## How About Weibull?

### Can I use it instead of MTBF?

Published: Monday, November 13, 2017 - 12:02

The term “Weibull” in some ways has become a synonym for reliability. Weibull analysis = life data (or reliability) analysis. The Weibull distribution has the capability to describe a changing failure rate, which is lacking when using just mean time between failures (MTBF). Yet, is it suitable to use Weibull as a metric?

### What to use instead of MTBF

Use reliability, the probability of successful operation over a defined duration. This typically includes a defined environment as well. It’s the definition of reliability as we use it in reliability engineering.

Instead of saying, “We want a 50,000-hour MTBF for the new system,” say instead, “We want 98 percent to survive two years of use without failure.” Be specific and include as many couplets of probability and duration as is necessary and useful for your situation. For example, you may want to specify that 99.5 percent should survive the first month of use, and that 95 percent should survive five years of use.

### Weibull is a distribution, one of many

Weibull, lognormal, normal, exponential, and many others are names of statistical distributions. They are formulas that describe the pattern formed by time to failure data (e.g., repair times, and many other groups or types of data).

Instead of Weibull analysis, you could easily also say, “We’re going to conduct a normal analysis.” In reliability work, I often first explore a set of life data by fitting a Weibull distribution to the data and plotting the probability density function (PDF) and cumulative density function (CDF). It’s a first look and not the end of the analysis.

Each distribution has four functions that are useful for reliability engineering work:

1. Reliability function

2. Cumulative density function

3. Probability density function

4. Hazard function

Because I tend to like being positive about a product, I often use the reliability function (calculated at specific points in time, *t*) instead of the CDF, which is the probability of failure over time, *t*.

The reliability function is a function of time; hence, my suggestion to always include a probability and duration when specifying or reporting reliability values.

### Weibull is a distribution, not a metric

The Weibull distribution, like other distributions, is a curve or equation. It is not a metric on its own.

Define the time intervals of interest, run out the calculations (I recommend using the reliability function for the appropriately fitted distribution), and then you have a metric.

Goals are not metrics, yet they should be something we can measure that help us make better decisions.

For example, setting reliability goals for one month, the warranty period, and during the expected use life. Then use vendor or testing data, and/or field data, to estimate the distribution of the life data. Then again, for specific time intervals of interest, calculate reliability.

Now you can compare your data to your goals and make informed decisions.

Just doing Weibull is not a metric.

In many circumstances it is clear that when someone says he is going to do a Weibull analysis, it’s really a life data or reliability analysis not limited to only fitting a Weibull distribution. At least I hope so. The result of the analysis may be an estimate of reliability during a time period of interest.

How do you use the term “Weibull?” Have you heard it misused?