Using Chi-Squared Distribution in Reliability Test Planning Calculations

Chi-Squared Distribution can be applied to compute Reliability or alternatively MTBF, when the failure distribution can be modeled as an exponential distribution.

Given this assumption holds, the MTBF can be calculated as below:

Where:

i> n.T is accumulated test time.

ii> f is the number of tolerable failures

iii> C.L. is the expected confidence level

MTBF can be calculated from Reliability Equation considering exponential distribution as below:

where R is the expected value of Reliability at the end of test time.

Finally, the Accumulated Time (n.T) is computed by multiplying the two-sided Chi.Squared value (looked up from the published tables) by the MTBF value computed as above.

In Windchill R&R, this can be done as below:

Step 1: Navigate to Chi-Square Test option in Test Planning Calculator.

Step 2: Specify the required parameters as below:

Optionally, you can also specify the test time item wise, rather than total time.

Step 3: Click on Calculate to display the Accumulated Test Time (n*T)