Methods for Monitoring Fractionally Sampled Multiple Stream Processes

摘要

This study considers multiple stream systems where it is possible to monitor only a fraction of the total streams at a given time. This situation is of interest in those processes where the speed of production is great and includes a large number of streams, but the ability to monitor the process is not fully automated and unable to keep up with the speed of production. A method for determining the probability of detecting a shift from target of any fraction of the streams (including none of the streams) is presented. In addition to the mathematics involved in computing this detection probability, a computer program is given which automates the process and quickly gives a result for any number of streams allowing an infinite number of combinations of stream shift scenarios to be examined. Results from several of these scenarios are tabulated and graphed. Adaptive approaches to system monitoring are applied to multiple stream processes in general and the fractional sampling problem specifically. This represents the first application of adaptive techniques to multiple stream processes. The average time to signal for an adaptively-monitored, fractionally- sampled multiple stream process is developed using a Markov chain procedure. The average time-to-signal results are used to identify promising adaptive sampling schemes for monitoring multiple stream processes using fractional samples. The adaptive fraction approach is shown to give superior results to the fixed fraction scheme and often yields satisfactory results compared with those obtained by sampling all the streams involved in a process.