Method Of Two SPRTs And Its Application

Since Wald(1947) proposed method of Sequential Probability Ratio Test (SPRT), SPRT has become an important tool for solving hypothesis test problems. It has so many excellent properties that it has been used widely.Some scholars developed new methods to solve a hypothesis test problem — using SPRT twice. In some degree, their ideas and methods are proper and some ideal results have been gotten. In this paper, these methods are summed up and new methods are developed, including parameters selection and the design of hypotheses.At present, there are two hypothesis test problems involved in Two SPRTs in sequential analysis research.The first one is simple hypothesis test problem. To reduce average sample number at some point, Lorden (1976) proposed the method of 2-SPRT, i.e. to use SPRT twice. Lorden, Huffman and Chen Jiading have proved that 2-SPRT is asymptotically efficient. In this paper, in symmetric normal case, a new method is used to select parameters of 2-SPRT by solving equation. Examples show that this method is quite applicable and efficient. Additionally, a new method of truncated 2-SPRT is put up in this paper.The second one is two-sided hypothesis test problem. To satisfy practical needs, many scholars turned two-sided hypothesis test problem into three hypotheses one byadding two proper hypothesis parameters, and used the method of two SPRTs to solve it. These hypothesis parameters, which have never been discussed before, are found in some requires also by solving equations. Only symmetric test of normal mean with variance known is considered here.