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How to Make a Weibull Analysis in 5 Steps – Part 1

As a novice practitioner, I believe is better to learn by doing. To see the impact from collecting the data till you communicate preliminary result. It is a self-fulfilling task that keeps you eager to learn more. One of those tools is the Weibull analysis for Life Data analysis. This tutorial is a first introduction to the area and possible cases.

I got introduce to the reliability engineering area due to the Weibull analysis. I needed to make a prediction on fleet components, and asses the component lifetime. Back then I didn’t have any methodology to follow with some rigor. Luckily I got introduced to this technique by some of my colleagues, and since then, I am learning more and more every time I use it.  

1. Short Introduction

I would recommend to spend some minutes having a look to the material. At the end, this blog post is a introduction.

The Weibull analysis have many applications in the field of engineering. Among others:

  • Reliability of components: How many spares do I need?
  • Batch defect detection: Are my failures due to a serial defect?  
  • Warranty cases: How much cost shall be expected due to warranty claims?
  • Risk analysis: How much should be tested? All the components? Till when?

Probably this technique is the most used technique to analyze and interpret life data. Also, some of the advantages are the flexibility of the Weibull distribution, interpretability of the parameters, and the straight relation to failure rates and bathtub curve.

O’Connor Patrick, Practical Reliability Engineering

There is plenty of good material out there, although for this introduction I will recommend this short presentation on the topic, “An introduction to Weibull analysis” by Rong Pang

2. Which kind of data are you dealing with?

Typically, Weibull analysis aim to describe the behavior of a population with specific failure modes (more on this later). As a simplification we need some failure data to start with the analysis. That data might be the usage of a certain component (miles, cycles) or time based.

Example:

We have a population of 20 bearings and 7 of them failed and been replaced after 412, 551, 858, 600, 700, 400 days/cycles of operations. The rest have survived. This is an example of right censored data. It is known that the bearings have failed due to the same failure mechanism.

Note: this is the data you can download in the template of this online app.

So this is the kind of data that we need to deal with. Ironically, this is the less analytical step, and were at least 50% to 80% of the time is spend in a typical analytical process.

3. Challenge the input data

The data needs to be interrogated. Does the data represent the truth?  Are mixed failure modes in the data? I will use the term failure mode and failure mechanism indistinctively. This not correct, but for this introduction will suffice. Maybe I will write another post talking about this point.

This is the engineering part of the analysis. If the analysis gets bad input data, the results will be bias. The old saying garbage-in, garbage out.

4. Online Weibull Analysis tool

And now the fun part! There are many tools out there in the market too do a simple Weibull analysis. Among others some of them with tutorials are MiniTab, JMP, Weibull++ and WinSMITH. This four options are commercial software, some more sophisticated than others.

Since this is an introduction, I will use an online tool that I put together, available in the browser for free.

Go ahead and play with the template data or introduce yours to get some results.

5. Interpret the results.

The software is not going to challenge the underlying assumptions with regards the models. It is necessary to challenge the results: Does the distribution fit well the data? Will another distribution fit better? Do we see any ‘artifacts’ in the data?

Example:

We can read that  the eta is 1.396 days. This means that 63,2% of the population is expected to have failed “around” that time. In the plot is where the blue line crosses the grey dotted line. 

Same reading but with 10% of the population (B10) is that after 558 days is expected that 10% of the population have failed (in our case 2 bearings, since is a population of 20). 

This fit is with the method MLE, which I will talk in another post.

Word of caution!

cc by Jill Stuart

This is a first introduction to the world of life data analysis and Weibull analysis, therefore as any novice you should be conservative when making any interpretation/prediction and challenge any assumption at every step. On top of it, I will not recommend to use this insight in a real life application yet. Use your new tool in the toolset in a safe environment, and develop your skills over time. That now you can walk, does not mean that you can run a marathon (yet).

As an extra, there is a weibull generator tab, in case you want to play with the different parameters and see the effect on the plot.

Conclusion

So you did your first Weibull analysis. This approach is over simplistic, but you will be surprised how in some industries beside Oil & Gas and Aerospace, this kind of technique is still far away from the field practitioners.

If you’d like to dig a bit deeper in the topic I will recommend to start with the book “The New Weibull Handbook” by Dr. Abernethy. You can get the old version freely available online, or the modern version at Amazon.

After that If you still feel like would like to go deeper I’d recommend “The Weibull Analysis Handbook” by Bryan Dodson

Now that you know how to make a weibull analysis, how would you approach this topic for new practitioners in the field?? Is this approach too complex? Over simplistic?