# Fulfilling MIL-STD-1540D Tolerance

#### Author John Van Baren

Random vibration testing is a tried and trusted method of subjecting assemblies and subsystems to vibration for design and operation qualification. Lately, however, customers have questioned whether tests are meeting standards.

Particularly, MIL-STD-1540D (PDF) references MIL-HDBK-340A (PDF) where “Table III. Maximum Allowable Test Tolerances” (page 21) calls for a ±1.5 dB tolerance from 20Hz to 1,000Hz, with a maximum bandwidth of 10Hz. The question is: should the test fail if FFT lines are out of tolerance on a random vibration controller?

Common vibration control tests use about 800 FFT lines, resulting in 2Hz bandwidth bins. It is typical for engineers to use 120 degrees of freedom (DOF), exceeding the required minimum of 100. Yet, several lines are still out of tolerance when running tests. Why is this occurring?

### FFT Lines Statistics

Statistically, we expect a Gaussian random test to have some lines out of tolerance (as described in the paper “Statistical Properties of the Random PSD”). On average, for 120 DOF, 0.199% of the PSD will be above +1.5dB, and 0.647% of the PSD will be below -1.5dB. Thus, we would expect more than 99% of the PSD to be within the ±1.5dB tolerance limit. We would also expect 0.846% of the PSD to be outside the tolerance limit.

For 800 lines, we should expect to see about 6 or 7 lines outside the specified tolerance band at any given time. For 120 DOF, probability shows that all lines will be within a ±1.5dB tolerance for only 0.11% of the time. Ironically, some control systems will consistently show all lines within tolerance for this test when using 120 DOF. However, the flip side of these statistics tells us that if there are no lines outside the tolerance band, then the data is non-Gaussian, or the DOF is much greater than 120.

Bearing this in mind, how can one possibly run a test to specs? The answer lies in the MIL specs themselves. The specifications state that “control bandwidths may be combined for tolerance evaluation purposes.” Thus, to run a successful test, one can average 5 neighboring lines together to satisfy the tolerance. In the case of 800 lines, the bandwidth is 2Hz, and a 10Hz maximum is allowed. This will always result in a successful test, provided the control is on target.

MIL-HDBK-340A, Vol. 1, Table III (PDF)