### 5 Critical Tools for Your Lean Deployment

As your customers demand more and organizations fight to stay competitive, the battle to create more value with fewer resources is ever present. How can you leverage Lean tools to thrive in your business?

# What I Learned from Treating Childbirth as a Failure

My wife and I are expecting a baby girl soon—very soon, in fact, as in "Will this blog post be published before the baby is born?" soon. The due date given is May 19th, but we stat geeks know that a point estimate just isn't good enough...we want probability intervals that reflect the uncertainty in the data.

I found a chart that lets me know the number of babies born to "spontaneous labor" by each week of pregnancy, but I'm interested in more precision than just the week.  I converted the data to days instead of weeks (for example Week 40 starts on day 280 and runs through day 286), and here it is:

 Week First Day Last Day Births 37 259 265 1166 38 266 272 3048 39 273 279 6616 40 280 286 8015 41 287 293 4852 42+ 294 * 1317

One of the more overlooked areas of statistics is Reliability, a field that was originally intended to estimate when parts would fail but has much broader applications than that. If you ever have ranges of values in which your data fall, rather than exact values, Reliability is the menu for you!

Data such as this, where we have a count of occurrences within a range of values (common when things are reported in whole days, weeks, etc.) but know the real distribution is on a continuous scale, is known as Arbitrarily Censored data. In this case I'd like to know the odds of the baby being born by certain days, which requires me to first find the distribution of the data. To do this I go to Stat > Reliability Survival > Distribution Analysis (Arbitrary Censoring) > Distribution ID Plot and complete the dialog like this:

Based on the excellent fit on the probability plot and high Correlation Coefficient, I'm going to use the 3-Parameter Weibull distribution for my analysis:

So from our original categorized data, we now have a continuous distribution to work with.

To learn some more about what this distribution means for when to expect a baby, I go to Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis and complete the dialog like this:

I also click on "Graphs" and choose to show a "Cumulative failure plot".

First I look at the "Characteristics of Distribution" table from the Session Window:

So what can I learn from this table?

• The Mean, also known as MTTF or Mean Time to Failure (remember these terms were created for part failures and not childbirth!), tells me that on average babies are born almost exactly at 280 days, or 40 weeks.
• The Median is about 280.5 days, so about 50% of children are born by half a day past 40 weeks.
• The First Quartile and Third Quartile tell me by which day 25% and 75% of babies are born, respectively, so the "Middle 50%" of babies are born between days 274.5 and 286...since for us day 280 is the 19th, that means we have a 50% chance of the baby being born between Sunday the 13th and Friday the 25th.

Minitab also gives a "Table of Percentiles" in the Session Window, but I prefer to use the Cumulative Failure Plot and again want to remind readers that the term "failure" is associated with a part or product failing and not a child being born...

This graph plots the day of pregnancy on the x-axis, and the percentage of babies born by that day on the y-axis.  So for a given day—such as day 285—we can find the corresponding point on the line and read that a little over 70% of babies are born by that day (our first was five days late).  We could also look at the cumulative probabilities of days 280 and 281—47.47% and 52.14%, respectively—to find that the odds of the baby being born at some point on the due date are about 4.67%.

Now that we have used what was originally very categorized data to form a continuous distribution, we could answer many questions more precisely, such as:

• When should a relative arrive on a 7-day stay to have the greatest chance of being there for the birth? (May 17th)
• What are the odds of the baby being born on a weekend? (28.6%)
• What are the odds of the baby being born on her great-grandmother's birthday, May 14th? (3.4%)
• What should we name her?  (Actually Parametric Distribution Analysis can't answer that but it's still a pretty great tool)

Read the followup to this blog post.

Name: Omar Mora • Thursday, August 8, 2013

Joel, this is a great post. You cannot imagine how popular is becoming among maintenance engineers in Costa Rica. The way you explain how to use Realibility analysis is other areas more than in "failure analysis" has create some possitive motivation for maintenance engineers to use Reliability in their day-to-day activities (of course, the Repairable Systems menu is still the most popular). Again, thanks for your contributions.

Name: Jason • Thursday, October 31, 2013

Hi Joel, I have questions about how you get the answers for the last few questions. Can we discuss it via email or skype.

Name: Joel • Thursday, October 31, 2013

Jason-

I'll email you momentarily and would be happy to answer questions through either channel.

Name: Kyle • Friday, March 21, 2014

Hi Joel,

I just discovered this post last week. Love it! I'm applying it to safety. I, too, have the same question. How did you get answers to the last four (4) bullet points?

Name: Joel • Wednesday, April 2, 2014

Kyle-

Now that this has come up twice in the comments, I think it's time for me to write a "Part II" to explain it! If you want the answer more urgently just let me know.