Calculate the time to failure from characteristic life

There is a simple formula to calculate the time to failure(TTF) for any probability of failure(POF) given the characteristic life. The characteristic life is usually taken at 63.2% or 50% probability of failure. An example to explain this can be considered with regards to plated through hole reliability in temperature cycling. A test of Copper plated through holes is performed to find the failures due to Copper fatigue in temperature cycling. 

Let's consider the case of an 8 mil PTH with 25µm plating. The plating quality is "Good". The board properties come from a stackup properties calculator. The temperature cycle has a delta of 150°C.

The IPC-TR-579 "Round Robin Reliability Evaluation of Small Diameter Plated-Through Holes in Printed Wiring Boards" model calculation shows that the "number of cycles to failure" are predicted to be 264.  In this tool the "Cycles to Failure" are calculated for 50% POF.

Use the following equation to convert this to any POF using the Weibull distribution

Where:

TTFin = Time to Failure input
TTFout = Time to Failure output
Pin = Probability for the TTFin prediction (Pin = 0.5 for the 50% reliability)
Pout = Probability for the TTFout prediction (Pout = 0.01 for 99% reliability)
Beta = beta (beta=4 is used for “Quality Factor: Good”)

Implemented in a spreadsheet:

The time to 99% failure is 760 cycles and similarly for any other value of wanted POF entered in the "Pout" field. In this case Pout = 0.01 means 99%.

This calculation works for any time to failure prediction where the Weibull parameter Beta is known. 

Copyright Gil Sharon July 16, 2015 . All rights reserved.