scholarly journals The VPRT: A Sequential Testing Procedure Dominating the SPRT

1993 ◽  
Vol 9 (3) ◽  
pp. 431-450 ◽  
Author(s):  
Noel Cressie ◽  
Peter B. Morgan
Keyword(s):  
Sample Size ◽  
Decision Problem ◽  
Sequential Analysis ◽  
Testing Procedure ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Sequential Decision ◽  
Probability Ratio ◽  
Sampling Cost ◽  
Sequential Probability

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

The Use of Wald’s Sequential Probability Ratio Test (SPRT) in Cocoa Pod Borer Management

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Albert Ling Sheng Chang
Keyword(s):  
Sample Size ◽  
Pest Management ◽  
Control Measure ◽  
Sequential Sampling ◽  
Sequential Probability Ratio Test ◽  
Effective Control ◽  
Ratio Test ◽  
Probability Ratio ◽  
Pod Borer ◽  
Sequential Probability

Sequential sampling plan (SSP) has been widely used in many engineering and quality control study. The advantage of using the SSP is the sample size is not fixed in advance, but is determined in part by the results of the sampling process. The application of the SSP is not limited to the industry, it also being used in pest management. This is because the SSP are generally more cost effective than plans based on a fixed sample size. Wald's Sequential Probability Ratio Test (SPRT) is one of the most common sequential sampling plans in insect pest management. It has been used to determine pest status at one time which could be used, through time, to monitor the status of the population and to take action when the pest density exceeded the Economic Threshold Level (ETL). Cocoa pod borer or CPB (Conopomorpha cramerella (Snell)) is a pest of concern to the cocoa growers in South-East Asia that has become one of the major factors that dampened the interest expressed in cocoa cultivation because of the heavy losses of cocoa pods due to the pest if effective control measure is not employed. The chemical control appeared to be one of the effective control measure used by the growers to control the CPB. Current practice used by the growers in applying the chemical is biweekly spraying which could see the increasing cost of chemical and labor used. The study was conducted to develop the Wald’s SPRT to monitor the CPB infestation level relative to the ETL based on counting the CPB eggs found on the pods aged 1 month before ripen or pod length 131 mm to 150 mm. The performance of the Wald’s SPRT was validated using independent data sets collected from Cocoa Research and Development Center (CRDC) Madai.

Operating Characteristic and Expected Sample Size of a Sequential Probability Ratio Test for the Simple Exponential Distribution

1965 ◽  
Vol 14 (1-2) ◽  
pp. 65-73 ◽  
Author(s):  
M. Raghavachari
Keyword(s):  
Sample Size ◽  
Exponential Distribution ◽  
Operating Characteristic ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Probability Ratio ◽  
Expected Sample Size ◽  
Simple Alternative ◽  
Sequential Probability Ratio Tests ◽  
Sequential Probability

Summary For the problem of testing the simple hypothesis H : θ = θ1 against the simple alternative K : θ = θ2 with θ2 > θ1 , where θ is the unknown parameter of the simple exponential distribution, the familar Wald's Sequential Probability ratio test may be adopted. It is shown in the present paper that for a class of sequential probability ratio tests, exact expressions for the operating characteristic and the expected sample size can be given. The nature of the expected sample size function and the effect of Walo's approximations to the stopping bounds of the sequential probability ratio test are also studied.

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