Graduate Thesis Or Dissertation
 

A Bayesian model for the determination of optimal sampling intervals

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  • There are a nearly unlimited number of situations in which the status of time-varying processes must be updated. The monitoring of these processes usually occurs at periodic intervals. Whether the monitoring is performed by man or machine, a decision must be made regarding the frequency of these activities, that is, an optimal sampling interval must be determined. This thesis presents two theoretical models, based on a Bayesian analysis, from which optimal sampling intervals can be determined. The necessary information for the use of these models includes the sampling costs, quadratic error costs, and a normally distributed measure of the uncertainty of the process as a function of the time since the last sample. This uncertainty can be measured either objectively, from historical data, or subjectively, from the decision maker's personal knowledge of the process. The first model assumes that immediately after sampling, the decision maker knows precisely the value of the process. That is, the variance at the time of sampling is zero. In the second model, this assumption is not made. A certain amount of uncertainty exists immediately after sampling. This uncertainty can be reduced by taking a larger sample size. With a knowledge of the value, or a distribution of the values of the process when a sample is taken, the decision maker "forecasts" values for the period until the next sample. Action will be taken on the basis of these forecast values. An error in these values will cause inappropriate actions to be taken. An error cost will be incurred on the squared difference between these two values. The extent of the difference will be dependent on the degree of uncertainty the decision maker has regarding the process. By sampling more frequently, he reduces the uncertainty and therefore the error cost, but increases the sampling cost. The sampling interval (and in the case of the second model, the sample size) that minimizes the sum of these costs determines the optimal sampling policy. This thesis develops the necessary eqUations and suggest solution techniques from which these optimal intervals can be determined. A sensitivity analysis is also performed to show the effects of changes in cost parameters on the optimal sampling interval.
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