MTBF to PoF

Received this questions the other day.

So if we were to go from a MTBF requirement of 7,500 hours @ 40 degrees C how would we address this requirement as a PoF? Would we say the PoF is 90% reliable after 7,500 hours of operation? Or would we state this as something else?

The discussion is on how to move towards using physics of failure (PoF) type approaches rather than parts count. The underlying question is about how to set reliability goals.

If the goal is 7,500 hours @ 40°C how should this be converted to a meaningful goal for use with a PoF approach?

As with most inquiries in reliability engineering we first need to understand the failure mechanisms. Are they temperature deponent? Are other stresses, like thermal cycling, humidity, salt fog, etc., as or more important in causing product failure? What are the use conditions? duty cycle? Also, what is the product’s function or functions? A reliability goal is more than a failure rate at some specific temperature.
A reliability goal consists of four elements:

• Function
• Environment/Use profile
• Duration
• Probability of Success

Stated another way, reliability is the ability of product to function as expected in a specific environment with a specific probability of success over a stated duration.

A goal that include only 7,500 MTBF and a temperature touches only on two of the four elements. It is missing the duration, function and most of the environment and use profile information. Granted we often understand the function and environment/use profile when discussing a specific product and these items are often well documented in specification documents. That leaves duration and probability of success. Stating a failure rate without a duration over which it applies is meaningless. If the failure rate only applicable for the first hour of operation, first month of operation or expected to apply over the entire service life of the product? We don’t know.

Independent of the means to estimate or demonstrate or measure the reliability of a product, the goal is simple to detail. Clearly state the function, environment/use profile, and include important duration & probability of success couplets. For example, for my passenger car, the function is to provide comfortable transportation for up to five people over North American roads (for me mostly in Northern California). Then the couplets.

99% reliability (probability of successful operation) over first 90 days – set as an understanding of effort to minimize early life failures that damage brand image and create buyer’s remorse.

95% reliable over first 3 years, other than schedule maintenance – set to minimize warranty related costs.

90% reliable over first 10 years – set to minimize cost of ownership.

Setting for early life failure periods, warranty and service life for consumer products set’s three points related to business and consumer expectations. For military products, maybe setting couplets based on mission duration and operation life may make more sense. Set couplets of duration and probability of success based on your business and customer requirements.

Note there is no mention or limitation of a life distribution with goal setting, also no confidence intervals. The goal is a statement of what is desired and the best evaluation of the goal is with customer use. It is the estimating, predictions, testing and modeling that we need to consider life distributions and confidence intervals.

So back to the presenting question. How should we convert 7,500 hour MTBF to a PoF requirement? If the duration is 7,500 hours as implied in part of the question, then the MTBF value permits us to calculate the reliability. R(7,500 hrs) = exp [ – 7,500 / 7,500 ] = 0.36 or only a 36% chance of successful operation over 7,500 hours. This simple calculation often is enough for those concerned to say they really want a low failure rate for up to 7,500 hours of operation. In that case, 90% reliable over 7,500 hours of operation makes more sense and much high reliability than 36% as implied when using 7,500 hour MTBF as the goal. 90% may not be adequate, and it will depend on the technology involved, the use environment, cost, and design. What’s important?

Physics of failure is a method to detail the effects of time and stress on the probability of failure for specific failure mechanisms. If there are models for the dominate failure mechanisms, then PoF provides an efficient means to estimate the life distribution. PoF is a modeling tool to estimate the time to failure distribution, it then can be compared to the goals (business and consumer driven) to determine if the product meets or does not meet the reliability goals.

The goal does not depend on the prediction method. Set the goal on what you and your customers want, is technical possible, and can afford.