Here is a Challenge: Life Data Analysis
Some years ago a few colleagues compared notes on results of a Weibull analysis. Interesting we all started with the same data and got different results.
After a recent article on the many ways to accomplish data analysis, Larry mentioned that all one needs is shipments and returns to perform field data analysis.
This got me thinking: What are our common methods and sets of results when we perform life data analysis?
The Life Data Analysis Challenge
So, here’s a challenge: Given the data in this lifedatachallenge.csv file, perform an analysis to answer two questions:
 How many returns should we expect next month?

Is the rate or returns increasing or decreasing?
3 [Bonus question] Based on your analysis and experience, what questions should we answer next?
Here is the data, lifedatachallenge.csv
Notes About the Data
It is made up data and kept relatively simple for the purpose of allowing a wide range of analysis approaches. The data represent the time to failure in days. The count of days are from shipment till the day, including weekends and holidays, the customer reported the failure.
The item is a battery powered portable hand drill for use by a home workshop or woodworking enthusiast. In other words, not a contractor. The drill is used sporadically for a wide range of uses and situations around a persons home, office, or workshop.
To keep things very simple there were 1,000 units shipped on one day and the failure data is all from that one day of shipments. Not all units have failed, only 75 have failed.
The data is in one column and not sorted nor in any particular order.
Reporting Your Results
There are two main points in this challenge.
First, please answer the two (three) challenge questions based on your analysis. Provide a summary of your analysis, graphics, charts, or what ever makes sense for us (me and your peers) to understand your results and how to you got them.
Second, please comment on what, if any, assumptions you made for your analysis. For example, if you assume the data is exponentially distributed (please, I really hope not!), list that as an assumption.
Third, I really do have a problem with keeping to two points today, please comment on what additional information you would like to have available, if any, to improve your analysis.
Please add your results to the comments section below, or email them to me (Fred) at fms@nomtbf.com
That is the challenge. Looking forward to your results and analysis.
Thanks for taking part and enjoy.
Hello Fred! I opened data in phone, but I do not see any state indicating sencored or failed units. Which ones and at which day these 75 failed?
Hi Jurgita,
All 75 in the data file have failed. there is no column to indicate censored or failed, as all in the data set have failed. The value is days till failures. The total units shipped in 1,000 thus 1,000 – 75 are right censored.
hope the helps.
Cheers,
Fred
Ok, now understood, thank you, Fred! One more question: do you have a deadline for this challenge? The date on the top 24th of May, does it mean it finished already? :)
No deadline – the date is when the post was published. cheers, Fred
Hi Fred,
I think you agree that failure times are enough for statistic engineer but are not enough for reliability engineer. We need know failed part, failure mechanism, the cause of failure.
Based on this data I can say 75 products from 1000 has some kind of manufacture defect and has failed. Failure time has Weibull distribution (beta=2.5; eta=2000). I think this defect “burned out” and does not appear on the rest of the products.
Thanks for the interesting question.
Hi Oleg, we have very little information concerning the data concerning failure mechanisms, etc. So, based on the analysis of the available data, what questions do you have?
For your analysis, how did you treat the censored data? What analysis approach did you take? Which software package and what assumptions or settings?
For example, using Weibull++ and ignoring the 925 right censored points, I get one fit, adding the censored data assuming the last point in the data is the censor point, using rank regression or MLE I get two other answers.
I have found other software package provide different answers as well.
So, two questions, which is right and why? Based on your analysis, rather than state conclusions, what questions should one be asking to help make the right conclusions?
Cheers,
Fred
Hi Fred,
In this example, the operational conditions of one hand drill and another can vary a lot (the item that has failed after 515 days and the item that has failed after 1460 days can have been used in a very different way – load, time cycle, environment…). So first question could be: can we group failures in a certain use pattern? Second question could be related to the failure reporting system (the questions mentioned by Oleg: failure effect? failure mode? potential failure causes? etc.)
With no more data and from a pure statistical point of view I can share these three approaches:
A. Parametric estimation approach without taking into account the censored data:
– Rank Time To Failure data
– Benard approximation for the time to failure probability
– Least Squares fit to Weibull (R^2=97.1%): BETA=2.48; ETA=2002
Question 1 response: 925 units x [1 R(3673+30 days)/R(3673 days)] = 84 expected returns during the next month.
Question 2 response: BETA >1 –> increasing failure rate –> increasing return rate.
In this case we do not use the information that 925 units have survived 3673 days and our estimation could be very conservative…
B. Parametric estimation approach with taking into account 925 right censored data:
– Rank Time To Failure data
– Mean order number and Benard approximation for time to failure probability
– Least Squares to fit to LogNormal (R^2=94.1%): MEAN=9.86; STANDARD DEVIATION=1.32
Question 1 response: 925 units x [1 R(3673+30 days)/R(3673 days)] = 2 expected returns during the next month.
Question 2 reponse: Failure rate function is increasing with time –> increasing return rate
In this case, we have used the censored data information, but they represent a big proportion of the data (>90%). Could our estimation be very optimistic? I guess it could, but I think we should use this information in the analysis.
C. Your “beloved” inservice MTBF = 1778 days
– Average failure rate during the period = 1/1778
Question 1 response: (constant failure rate assumption during next periods) 925 units x 1/1778 x 30 days = 16 expected returns during next month
Question 2 response: constant failure rate assumption during next periods –> constant return rate
In this case, assumption shall be checked (if possible…). Here we could not know if our approach seems to be conservative or optimistic as we have make our analysis too simply…
I am looking forward to listening your thoughts
Cheers,
Ricardo
Thanks Ricardo for the detailed analysis – The weibull with censored data, which I think is the way to go, although I would use Maximum Likelihood Estimation method given the large number of censored data… Cheers, Fred