Sequential Methods and Change Detection

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Sequential methods have the benefit of saving money by reducing the number of observations that have to be collected, thus reducing the duration of the trial, and they satisfy the ethical requirement of stopping all trials as soon as possible for the benefit of patients. Online change detection is used in safety monitoring in industrial environment or in clinical trials. Here the problem is to detect change quickly, and alert the user of a disturbance in the process. On the other hand, in sequential tests a decision on which of two (or several) hypotheses is true has to be made as soon as possible. In the past, the most popular methods for online monitoring were open ended. This means that the once monitoring has been started it went on until an alarm was raised. One such method is the Shewhart chart, which was designed in the 1930's and is still the most frequently used in industry. Another open ended monitoring is the famous cumulative sum chart (CUSUM) of Page dating back to 1954. One can show that all open ended sequential tests have some features that make their use undesirable. Continuing testing indefinitely is thus not recommended. My solution to this problem was to design several truncated sequential tests. One line of further investigation will analyse and compare the properties of the open ended and truncated tests. The new methods are not difficult to apply, so if their benefits are demonstrated and if they will be widely known and accepted, then significant saving of time and expenses will be the result relative to the currently dominant fixed sample size methodology. The tests are the continuous analogues of the group sequential tests, which are popular in clinical trials. The new methodology has now been applied with success in some frequently occurring situations in the medical field. The plan is to extend their use to industrial and economic models, and to show their benefits relative to the current methodologies of choice. This line of investigation requires the knowledge of mathematically sophisticated economic models.