Chi Squared Distribution Calculator
Is your vibration controller squaring with Chi?
Why does the random spectrum generated by a Vibration Research controller (without using iDOFTM) look ragged? Because it is supposed to look exactly that way! Evidence now exists that some commercial random controllers actually use more than the number of DOF specified in their setup parameters for PSD calculation. This error can result in the appearance of a tighter ±dB match between the Demand and Control spectra than theory and the operator-entered DOF support. Controllers made by two different manufacturers have been found with this defect. Strong evidence of non-Gaussian signal behavior has also been found in controllers offered by three competitors.
Several testing methods to disclose and characterize such undesirable statistical behavior have been discussed and demonstrated in this case study. The simple use of a spreadsheet combined with text export of an instrument’s PSDs makes very good sense. The test is simple to perform and meaningful answers can be had with just a few minute’s work. If your controller does respect the laws of physics and probability, the tables and graphs in this article can aid your test design and planning efforts. If your controller doesn’t understand the χ2 distribution, it can confuse and confound your effort to conduct your tests scientifically. Don’t let this happen!