|Abstract or Summary
- 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.