Sequential probability ratio test published in 1991"
Book•
24 Apr 1991
TL;DR: A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 20th century as mentioned in this paper, where the sample size depends in a random manner on the accumulating data.
Abstract: Sequential analysis refers to the body of statistical theory and methods where the sample size may depend in a random manner on the accumulating data. A formal theory in which optimal tests are derived for simple statistical hypotheses in such a framework was developed by Abraham Wald in the early 1
349 citations
TL;DR: In this paper, the authors discuss the design and testing of redundant sensors in nuclear power plants to monitor critical physical variables such as pressures, temperatures, and radiation levels, such as radiation levels.
Abstract: It is common practice in nuclear power plants to install redundant sensors to monitor critical physical variables such as pressures, temperatures, and radiation levels. The design and testing of an...
75 citations
01 Dec 1991
TL;DR: In this article, a sequential sampling plan for the inverse gaussian process mean when the value of the shape parameter of the density is known is presented in the context of reliability testing and acceptance sampling data acquisition is often in the face of scarce and time-consuming.
Abstract: The inverse gaussian distribution is a flexible model which has been extensively applied in the theory of generalized linear models and accelerated life testing where early failure times predominate. More recently it has received attention in areas such as quality control, and as an underlying model that provides an alternative to the analysis of variance. In reliability testing and acceptance sampling data acquisition is often in the face of scarce resources and may be both costly and time-consuming. In such settings it is desirable to reach a statistically sound decision as quickly as possible. Based on sequential probability ratio tests (SPRT), sequential sampling plans provide one method of arriving at a timely, statistically based decision. A sequential sampling plan for the inverse gaussian process mean when the value of the shape parameter of the density is known is presented in this paper.
21 citations
TL;DR: A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated, and a theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average numberof permutations for various alternatives.
Abstract: A sequential method for approximating a general permutation test (SAPT) is proposed and evaluated. Permutations are randomly generated from some set G, and a sequential probability ratio test (SPRT) is used to determine whether an observed test statistic falls sufficiently far in the tail of the permutation distribution to warrant rejecting some hypothesis. An estimate and bounds on the power function of the SPRT are used to find bounds on the effective significance level of the SAPT. Guidelines are developed for choosing parameters in order to obtain a desired significance level and minimize the number of permutations needed to reach a decision. A theoretical estimate of the average number of permutations under the null hypothesis is given along with simulation results demonstrating the power and average number of permutations for various alternatives. The sequential approximation retains the generality of the permutation test,- while avoiding the computational complexities that arise in attempting to co...
15 citations
TL;DR: In this article, a truncated sequential probability ratio test (TSPRT) was used for the acquisition of a direct sequence spread spectrum signal using a sliding-correlator linear detector, and the design parameters of the TSPRT were chosen so that the average sample number (ASN) is approximately minimized while the maximum ASN is always smaller than that for the fixed dwell scheme with similar false alarm and miss probabilities.
Abstract: An acquisition scheme for a direct sequence spread spectrum signal using the truncated sequential probability ratio test (TSPRT) was studied. Coherent demodulation is assumed. For testing the synchronization, a sliding-correlator linear detector was employed. Since the partial correlation of PN sequences is difficult to characterize by a simple model, the worst case was considered. Linearized bounds of the partial correlation were used for designing the TSPRT. The design parameters of the TSPRT are chosen so that the average sample number (ASN) is approximately minimized while the maximum ASN is always smaller than that for the fixed dwell scheme with similar false alarm and miss probabilities. Some simulation results were obtained and they agree well with analytic results.
9 citations
TL;DR: In this article, the robustness of the sequential probability ratio test on the mean of the negative binomial distribution to misspecification of the dispersion parameter, k, is investigated.
Abstract: The usual sequential probability ratio test on the mean of the negative binomial distribution assumes that the dispersion parameter, k, is known. This paper addresses the robustness of this test to misspecification of k. The operating characteristic surface is examined as a function of both the mean and k. By examining this function over a range of values of k, one can assess the robustness of the test with regard to improper specification of k. Both analytic and simulation results are presented. The analytic approach taken is generalized to other multiparameter distributions. This problem is motivated by the sampling of insect pests to determine whether their density exceeds an economic threshold.
8 citations
14 Apr 1991
TL;DR: The binary hypothesis testing problem is formulated in the higher order statistics (HOS) domain, with the advantages that the test is insensitive to additive Gaussian noise of unknown covariance and insensitive to signal shifts.
Abstract: The binary hypothesis testing problem is formulated in the higher order statistics (HOS) domain, with the advantages that the test is insensitive to additive Gaussian noise of unknown covariance and insensitive to signal shifts Unlike detection with a matched filter, the asymptotically maximum likelihood HOS-based test requires no prewhitening and no synchronization The asymptotic normality of the test statistic is exploited to formulate three sequential detection tests: a fixed sample size test, a sequential probability ratio test (SPRT), and a truncated sequential test The SPRT performance is examined through the average sample number by comparing a large sample analytical expression with a Monte Carlo experiment The results validate the test assumptions >
7 citations
TL;DR: The triangular test was extended to the situation of non-comparative trials with a binary outcome and the average sample size was close to Wald's continuous SPRT and compared favourably with the multistage methods proposed by Herson and Fleming.
Abstract: Phase II cancer clinical trials are non-comparative trials which are designed to determine whether the response rate p to the treatment under study is greater than a certain value p0, that is, to test H0, given by p less than or equal to p0 against H1 given by p greater than po. By choosing type I error alpha and the power 1-beta and by specifying H1, that is, by choosing a clinically relevant improvement p1), one can compute the number of patients N to be included for a fixed-sample approach. Various other approaches have been proposed such as multistage methods and Wald's continuous sequential probability ratio test (SPRT). As an alternative approach, we extended the triangular test (TT), proposed by Whitehead for comparative trials, to the situation of non-comparative trials with a binary outcome. We expressed H0 and H1 in terms of the log odds-ratio statistics, namely log [p(1-p0)/p0-(1-p)]. With this choice, the two statistics of interest, Z and V, have simple expressions: Z is the difference between the observed number of positive outcomes and the expected number under H0 and V is the variance of Z under H0. After every group of n patients, Z is plotted against V, and the trial proceeds until a boundary is crossed. In our simulations, type I error alpha and the power 1-beta were close to nominal values with the TT and the average sample size was close to Wald's continuous SPRT and compared favourably with the multistage methods proposed by Herson and Fleming. Given its statistical properties and its easy use, the TT should be considered for planning and analysing cancer phase II trials.
5 citations
TL;DR: In this article, sequential tests for a stepped-up reliability esti mator and coefficient alpha are developed, and the efficiency of the tests relative to each other and to fixed-sample tests is established, as well as the robustness of the alpha test.
Abstract: Sequential tests for a stepped-up reliability esti mator and coefficient alpha are developed. In a series of monte carlo experiments, the efficiency of the tests relative to each other and to fixed-sample tests is established, as well as the robustness of the alpha test. Both tests proved to be efficient, and the alpha test proved to be reasonably robust to deviations from normality and deviations from equal item error variances. On average, 47% of the sample size can be saved if a sequential test is ap plied instead of a fixed-sample test.
2 citations
28 Oct 1991
TL;DR: In this paper, the backward sequential probability ratio test (SPRT) is applied in the multivariate observation case to detect system degradations which are characterized by the presence of a systematic jump bias in innovations.
Abstract: The idea of the backward sequential probability ratio test (SPRT) is applied in the multivariate observation case to detect system degradations which are characterized by the presence of a systematic jump bias in innovations. The results of numerical simulations show its usefulness. It uses the logarithm of likelihood ratio function evaluated in reverse from the current observations to the past ones rather than from the past to the current ones as in A. Wald's conventional SPRT (1947). By doing this, it is possible to prevent the failure detection system from experiencing the extra time delay caused by the difference of the characteristics of failure processes from Wald's original SPRT formulation. >
2 citations
28 Oct 1991
TL;DR: A system based on the application of sequential analysis is presented for the fault prediction of a main diesel engine and a linear or nonlinear model in the trend analysis is used.
Abstract: A system based on the application of sequential analysis is presented for the fault prediction of a main diesel engine Under normal working conditions the values of monitored parameters are represented by a stationary time series Before an actual fault occurs, the system appears to be in an abnormal condition, which sometimes may be represented as a nonstationary time series In order to determine whether the time series is stationary or nonstationary, the sequential probability ratio test is applied A linear or nonlinear model in the trend analysis is used Analysis of the working performance of cylinder units and troubleshooting of a fuel oil system are considered as examples >
TL;DR: A general group sequential statistical decision model is investigated using a Bayesian approach and Bayesian dynamic programming and it is shown that the so-called onion-skins conjecture is false.
Abstract: A general group sequential statistical decision model is investigated. Using a Bayesian approach and Bayesian dynamic programming, we examine structural properties of the cost functions and of optimal sampling procedures. In particular, we consider variable-sample-size-sequential probability ratio tests and show that the so-called onion-skins conjecture is false.
Journal Article•
TL;DR: To remedy the defect of test delay in SPRT, a modifed SPRT method is prescnted in which means and variants are all changed.
Abstract: In this paper,the failure detection system based on the sequential probability ratio test (SPRT) is in-troduced.To remedy the defect of test delay in SPRT,a modifed SPRT method is prescnted in whichmeans and variants are all changed.Some analyses are also given.
09 Oct 1991
TL;DR: Several strategies developed for classification of terrain regions, based on the SPRT algorithm, are presented and the classification scores are shown for statistic synthetic patterns as well as for remote sensing data taken from an aerial view over cultivated regions.
Abstract: This paper presents several strategies developed for classification of terrain regions, based on the SPRT algorithm (Sequential Probability Ratio Test [1]). The SPRT algorithm is considered to be appropriate to two-class-classification and will be extended by the introduced strategies for resolution of multi-class-classification problems. A comparison between the classifiers is made and the classification scores are shown for statistic synthetic patterns as well as for remote sensing data taken from an aerial view over cultivated regions.
14 Apr 1991
TL;DR: It is proved that Page's (1954) repeated sequential probability ratio test (SPRT) procedure is asymptotically optimal in view of this more practically useful criterion.
Abstract: Well-known procedures exist for sequentially detecting abrupt changes in the distribution of a stochastic process with independent and identically distributed (IID) samples An analysis is made of the asymptotic optimality of a class of such procedures by comparing expected delay as the false alarm rate is sufficiently small The criterion used as minimum expected delay, while previously the procedures were found to be optimal in the sense of minimizing only an upper bound of the expected delay It is proved that Page's (1954) repeated sequential probability ratio test (SPRT) procedure is asymptotically optimal in view of this more practically useful criterion >