Chi Squared Distribution for Reliability Demonstration Testing

When planning a Reliability Demonstration Test (RDT), your objective is to demonstrate a certain reliability (or MTBF) at a certain Confidence Level (CL).

If you want to determine what MTBF at a particular CL you have demonstrated, if you tested T number of hours, you would use the formula listed below.

Of course, the actual test time would be dependent upon the Acceleration Factor (AF) and the number of samples on test.

The AF will be determined from the acceleration of environment, duty cycle, and/or electrical parameters (voltage, current, or power).

A RDT will demonstrate that based upon the test results, the true population MTBF is at least Theta hours at a (1-alpha) CL.

The demonstrated MTBF (Theta) for the specified CL will be calculated using the following formula:

Theta = 2 * T / Chi SQ [(2r+2), alpha]

where
Theta = Demonstrated MTBF
T = Test time X Number of test items X AF
Chi SQ = Chi Squared distribution, the one used because
it best fits our demonstration model
Alpha = (1 – C.L.)
r = number of failures
2r+2 = Chi SQ degrees of freedom (Time terminated test)