Plot the Data

Just, please, plot the data.

If you have gathered some time to failure data. You have the breakdown dates for a piece of equipment. You review your car maintenance records and notes the dates of repairs. You may have some data from field returns. You have a group of numbers and you need to make some sense of it.

Take the average

That seems like a great first step. Let’s just summarize the data in some fashion. So, let’s day I have the number of hours each fan motor ran before failure. I can tally up the hours, TT, and divide by the number of failures, r. This is the mean time to failure.

$latex \displaystyle&s=3 \theta =\frac{TT}{r}$

Or, if the data was one my car and I have the days between failures, I can also tally up the time, TT, and divide by the number of repairs, r. Same formula and we call the result, the mean time between failure.

And I have a number. Say it’s 34,860 hours MTBF. What does that mean (no pun intended) other than on average my car operated for 34k hours between failures. Sometimes more, sometimes less.

Any pattern? Is my car getting better with age, or worse?

A Histogram

In school we used to use histograms to display the data. Let’s try that. Here’s an example plot.

 

 In this case the plot is of service and repair times (most likely similar to the times the garage has my car for a oil change and tune up). Right away we see more than just a number. The values range from about 50 up to about 350 with most of the data on the lower side. Just a couple of service times take over 250 minutes.

Using just an average doesn’t provide very much information compared to a histogram.

Mean Cumulative Function Plot

Over time count the number of failures. If the repair time is short compared to operating time, than this simple plot may reveal interesting patterns that a histogram cannot.

Here is a piece of equipment and each dot represented a call for service. The x-axis is time and the vertical axis is the count of service calls. While it’s not clear what happened shortly after about 3,000 hours, it may be worth learning more about what was going on then.

 

Even after the first there or four point after 3,000 hours would have signaled something different is happening here.
MCF plots show when something is getting worse (more frequent repairs) by curving upward, or getting better, (longer spans between repairs) by flattening out. Again, a lot more information than with just a number.

Plot the Fitted Distribution

Let’s say we really want to assume the data is from an exponential distribution. We can happily calculate the MTBF value and continue with the day. Or, we can plot the data and the fitted exponential distribution.

Let’s say we have about five failure times based on customer returns out of the 100 units placed into service. We can calculate the MTBF value including the time the remaining 95 units operated, which is about 172,572 hours MTBF. And, we can plot the data, too.

Here’s an example. What do you notice, even with a fuzzy plot image?

 

The line intersects the point where the F(t) is 0.63 or about the 63^rd percentile of the distribution, and the time is at the point we calculated as the MTBF value (off to the right of the plot area).
Like me, you may notice the line doesn’t seem to describe the data very well. It seems to have a different pattern than that described by the exponential distribution. Let’s add a fit of a Weibull distribution that also was fit to the data, including the units that have not failed.

 

The Weibull fit at least appears to represent the pattern of the failures. The slope is much steeper than the exponential fit. The Weibull tells a different story. A story that represents the story within the data.

Again, just plot the data. Let the data show you what it has to say. What does your data say today?

The Fear of
Reliability Statistics

When reading a report and there is a large complex formula, maybe a derivation, do you just skip over it? Does a phrase, 95% confidence of 98% reliability over 2 years, not help your understanding of the result?

Hypothesis testing, confidence intervals, point estimates, parameters, independent identically distributed, random sample, orthogonal array, …

Did you just shiver a bit?  [Read more…]

5 Ways Reliability Was Important to Me Today

I suspect reliability of the products and services in your world plan an important role in your day to day existence. For me, maybe I just pay attention to reliability, yet today in particular I tried to notice when things were just working as expected.

Rather then consider everything that touched my life today, I’ll narrow this down to just five. [Read more…]

Statistics and the Bad Reputation

In a recent reliability seminar I learned that the younger engineers did not have to take a statistics course, nor was it part of other courses, in their undergraduate engineering education. They didn’t dislike their stats class as so many before them have, they just didn’t have the pleasure.

Generally I ask how many ‘enjoyed’ their stats class. That generally gets a chuckle and opens an introduction to the statistics that we need to use for reliability engineering. I’ll have to change my line as more engineers just do not have any background with statistics.

I suspect this is good new for Las Vegas and other gambling based economies.

Statistics are hard

On average there are a few folks that get statistics. No me. There are those that intuitively understand probability and statistics, and demonstrate a mastery of the theory and application. No me.

I like many others that successfully use statistical tools, think carefully, consider the options, check assumptions, recheck the approach, ask for help and still check and recheck the work. Statistics is a tool and allows us to make better decisions. With practice you can get better at selecting the right tool and master the application of a range of tools.

Sure, it’s not easy, yet as many have found, mastering the use of statistics allows they to move forward faster.

Statistics are abused

Politicians, marketers, and others have a message to support and citing an interesting statistic helps. It doesn’t matter that the information is out of context nor clear. When someone claims 89% of those polled like brand x, what does that mean? Did they ask a random sample? Did they stop asking when they got the result they wanted? What was the poll section process and specific questions? What was the context?

The number may have been a simple count of positive responses vs all those questioned. The math results in a statistic, a percentage. It implies the sample represented the entire population. It may or may not, that is not clear.

We hear and read this type of statistic all too often. We discount even the well crafted and supported statistic. We associate distrust with statistics in general given the widespread poor or misleading use.

To me that means, we just need to be sure we are clear, honest and complete with our use of statistics. State the relevant information so others can fully understand. Statistics isn’t just the resulting percentage, it’s the context, too.

Statistics can be wrong

Even working to apply a statistical tool appropriately, there is a finite chance that the laws of random selection will provide a faulty result. If we test 10 items, there is a chance that our conclusion will show a 50% failure rate even though the actually population failure rate is less then 1%. Not likely to happen, yet it could.

We often do not have the luxury of the law of large numbers with our observations.

So, given the reality that we need to make a decision and that using a sample has risk, does that justify not using the sample’s results? No. The alternative of using no data doesn’t seem appealing to me, nor should it to you.

So, what can we do, we:

• Do the best we can with the data we have.
• Do exercise due care to minimize and quantify measurement error.
• Strive to select samples randomly.
• Apply the best analysis available, and,
• Extract as much information from the experiment and analysis as possible.

As with wood working there are many ways to cut a board, with statistics there are many tools. Learn the ones that help you characterize and understand the data you have before you. Master the tools one at a time and use them safely and with confidence.

How Many Assumptions Are Too Many Concerning Reliability?

When I buy a product, say a laptop, I am making an educated guess that Apple has done the due diligence to create a laptop that will work as long as I expect it to last. The trouble is I don’t know how long I want it to last thus creating some uncertainty for the folks at Apple. How long should a product last to meet customer expectations when customers are not sure themselves? [Read more…]