Incorporation of Statistical Information for Polynomial and Transcendental Interpolation

One of the principal considerations in the implementation of automated testing systems is the "cost" of accumulating test data. Because testing is controlled and recorded by a digital computer, only discrete data points are gathered. Also, an elapsed waiting time is necessary in order to establish the test conditions prior to performing a measurement. Due to these factors, the number of measurements has a major influence on the cost of testing devices automatically. It now foliows that automated testing of continuous systems will entail interpolation. This paper treats the situation wherein statistical information is substituted for some of the deterministic data in interpolation and extrapolation procedures. The principle advantage with this approach is that a reduction in the number of measurements required to characterize a device through interpolation and extrapolation is achieved. A consequence of utilizing the statistical data is that the device function is said to lie within statistical bounds. In addition to introducing the proposed approach, this paper describes practical considerations in obtaining the required statistical information. A hypothetical example is given in order to illustrate the application of the proposed techniques.