Have you said or have you heard someone say,
- “Let’s assume it’s in the flat part of the curve”
- “Assuming constant failure rate…”
- “We can use the exponential distribution because we are in the useful life period.”
Or something similar? Did you cringe? Well, you should have.
There are few if any failure mechanisms that actually occur with a constant hazard rate (we often even use the technically incorrect term failure rate, when talking about the instantaneous failure rate or hazard rate). The probability of failure over a short period of time now and some time in the future, say next year, is most likely going to different.
So, why do we cling to the assumed constant failure rate?
Anto Peer, Diganta Das, and Michael Pecht wrote in Appendix D, “Critique of MIL-HDBK-217” within the National Academy of Sciences book Reliability Growth: Enhancing Defense System Reliability about the nature of failure (hazard) rates. The original handbook gather data and calculated point estimates for the failure rates. Later editions of the handbook included the assumption of the generic constant failure rate model for each component. The adoption of the exponential model, which implied calculations, started in the 1950’s.
In part due to the contractual obligation to use the 217 handbook and widespread adoption of the prediction technique, the constant failure rate assumption became part of the ‘how reliability was done’. James McLinn in a paper in 1990 commented that the users of the system worked to propagate the method rather than improve the accuracy of the method. (McLinn 1990)
How do we know the failure rate changes?
Beginning in the 1950’s researchers and analysts notice component did exhibit changing failure rates. They also notices the range of failure mechanism that occurred and began modeling failure mechanisms. The work to predict failure rates based on the physical or chemical changes within a component due to applied use stress became known as physics of failure.
Numerous studies and data analysis have shown either a decreasing or increasing failure rate with time. One example is the work by Li, et.al (2008) and Patil, et.al. (2009) showing the increasing failure rate behavior for transistors.
You own data most likely shows the non-constant failure rate behavior. All you need to do is check the fit of the data to an exponential distribution to see the discrepancy.
Today we have the embedded assumption of a constant failure rate and the reality of non-constant failure rates. We also face the need to accurately describe the probability of failure based on field data, experimental data, or simulation. Simply avoiding the assumption of a constant failure rate frees us to use the information contained within time to failure data and models.
McLinn, James. 1990. Constant failure rate – A paradigm in transition? Quality and Reliability Engineering International 6:237-241.
Li, Xiaojun, Jin Qin, and Joseph B Bernstein. 2008. Compact modeling of MOSFET wearout mechanisms for circuit-reliability simulation. Device and Materials Reliability, IEEE Transactions on 8 (1): 98-121.
Patil, Nishad, Jose Celaya, Diganta Das, Kai Goebel, and Michael Pecht. 2009. Precursor parameter identification for insulated gate bipolar transistor (IGBT) prognostics. Reliability, IEEE Transactions on 58 (2): 271-276.