A great summary about the evolution of sequential hypotheses tests and the early stages of the development can be found in Walds paper in Chapter B. A test can solely be called sequential, if the number of observations is not predetermined, but it is dependent on the outcome of the observations. The results of Neyman and Pearson inspired Abraham Wald in the mid-1940s to reformulate it as a sequential analysis problem. The lemma states that when performing a hypothesis test between two simple hypotheses and, the likelihood ratio test which rejects in favour of when where is the most powerful test at significance level for a threshold. The Neyman-Pearson lemma offers a rule of thumb when all the data have been already collected. Jerzy Neyman and Egon Pearson analysed the efficiency of hypothesis tests and have published their work in 1933. The so-called Bayes’ theorem in probability theory has been established by Thomas Bayes in the early 1700s. However, new methodologies and applications of statistical hypothesis tests are published every year. In the literature, several theories have been already proposed to extend the applicability of the mathematical background or to optimize calculation. Since the century there has been a growing interest in statistical hypothesis testing. Application example for thermomechanical fatigue test monitoring and another for vibration based rotational speed estimation of a four-cylinder internal combustion engine is discussed in this paper. The new method also gives representative visual information about the structure of detected events. The method provides straight information about the endpoints and possible duration of the detected events as well as shows their significance level. A peak determination algorithm has also been developed to find significant peaks and to store the corresponding data for further evaluation. A novel method called Scaled Sequential Probability Ratio Test (SSPRT) produces 2D array of data via special cumulative sum calculation. In some cases background noise covers the events and simple threshold or power monitoring methods cannot be used effectively. This information can be used for condition monitoring, state identification, and many kinds of forecasting as well. Events in acquired data series, their duration, and statistical parameters provide useful information about the observed system and about its current state.
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