Sequential Methods and Change Detection

序贯方法的好处是减少了必须收集的观察次数，从而缩短了试验的持续时间，从而节省了资金，并满足了尽快停止所有试验以造福患者的伦理要求。 在线变化检测用于工业环境或临床试验中的安全监测。这里的问题是快速检测变化，并提醒用户过程中的干扰。另一方面，在顺序测试中，必须尽快决定两个(或几个)假设中的哪一个为真。 过去，最流行的在线监测方法是开放式的。这意味着，一旦启动了监控，它就会继续进行，直到发出警报。一种这样的方法是休哈特图表，它设计于20世纪30年代的S，至今仍是工业中使用最频繁的。另一个不限成员名额的监测是追溯到1954年的著名的佩奇累计和图表(CUSUM)。人们可以证明，所有的开放式顺序测试都有一些使它们的使用不受欢迎的特征。因此，不建议无限期地继续测试。我对这个问题的解决方案是设计几个截断的顺序测试。 进一步的研究将分析和比较开放式测试和截尾测试的特性。新方法应用起来并不困难，因此，如果证明了它们的好处，如果它们将被广为人知和接受，那么相对于目前占主导地位的固定样本量方法，将显著节省时间和费用。这些测试是临床试验中流行的分组序贯测试的连续类似。 新的方法现在已经成功地应用于医学领域中一些频繁发生的情况。该计划是将它们的使用扩展到工业和经济模型，并展示它们相对于当前选择的方法的好处。这方面的调查需要了解复杂的数学经济模型。

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.