# How do I properly compute mean time to failure?

I have a product of which we have shipped something like 500 units over the last five years. This product is not intended to be user serviceable; a failure of any component results in the unit being replaced. The majority of these units have never seen problems and are still working fine. Some have been damaged and come back for repairs.

How would I go about computing mean time to failure (MTTF)? Would I include only the units that have failed? Or would I also figure in all units that are currently operating? What about the fact that I only have the date of sale, not the date of installation? And that I don't know what fraction of the installed time the unit is running? Should I just make reasonable assumptions?

• What is the expected accuracy of MTTF? – Mahendra Gunawardena Aug 26 '15 at 11:58
• @MahendraGunawardena I have no idea how I would begin to answer that question, unfortunately. – Stephen Collings Aug 26 '15 at 12:59
• Is it possible to go to customers and ask them what sort of operating time the units they've bought see? Even if it's a rough estimate, I imagine that'll give you a better sense of uptime than you could get just by guessing on your own. – Trevor Archibald Aug 26 '15 at 14:12

First off, always remember that garbage in = garbage out; so if your data is garbage then your statistics will be garbage.

In this situation your optimal data would be something like Run Hours Until Failure and your entire dataset would have failed already. With this in mind you may want to choose a conservative number from whatever statistic you calculate.

Since you only have failure from sale date this may be skewed toward a higher MTTF.

Since not all of your product has failed yet you can look at a smaller subset of your population, say the 1st six months of production. A higher percentage of these have failed most likely (since the product you sold last week shouldn't fail this week, hopefully).

If your failure proportion is still too low then you may have to try to fit the data to a distrubution keeping in mind that you only have the low proportion of the distribution, i.e. you must extrapolate from the dataset to a fitted curve.

For example, Weibull Distribution would work well here and is commonly used for MTTF data. The idea here is to fit the proportion of your dataset which has failed to a corresponding proportion of a distribution. If your proportion of products in your dataset which have failed was 48.66% then you would fit it to that probability on your hypothesized distribution as shown by the shaded area in the following image.

This can be rather intensive, however, for anything besides an exponential distribution.

Another method of extrapolation is by Degradation Analysis

If you don't have hard data, making assumptions (preferably "reasonable" ones) is the only option you have. (Maybe that's why engineers used to call their slide rules "guessing sticks...")

You can't ignore the fact that most of the units have not failed so far. A plausible approach to this would be to use the times-to-failure that you know, to fit the parameters of statistical model of the failure process. You also need to check that the predictions of the model are consistent with the raw data, before you use it to forecast anything.

A commonly used model in reliability engineering is the Weibull distribution, which can represent quite a wide range of different "root causes" of failure, and will automatically adjust to use the "best" shape of probability curve (within limits, of course) to match your real-world data.

Google will find plenty of hits for "Weibull distribution tutorial" etc, but if you are new to this it would be a good idea to get an overview of "reliability engineering" before you pitch into the details. A good place to start would be a professional engineering organization, for example the American Society for Quality (ASQ).

The most practical way to make the estimate would be to use some computer software rather than figuring out how to do the math by hand, but without more specifics of the problem, it's hard to recommend any particular package.

• Your comment about making sure the predictions are consistent with raw data was spot on! We put together a Weibull distribution spreadsheet. From the very limited set of failures thus far, our MTTF came out to be something like six months, with an expected 99% failure rate within five years. This is completely inconsistent with reality. So that raises the question... what now? – Stephen Collings Aug 27 '15 at 14:56

The statistical tool Weibull as suggested by the previous two responded is the tool of choice for Mean Time To Failure (MTTF) calculations. Based on your comment as capture below, it appears that Weibull Analysis didn’t generate expected results.

Most statisticians that I have worked with recommend a sample size of 30 for most statistical analysis. My suspicion is that the limited data size might not be helping the analysis. I suggest starting with a simple average and standard deviation calculation for time to failure based on the available data. You might have to make few reasonable assumptions when calculating time to failure base on your product. For example

Assumption: Time to failure (days) = Return date – Ship date

With current technology and available data you might be able to refine your assumptions too.

Improved Assumption: Time to failure (days) = Customer product return ship date – Customer initial product receive date

The point that I am making is good reasonable assumptions will help generate a good data set. Also in my experience basic average and standard deviation calculation will help gain good insight into the problem at hand.

The other point to be aware is determine if the failures are due to

• Special cause
• Common cause

Root cause analysis need to be performed on special cause failures and corrective action needs to be implemented. Common cause failures are just part of doing business in the specific industry and with the specific customer base.

Hope this response finds a reasonable solution to the problem at hand.

References:

• Nice mentioning of special cause failures. They could be attributed to manufacturing but they could also be attributed to field use outside of suggested operating parameters which would void the warranty. Would you agree not to include special cause failures in MTTF? – Acumen Simulator Aug 31 '15 at 17:19
• Also, what parameter are you testing? Since it is a small population that has failed, I would try to find a distribution for "% of total made during Year X that failed" instead of finding a distribution for the actual items. You might find some interesting results that way. – Mark Aug 31 '15 at 18:23
• @user38826, I agree MTTF should not include special cause failures. Base on OP previous I am too sure of OP has address any failures due to special cause. My response is in line with Mark comment. It might be worth while investigate that special cause failures are not included in MTTF. – Mahendra Gunawardena Aug 31 '15 at 23:21