Pith and Vinegar

noreply@blogger.com (John Borneman) — Wed, 21 May 2025 13:40:00 +0000

Engineers solve problems. No matter the type, technical, logistical, or other. So, remember John’s basics of problem solving.

Challenge everyone’s assumptions, especially your own.

A corollary to this would be; Consider people’s motives when they give advice or solutions. One reacts to one’s reward system

Compare and contrast. What ‘IS’ the issue? What “IS NOT” the issue?
Dive deep, then dive deeper (keep asking “why”)
Perform good statistical analysis of your data but don’t over-complicate it. A lot can be learned from Box Plots, histograms and data plotted in time order. Never assume data is normally distributed without testing the data.
Procedures are great but don’t use them as an excuse to stop thinking
Every once in a while, managers’ need to be challenged. Managers are not always right.
When communicating do not “bury the lede”. Give the important points first, then go into detail.
A good engineer knows how to get things done within the system... a great engineer knows how to get things done despite the system.

And lastly remember that Engineering is one continuous struggle with entropy.

The Myth of the Universal Problem Solving Method

noreply@blogger.com (John Borneman) — Mon, 08 Mar 2021 22:55:00 +0000

Fellow Statistical Problem Solvers;

I wrote the following after reading the article posted on Linkedin called "Planning the Abandonment of Six Sigma" by Dr. Gregory Watson. Dr. Watson posits that the many current models used in problem solving each have unique reasons why they are not universal models and that such a universal continuous improvement model is needed, particularly to meet the needs of "Quality 4.0".

Okay. I have never been a "buzz word" person and Quality 4.0, like its parent, Industry 4.0 are to me just fancy ways of framing concepts without solving anything. All Quality (or Industry) 4.0 says is that things are changing including information collection and evaluation and that we need to learn how to deal with and use those changes to thrive.

Here is a quote from Juran.com "The core concept of Quality 4.0 is about aligning the practice of quality management with the emerging capabilities of Industry 4.0; to help drive organizations toward operational excellence."

Lots of pretty words that (to me) boil down to; "Hey! Things are changing. Let's use that and keep making things better!" Which is what you and I have been doing all along.

But back to Dr. Watson's article. First, to his credit, he does a great job outlining many of the top improvement models and bringing out their weaknesses. Also the new IAQ model does make some of the currently unspoken steps, more clear.

I won't dwell on his assertions that DMAIC does not engage in a 'strategy formulation process' nor complete the improvement process controls. I strongly disagree. DMAIC's failures are management failures not process failures - as could be said for any method.

To me, the issue that any call for a new and improved continuous improvement model includes the assumption, especially in many managers minds, that a continuous improvement engineer should not need their brain. If we can be given a list of steps, and we follow those steps, an answer will pop out. Sorry, but any improvement effort requires a trained investigator to think, adjust, and use whatever tools are needed to reach the solution. This may even mean moving outside a specific model into uncharted territory.

As a (primarily) DMAIC practitioner, I have learned that the DMAIC is a flexible process that can be pared down or expanded up. And it always must include problem identification strategies going into a project and also consider implementing sustainable changes at the end. But this is also true for the other models.

I guess that having a one size fits all model is a great goal. Don't misunderstand. We should all continue to explore "improvements to the improvement process." But remember that often we have different models because they are each tuned to a specific need. Why would I ever consider using a financially based model to solve a shop floor quality issue? But its damn good for finances.

The new "IAQ" model proposes a seven step process (Characterize, Investigate, Explore, Solve, Evaluate, Implement, Monitor).

Think about those seven words and think about what you do every day as you find and solve problems. Sound familiar to you? To me the IAQ is just re-branding current concepts by changing the names. Its DMAIC. Its PDCA. Its the '8 Step Problem Solving Process" and all the others.

All improvement models, whether DMAIC, PDCA, 8-Step, Shainin, or others are subsets of an unspoken "master" model. This master model could potentially be described as "Find" problems, "Solve" problems" and "Fix" problems. In this case the PDCA model approaches our perceived "Master" model the closest and to be honest, that is what the IAQ model really does and does well. It provides that master concept. But I reject it replacing all other models, but I would embrace it being used, especially as a learning tool.

Bottom line is, that as an investigators of problems, we have a calling to learn as many tools as possible and to apply the appropriate tool for the particular job at hand. It may be a simple PDCA one time, a full DMAIC another, and a Shainin based process the next. Or (and most important) it may be an amalgam of two or more models. Maybe I get part way into my PDCA work and realize that a DMAIC SIPOC would be a great way to frame my issue. However, as I am "Defining" my problem, I pull in some Shainin "FACTUAL" (c) tools to help narrow down my problem definition at which point I find I need to transition into a Design for Six Sigma process.

Continuous Problem solving needs to be fluid, flexible, and adjust to the situation. That's all. It takes work. It takes training. It takes lots of study on ones own time. It also takes mentoring and coaching. What it does not take is a universal method with checklists that anyone can do.

noreply@blogger.com (John Borneman) — Tue, 03 Nov 2020 04:04:00 +0000

My book "The Brass Man and Other Stories" received a very good review from Reedsy.com (Discovery). One phrase from the reviewer, Christopher Rhine, that I really liked was, "The namesake of the collection and entire second half is brilliantly commanded by “The Brass Man,” a multi-generational, Foundation-like septpartite story following a brass-enclosed, robot named Sini during the multiple crises of a small island town."

Yes! "Foundation-like" Woo Hoo.

http://www.amazon.com/dp/B089M1FBNZ

The Brass Man and Other Stories

noreply@blogger.com (John Borneman) — Tue, 02 Jun 2020 23:50:00 +0000

I have self published a book of short stories and one novella!

amazon.com/author/johnborneman

Shared Moment

noreply@blogger.com (John Borneman) — Mon, 20 Apr 2020 00:33:00 +0000

She was his last customer of the day.

He watched her as she unloaded the
grocery cart. She watched him as he
scanned her items past the register.

When he handed her the receipt they
both felt a spark as their fingers
brushed.

Their eyes met and they laughed
realizing that it was a winter day,
with low humidity, and they were
both standing on carpet.

Evaluating the Risk and Reward of your Statistical Analysis

noreply@blogger.com (John Borneman) — Fri, 14 Feb 2020 17:11:00 +0000

Most of us out there who perform statistical analyses to guide them and their organizations to solve problems do not have advanced degrees in statistics. We’ve attended classes at university, we’ve been to varying levels of Six Sigma training, or we’ve done self-study.

But I think I am safe to say that one thing we all have learned is that statistically evaluating a set of data is complicated and rife with uncertainty. We choose statistical tools to use among many possible tools and numbers ‘pop’ out telling us if our hypothesis is correct or not. From that data, we proceed to either take an action or not take an action depending on the statistical results.

But how many of you finish with your analysis and wonder, what if my analysis is wrong? Did I have enough data? Did I choose the proper statistical tool? Do I even know the proper statistical tool? Arghh!! (*)

Most of us who are in decision making roles that require analysis of data to determine choices are cautious people and risk averse. But we had our training. My ANOVA said that part A is better than part B so why ask more questions?

I suggest that after any statistical analysis and before taking an action based on that analysis, we ask two more questions.

What is my confidence I am right?
What is my risk of being wrong?

And I don’t mean the statistical definitions of ‘risk’ and ‘confidence. I mean just sit back and take a broad overview of your data, where it came from, how you evaluated it and ask yourself how strongly you feel your results are true and ask yourself to decide what the impact is on your customer if your analysis is wrong?

Then you can decide what to do?

But how?

I came up with a simple chart to help guide what action to take. I don’t know whether this is original or not, but here you go anyway.

Let’s look at each box in a little more detail.

1. Confidence of Being Right is HIGH, Risk of Being Wrong is LOW (green quadrant)

You’ve done your analysis. You’ve used multiple tools, did your “Practical / Graphical / Analytical” analysis and you feel very good that you’ve found something significant and the benefits are measurable..

You find that the cost to implement is acceptable and after some thought and study you realize that if you are wrong, the implications to the customer are minimal.

So, you recommend to Do It.

2. Confidence of Being Right is HIGH, Risk of Being Wrong is HIGH (blue quadrant)

However, you find that the cost to implement is very high or you find that the effect on the customer if you are wrong is high.

Maybe wait and collect some more data. Even if your are pretty certain about your results,more data might help convince management, your customer (and you).

3. Confidence of Being Right is LOW, Risk of Being Wrong is LOW (tan quadrant)

However, you find that the cost to implement is acceptable and after some thought and study you realize that even if you are wrong, the implications to the customer are minimal.

So, you can decide make the change. After all the risk of being wrong is low and cost to implement is also low. In parallel you might decide to find someone more experienced than you to check your work and see if they agree.

4. Confidence of Being Right is LOW, Risk of Being Wrong is HIGH (red quadrant)

You’ve done your analyses. You’ve used multiple tools, did your “Practical / Graphical / Analytical” analysis. But you are still not certain if you’ve found something significant. Maybe you’re uncertain if the tools you used apply to this data set. Maybe you are not certain if the data was collected properly. Or maybe you don't know if you have enough data.

You also see that the cost to implement is very high or you find that the effect on the customer if you are wrong is high.

You Don’t Do It. You might return to this sometime if more data is collected or if something else changes. Or, you might decide to find someone more experienced than you to check your work and see if they have suggestions on how to become more confident

Please comment below if you’re experience is different or if you feel this is way off base.

* I suspect Doctors of Statistical Science also have these 'argghh' moments

Evaluating the Validity of Data Reported in Social Media and the Press

noreply@blogger.com (John Borneman) — Mon, 13 May 2019 17:11:00 +0000

I was going to write a blog posting on this topic, but then I found this excellent article written by The Writing Center of the University of North Carolina. Yes, maybe I wimped out, but this is really a good summary of how to look at data critically.

https://writingcenter.unc.edu/tips-and-tools/statistics/

However, just to reinforce a couple points.

Don’t trust data because its quoted on one of your social media ‘friends’ posts. You may trust Bob, and Bob trusts Alex, who has always trusted Sanjay, who trusts Cindy, who trusts Cal, who has an agenda and is distorting the truth.

As the article points out, there are three ways to calculate the center of a data set (Mean, Median, Mode). Often those with an agenda choose the one that helps to make their point the best.

Finally, I am always suspicious when a data set makes me say ‘Yes! That’s just what I thought. I knew I was right.”

Am I falling for a biased study, because it matches my beliefs? Question yourself as much as you question others.

Outlier Identification

noreply@blogger.com (John Borneman) — Mon, 15 Apr 2019 13:02:00 +0000

Its been a while since my last post. But I can assure you that this post is not an outlier... or is it?

Identifying outliers in a data set is one of the most difficult tasks we face as problem solvers. Mostly because there are no definitive tests which absolutely identify whether a data point is unique or if it is a natural, expected part of the data set.

Outlier identification reminds us that being a statistical practitioner requires more than a good handle on statistical tools and good knowledge of the process from which the data was collected. Outlier identification requires the ability to use one's mind to take in all this information and make the right decision. Well, at least not make the wrong decision.

The attached is a summary of some methods to look at outliers. It is not a complete compendium of the issue. Please comment below if you have other methods for outlier identification that you have used, or if you feel my presentation needs corrected or adjusted.

Outlier Indentification

Does country radio play more male singers than female singers?

noreply@blogger.com (John Borneman) — Fri, 13 Jul 2018 15:01:00 +0000

I admit that I do not listen to much country music but when I do, it always seemed to me that the playlists on country radio are almost entirely men.

But is this a fair claim? Can statistical analysis help us decide?

When I first started thinking about this I realized that it is probably not fair to compare radio playlist counts of men and women singers to the proportion of men and women in the population (50/50). I do know that this sounds odd.

We need to consider that if the proportion women in the business of recording country songs is less than 50%, then we cannot expect the number of records by female artists that are ‘available’ to be played to be 50% of all country records. If fewer women are recording, then fewer women are available to be played on the radio.

To try to find out the real proportion of men to women who are in the business as a country artist I searched on line and found two lists of country artists which appeared to be independent of radio playtime.

In Wikipedia I found a list of “modern” country artists and I categorized these artists and groups by gender. The other list was from Country Notes which has attempted to create a complete list of all country artists from the early days through today. This list even contains a few pop stragglers such as Lionel Ritchie and Olivia Newton John who veered into the country lane.

Note: Group acts are counted as male or female depending on the lead singer (so Sugarland is counted as Female and Old Dominion is counted as Male).

From these two lists the ratio of male country artists to female country artists is about the same. The wiki list shows a ratio of 66% men to 34% women and the Country Notes list shows a ratio of 63% men and 37% women.

Given an assumption that more women are in the business today than in the early days, I picked a ratio of 65% men to 35% women as the make-up of all Country artists “available” to be played. One can see that this is much different number than 50% men and 50% women.

Therefore, right or wrong, when we listen to country radio, we should expect to hear about 65% of the songs feature male singers and about 35% of the songs feature female singers.

A side issue of “why” less women are in the country music business is a deeper topic and may actually be the real point of the issue. However, this article is not going to address that. I am just going to look at the numbers.

Now that we know what our expected proportion of male singers to female singers is, we can search the playlists from a sample of country music radio stations and calculate the percentage of men and women being played on the radio. We would compare this observed proportion to our expected proportion. I also took data from the Billboard Top 50 for the years 2016 and 2017 as well.

But how do we determine if the observed percentage of men versus women on a playlist is significantly higher than expected? If we find that a station is playing 66% male singers and 34% female is that significant? Is 70% men versus 30% women significantly different from our expected 65/35 ratio? Is 80/20 significantly different?

One method that can help us decide is a statistical tool called the Chi-Squared analysis for categorical data. This tool takes data such as Yes/No, Male/Female, Democrat/Republican/Independent and helps us to calculated differences.

This tool is used often in sociology, medicine, and biology studies and evaluates the observed proportions and compares them to the expected proportions. It then lets us know if the observed is significantly different than expected. For instance Chi-Squared analysis has helped to answer questions such as is there a difference in the effectiveness of Drug A between men and women or between Adults and Children.

Of course caveats to the results of this particular study apply.

This study looks only at the numbers not at the reasons.
Data from only four country radio stations was collected. Also the data from these stations is for one specific day’s playlist.
I do not know how Billboard determines its “Top 50”.
Chi-Square tests are sensitive to sample size. With small samples sizes it is harder to show a significant deviation between observed and expected.
These results do not mean to imply any intentional bias by any organization or radio station.
These results cannot explain ‘why’ more male singers are played than women.

Example Chi-Square Calculation:

Results:

Of the two samples from a major song ranking service's Top 50 list, the Top 50 for 2017 did not show a difference between observed and expected and the 2016 Top 50 did show a significant difference may exist (more men on the list than women)

Of the five radio stations sampled, 3/4 showed a significant difference may exist (more men played on the radio than women)

So there you go. The answer to the question “Does country radio play more male singers than female singers?” is a resounding “maybe.”

Capability and MSAs are NOT the same thing!

noreply@blogger.com (John Borneman) — Thu, 10 Aug 2017 11:27:00 +0000

I have found that people often confuse MSA’s and Capability Studies. Far too often, I hear the question ‘when will we run the capability study on the tester?’ And while I am sure that you few braves souls who read my blog do not fall into this trap, you might know of people who do. Maybe giving them this link will help.

MSA’s are for tests and gages. Capability studies are for the processes being measured.

Or to state it another way, MSA's give us confidence that we can measure the capability of our process to produce parts to our customers specification.

One can talk about the 'capability' of a tester, but only when the word is being used in its classic sense, i.e. ' the extent of someone's or something's ability.'

Let's review....

Measurement System Analysis

A measurement system is a collection of procedures, gages and operators that are used to obtain measurements. Measurement systems analysis (MSA) is used to assess the ability of a measurement system using the following statistical metrics; stability, repeatability (test / re-test variation) and reproducibility (operator variation).

The most common metric for an MSA is the Gage R&R value. This value is a ratio of the variation due to the measurement error (repeatability and reproducibility) to the total variation of the system (including both part and measurement variation).

Gage R&R = Variation due to R and R / (Measurement + Part Variation)

Sometimes, one cannot find parts that demostrate part variation to use in the MSA. An example is in electronics with electrical testing (in-circuit tests or functional testing). These systems make hundreds of measurements and it is impractical to attempt to create or find part variation to use in the MSA.

In these cases we usually run the MSA with ten or so parts off the line. In these cases, the part variation will be very low. Therefore the Gage R&R should be calculated as a percent of the tolerance spec range.

Gage R&R = Variation due to R and R / Tolerance Range

Capability Analysis

From Wikipedia…. “The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk, Ppk, Cp, and/or Pp).

The output of this measurement is usually illustrated by a histogram and calculations that predict how many parts will be produced out of specification

Two parts of process capability are: 1) measure the variability of the output of a process, and 2) compare that variability with a proposed specification or product tolerance.

Cp (or Pp) = Spec Range / (6 x total system variation (std dev))

Capability studies assume that the measurement variation is low enough to not be a factor, and that the “total variation of the system’ is effectively due to process and part variation.

Remember that to do a proper capability study we need a successful MSA, a stable process, and an large enough sample size to be statistically significant (usually about 90 pieces). Getting a good capability study from prototype builds is difficult due to the (usually) small sample size.

iSixSigma Article

noreply@blogger.com (John Borneman) — Mon, 10 Jul 2017 17:11:00 +0000

My new article is on iSixSigma: A Study of Estimates of Sigma in Small Sample Sizes -

https://www.isixsigma.com/sampling-data/a-study-of-estimates-of-sigma-in-small-sample-sizes/

Studying the Capability of Capability Studies - Part 3

noreply@blogger.com (John Borneman) — Wed, 19 Oct 2016 18:09:00 +0000

Sample Size

As most of you know, statistical tests calculate a mean and confidence intervals on the mean. We are all familiar with the fact that as our sample size decreases our knowledge of the “true” mean becomes less and less certain. This is important for tests that use the mean -- such as the t-test and ANOVA.

Below is an example of two data sets “Apples” and “Oranges”. In the first experiment we only had 15 samples of Apples and 15 samples of Oranges. Plotting the means with their calculated confidence intervals shows that we cannot differentiate between Apples and Oranges (since the confidence intervals overlap, we cannot be certain that both means are not equal).

But if we increase the sample size to 100 Apples and 100 Oranges, our confidence intervals decrease and we can now tell that Apples do have lower values than Oranges.

I am sure that most of you are realizing where this diversion from capability is heading.

Capability studies (and Gage R&R studies) use the standard deviation as a primary statistic and like the mean, the standard deviation also has a confidence interval.

The confidence interval of the standard deviation is also dependent on the sample size. As the sample size increases our estimate of standard deviation becomes better. For those who like this stuff, here is the formula for confidence interval on the Standard deviation.

Given a standard deviation of “1” and using the formula above, we can now plot the how the confidence intervals contract as sample size increases.

In other words, as my capability study’s sample size becomes smaller, the range in which the “true” standard deviation can exist becomes larger.

So, here’s the kicker.

One can calculate the upper and lower limits of Pp for various sample sizes and alpha values and look at the potential range of Pp or Ppk for a capability study.

Let's look at two examples of how this works.

Example One: From the chart above, let’s assume an alpha of 0.05 and a sample size of 15 units. Let’s also assume that we ran our capability study and calculated Pp = 1.67.

Now we could stop here and report to our customer that our Pp = 1.67. But, if we do the calculations we see that the actual Pp could lie between Pp= 1.1 and Pp = 2.2. If your customer has a savvy Six Sigma expert, you could be busted.In my Six Sigma youth, I was busted. Lately, I've been doing the busting. I like that better.

Example Two: If we increase the sample size of the capability study to 120, and if our calculations find a Pp = 1.67, then the actual Pp could be between Pp = 1.5 and Pp = 1.8. With the larger sample size we are much more assured that the Pp is actually close to 1.67. In this case, we would have a much better chance of defending a Pp = 1.67.

In summary, never forget that the likelihood that the Pp value you report is effectively correct is dependent on the size of your sample. This is one reason to avoid capability studies on small prototype builds and experimental runs.

We can also see from the charts above that once we have a sample size greater than about 90 pieces, the incremental improvement (decrease) in the range of our standard deviation (and thus our Pp) becomes small enough to ignore.

I hope that you have enjoyed these blog postings on the vagaries of Capability studies (Cp versus Pp, Data distribution, and Sample size). Practically we cannot always control these factors, but we can at least go into our study with our eyes open and a clear understanding of our ‘risk of being wrong’.

Hmmm... Maybe my next topic will be "The Risk of Being Wrong"

Capability of Capability - Part 1
Capability of Capability - Part 2

Studying the Capability of Capability Studies - Part 2

noreply@blogger.com (John Borneman) — Tue, 18 Oct 2016 16:30:00 +0000

In the previous post I listed three items to watch out for when evaluating capability study results.

Cp versus Pp
The distribution of the data
Sample size

In part one, I discussed Cp versus Pp and hopefully helped cast some light on the differences between these two measures of capability.

In this blog post I will deep dive deep into the distribution of data. As a reference you may want to review my earlier blog post Normal Data is Nearly Never Normal.

The thing to remember is that the standard capability study assumes your data is normally distributed. This assumption of normality, while not so critical in other statistical tools, is very important in capability studies.

Cp and Pp are giving us predictions based on a sample of how our population will behave out in the far tails of the normal curve. These measures are using mean and standard deviation to create a normal distribution, and from this predict how many of our parts, over the entire population of parts, will fall outside our tolerance limits.

If we assume our process is normally distributed, and measure Pp = 2.0 (6 sigma process), this means we are predicting extremely low ppm levels of defects, less than 0.002 ppm (3.4 ppm with the irritating 1.5 shift).

What this means (regardless of your position on the 1.5 shift) is that if the data is not actually normal we could either over estimate or under estimate our risk.

Below is an example of this. Using Minitab, I generated 1000 rows of random data using a Weibull distribution (Shape = 1, Scale = 100, Threshold = 10). I somewhat arbitrarily chose 0 and 400 and spec limits. I performed a Capability study using three variations. (1) assuming the data was normal (2) assuming the data was Weibull, and (3) assuming the data was normal but setting the zero lower limit as a lower boundary.

Weibull data calculated as Normal. Ppk = 0.38, Expected ppm outside limits = 127,006

Weibull data calculated as Weibull. Ppk = 0.69, Expected ppm outside limits =102,069

Weibull data calculated as Normal. 0 = LB. Ppk = 1.02, Expected ppm outside limits =1132

This example, while maybe not the best, does illustrate several things. Firstly, that one can get many different calculations for Ppk and 'expected ppm defective' depending on your assumptions. In this example, if the engineer did not check the distribution, but did realize that the lower spec limit was a lower boundary, he or she would assume the process had a Ppk of about 1.02. But if he or she checked the distribution and ran the study using a Weibull distribution, the Ppk would be worse -- closer to 0.69.

Bottom line is that one must be practical. I often attempt to find a distribution or transformation that fits and if so, I use that to calculate Pp, etc.

But if I cannot find a good fit (for instance data that is heavily left leaning toward zero) we may find that the fit to normal is horrible, but the fit to other distributions is only marginally better.

I am not sure if a Doctor of Statistics would approve, but in these cases I do two things. One, I pick the distribution or transformation with the lowest Anderson DaArling value and run the Capability study using that. I then create a Time Series plot (if the data is in time order) or a Box Plot and add the spec limits to that.

This gives me a "practical" view of the range of the data in relation to the specification limits and I can gage whether my estimate of Ppk makes sense.

Have fun. Use the comments to add, comment, correct, spindle or mutilate.

Next time. "Sample Size and Pp"

Studying the Capability of Capability Studies - Part 1

noreply@blogger.com (John Borneman) — Wed, 12 Oct 2016 14:28:00 +0000

Ok. I admit I was trying to be funny in my post title. But the issue in today's blog is "how capable is the capability study?" Or to state another way, "when should we be careful in how much we trust our capability study results?"

Here are three items we should be aware of when designing, running and calculating a Capability study.

Cp versus Pp
The distribution of the data
Sample size

This post will discuss Cp versus Pp. Future post will cover distribution of the data and Sample size issues.

First lets agree to just discuss overall capability, i.e. Tolerance Range / 6*sigma. Everything discussed below will apply to Cpk and Ppk as well.

Cp versus Pp

Okay. Diving right in. As many of you already know, the difference between Cp and Pp is in how the standard deviation (sigma) is calculated.

Cp uses a standard deviation calculated from the "Within" variation (when there are logical sub-groups).

Pp uses all the data regardless of sub-groups to calculate the standard deviation.

As an example, assume I am printing solder paste onto a PCB (for the non-electronics people, think of silk screen printing of T-shirts, only not really).

I could do one of three things.

Select one pad and measure the paste thickness, then repeat that same measurement for each sequential PCB until I reach my desired sample size.

Cp (using 'Within' sigma) would be calculated from the Moving Range (ala I-mR charts).
Pp would be calculated using the total data set and the standard formula for sigma.

Select several pads on the PCB (maybe five total, one on each side and one in the middle) and measure thickness of all these pads for each PCB used in the capability study.

Cp would use "within" sigma calculated from the pooled standard deviation of the five pads in each PCB across every board. (Pooling is similar to averaging the standard deviations of each sub-group. Its complicated. Another post for the future.
Pp would, as before, use the entire data set and the standard formula for sigma.

Collect measurements of paste thickness for each PCB in the Capability study but do not keep track of the order of the build, or sub-groups of any kind.

Cp is not possible in this case. Warning! Minitab will still assume the data is in time order and calculate a Cp but in this case Cp should be ignored.
Pp - yep. Use all the data.

The "within" variation (sigma) will always be equal to or smaller that the sigma calculated from the entire data set. Therefore Cp will always be equal or higher than Pp. Or, one can think that the Cp will contain only the common cause variation and is therefore one measure of how good the process can become if all the special causes are eliminated. Pp contains both common cause and special cause variation and is one measure of how the process is doing today.

It may help to see an example (below) to understand the difference. Let pretend we are measuring drilled holes in a PCB.

The Minitab charts below show "drilled hole" data that is normal/ We also see from the Time series plot that there is a gentle descent of the data over time -- a special cause event which could be due to drill wear.

We can also see that the Cp = 36.42 while Pp = 1.45.

We can interpret these results to mean that as of today our process has a capability of 1.45, but if we could identify and eliminate the special cause condition we could be as good as 36.42. Maybe not the best example, but I hope it help illustrate the concept.

Quite often if you -- as a customer -- asks for capability data, you will get a list of data and a "Cp" value. You need to always question the supplier if the data is in time order or if there are logical sub-groups. Is the capability reported actually Pp?

Bottom line is that many people speak of and report Cp (or Cpk) values when they are really giving us Pp (or Ppk). The differences are subtle, but can be critical.

Use the comments to give me your thoughts.

Normal Data is Nearly Never Normal

noreply@blogger.com (John Borneman) — Wed, 24 Aug 2016 15:38:00 +0000

Yes, I said it.
Normal data is nearly never normal.

In our Six Sigma classes we study outliers, shift, drift, and special cause events. But what we don't always realize is that the "odd" data points are quite often ubiquitous and not as rare as we would like.

First, let's look at a set of data that is behaving itself. The chart below is for a set of screw torques taken sequentially from a 'smart' driver. We can see that the data is normal (p=0.895) and the histogram and time series plot back that up.

So let's look at another set of data. Solder paste print height (think screen printed solder for you non-electronic assembly folks).

Yes! It's also normal. p= 0.095 which is greater than 0.05, right? I'm good to go.

Well.... obvious there is some discrimination issues here. The data is lumped into groups. Probably won't affect my calculations. But do I see something going on in the time series data? A pattern of rising and falling?

One very good tool for bringing out these patterns is called "Resistant Smooth" which according to Minitab "smoothes an ordered series of data, usually collected over time, to remove random fluctuations." (how Resistant Smooth works is a topic for another blog post).

Here is the actual solder print data compared to smoothed data.

So, maybe a pattern here. What do you think? At least you can now walk the process and see if you can find if the pattern is real and if so, where it is coming from.

So. Solder paste data is normal, right? Or at least normal enough to run a capability study. So we take solder paste height data from another process and run our normal capability calculations and....

What the heck!? Quick. What does the time series chart show?

Obviously there is something going on here in the process that creates a dual distribution. It appears to be time to go the gemba and see what is happening.

I guess the message here is two-fold. One, don't assume normality, even if past data has proved to be normal. Stuff happens. Two, unless you are performing tests that are sensitive to normality (e.g. capability) don't obsess over the distribution. Use non-parametrics, use logic, find the patterns, find the causes of the "odd" data points. Go to the gemba. Dig deep and learn.

And remember.

Normal data is nearly never normal.

Hope for the Future

noreply@blogger.com (John Borneman) — Tue, 19 Jul 2016 11:59:00 +0000

I have always hated the dark projections of our future, the generated and re-generated lists of the top ten terrible things that our future has in store.

It is easy to look at the dark side of things. Ironically the toughest part is to look for the positive.

So here is my Top Great things to expect in the future list.... Remember. You heard it from this futurist first.

1. We'll eliminate the use of oil in under 50 years via cheap, low-impact methods. Fuel cells will lead the charge, but will not be the ultimate answer.
2. We'll find that the computer models for global warming are more aggressive than actuality, but the end of oil will render the argument moot.
3. We'll send people to Mars and beyond. Man will live on more than one world thereby drastically improving humanities chances of survival.
4. We'll finally learn that the world has '7.9 billion and growing' cultures and we will celebrate each and every one of them.
5. We will realize that the only issues of true import are related to health and happiness.
6. We'll develop cheap portable power generators that can be carted to remote populations and run without much attention.
7. Electricity will be replaced with something new, cool, and wonderful within 50 years.
8. We'll become less connected to technology rather that more. We'll rediscover the joy of sensing the world through our eyes, ears, and touch.
9. We'll find out that someone else is out there -- and that they aren't interested in enslaving or eating us.
10. Pandemics will be no longer be possible.

Now. Don't wait for it. Go make it happen!

Statistical Poo

noreply@blogger.com (John Borneman) — Wed, 22 Jun 2016 13:41:00 +0000

What you are looking at below is a photo of the hand rail on our front porch steps. The X is the top of the rail. The rail descends to the bottom step toward the top of the picture and the post is about three feet high near the bottom of the picture. See the white specs? They are three feet below the X.

Now. About those white specs...

Birds come and sit on the rail (I said "sit"), mostly on the "X" and they can sit facing any direction in 360 degrees (blue arrow). . I suspect this is true because of the nice semicircular ring of poo on the porch and on the rail.

Now, to go a little Bayesian on you, our prior estimate of the probability of a bird facing any particular quarter of the blue circle, knowing nothing else, would be p=. 25 for any quarter of the circle.

But studying the data shows us that there is more poo on the porch than on the rail. This shows us that most birds prefer looking out toward potential cats rather than in towards the front door. Otherwise I'd be writing about a ring of dead half eaten birds.

We also note that the arc of poo has a gap on the right side. Hmm. Arc of Poo? Sounds like a literary novel doesn't it?

DEEP VOICE: "Coming to bookstores everywhere, "Arc of Poo", by the Murray Award winning author, John Borneman. "

Sorry. Lost focus.

The data shows us that given birds always poo while sitting on a post, that they prefer facing between ENE to NNW. Birds prefer a quarter of the circle slightly off top dead center. Also a few brave birds do like looking at the southern quadrant towards our door given the evidence of poo on top of the rail (it is a nice door!). Bayesian calculations would include an estimate of the prior, P(bird facing north) and P(poo found on south side of rail), our new data expressed as probability of poo in a quadrant given the bird is facing north and the probability that the bird is facing north given no poo is evidenced (constipated bird).

From this we can calculate a posterior distribution or the probability that a bird is facing north given poo is found on the southern quadrant.

This leaves two questions. One. Why does this matter?

Well. One point is that data and statistics are everywhere. Now bird poo stats may only be of interest to ornithologists But the larger point is that one should not be afraid to look for patterns and probabilities in everything. These patterns of numbers and other data types help us understand both our professional and our personal lives. You will be surprised what you can learn.

The other point is that this silly bird poo example is a good illustration of Bayesian probability calculations. What if we substituted the presence of a bird facing north with the presence of a cancer in one part of your body? And what if we substitute the evidence of bird poo found, with a test for this type of cancer?

We now see that calculating the probability of cancer given a positive result of a test would be very good information to know. In fact Bayesian calculations for various medical conditions have shown that in some cases, a positive result on a test may only have a low probability that you actually have the condition.

Here is a link to more than you want to know about medical testing and Bayesian approach.

Oh. I said two questions. The other question? Why am I sitting here on the porch writing about poo when I should be cleaning it up? Funny. Asked and answered.

Contributing to the Minitab Blog

noreply@blogger.com (John Borneman) — Wed, 15 Jul 2015 14:22:00 +0000

I was involved in finding the mistake mentioned in this three part Minitab blog series. Part three covers my analysis of the data.

Lessons from a Statistical Analysis Gone Wrong

The original Minitab challenge was to use statistics to compare the horse American Pharaoh with previous Triple Crown contenders.

While I am still not sure of the validity of using this data set (Kentucky Derby race finishing times) in a Capability Analysis*, it does illustrate the need for getting good data (not truncated data) and the need to question transformations before using them.

The Minitab blog is still one of my favorite statistical blogs.

* as my horse loving wife pointed out, the owners and jockey run the race to beat the other horses, not to set a new record. So the data may not be independent and/or from the same distribution. Regardless, Big Red is still impressive after all these years.

Finally. Another Statistics Post by John!

noreply@blogger.com (John Borneman) — Fri, 08 May 2015 12:37:00 +0000

I know, who cares? But you're getting my latest posting anyway.

Every since Fisher presented the "p-value" as a method to judge statistical validity of a hypothesis (null hypothesis significance testing or 'NHST'), statisticians have been arguing about it.

Recently the editors of Basic and Applied Social Psychology (BASP) announced that the "journal would no longer publish papers containing P values because the statistics were too often used to support lower-quality research." BASP prefers using effect size and descriptive statistics.

Many statistical journals and blogs commented on this including two of our favorite blogs, Minitab and John D Cook's blog.

While not a statistician, I have noticed one thing that may or may not be significant (Hah. See what I did there?). Most of the arguments of p-values come from the 'soft' sciences where groups of people are being tested, e.g. psychology or medicine and where the effect (or lack thereof) of a treatment is critical to understand in detail.

I also note that the goal of these 'softer' sciences (and I am NOT criticizing these sciences at all), is to find if a treatment has a marked effect. Does Drug A really help reduce symptoms? Does procedure X really improve psychological responses? Also in these type of studies, covariates and confounding is much more of a concern.

These types of studies are drastically different than in the engineering world where we are often happy eking out tiny improvements. We are happy with small improvements of variation, or tiny shifts of the mean -- as long as the cost of these improvements are reasonable (various caveats apply to this statement).

However, whether an investigator is measuring the diameter of a ground metal shaft, or the effect of a drug on smoking cessation, one must not relay on any one statistical test or metric. Also, if one has performed an experiment, any experiment, and p = 0.05, then that should not tell the investigator that they have found an effect with significance. It tells one that, depending on other factors including effect size, economics, variation, one may be justified in running additional experiments.

Finally, I found a neat article, Statistics: P values are just the tip of the iceberg, which lays out a nice way to look at how data should be evaluated. The author's
"data pipeline" is something that I do with all my data.

Collect the data --> clean the data --> subject that data to non-parametric exploratory data analysis --> evaluate various models and create statistical summary statistics (effect sizes, etc) --> then look at the p-values of any hypothesis tests you may want to run.

I suggest making a copy of the chart shown in the article and post it on your desk, next to your monitor, beside your coffee mug.

Here is another great article on the history and real intent of p-values and null hypothesis significance testing.

Let The Data Speak For Itself

noreply@blogger.com (John Borneman) — Thu, 31 Jul 2014 13:48:00 +0000

As a Six Sigma practitioner (and not a trained statistician), it is very easy to learn all the statistical

tools such as ANOVA and the t-test, Capability Study, MSE, and Control charts. Statistical analysis

tools, such as Minitab, makes completing ones analysis just a matter of clicking buttons.

In all the delight of creating wonderful charts and analyses, it is difficult for any Statistical

Practitioner, no matter how experienced to forget that not all data sets have a normal distribution, and

not all statistical tools are robust to non-normal data.

What I like to do first is channel John Tukey, one of the main proponents of exploratory data analysis

(EDS). Dr. Tukey encourage researchers to first examine the data without any assumption of distribution.

Let the data speak for itself. One tool, created by Dr. Tukey is the Box Plot, a graphical tool that

shows the data in quartiles, with outliers indicated.

Another very good tool for comparing data sets without assuming a distribution is to create an Empirical Distribution Function graph (EDF) for each data set and compare how well they overlap each other.

The best way to explain the EDF is by example. Say, I have set of data points that I have arranged in

order from lowest value to highest value [2,3,5,7,9,10,11,12,15,19]. We can therefore see that 100% of

the data lies at or below the value "19" (10th value/10 total data points). Also that 50% of the data

lies at or below the value "9" (the 5th value/10), and that the value "2" comprises 10% of the data

(1/10). From this we can plot a graph with the percentage (or proportion) on the Y axis and the data points on the X axis

But how do we use this technique to help us evaluate data? If one is faced with two data sets, for instance time to complete a task under Condition 1 versus time to complete a task under Condition 2. The Six Sigma problem solver wants to see if the two data sets are the same. But since he or she is not sure if the data is normal ('time to an event' data is often not normal), they may use the EDF comparison first.

Let us first look at the raw data. Always a good start (see Data Sets A). We can see the two data sets (Data 1 is the time to complete the task under Condition 1 and Data 2 is for Condition 2).

We can make a a couple conclusions from this data. Data 1 and Data 2 have similar low times, but Data 1 has some times much higher than Data 2.

But lets calculate the EDF data (seeData Sets B). We can see that we now have the data sets aligned with the proportion data. So lets plot the EDF (see CDF Data 1-2). The shapes of the two EDFs for Data 1 and Data 2 are very disimilar. the EDF graphical comparison highlights these differences.

Where this really comes in handy is when two data sets are more similar (see CDF KS1). See that the maximum difference between the two EDF curves are highlighted. This max distance value (in this case 0.85 - 0.55 = 0.3) can be used to calculate a statistic for significance. This is called the Kolmogorov-Smirnov Test and more on this may be found HERE.

This test may be done by creating the graphs in Excel and using the simple calculations of the KS-Test. Also Minitab has a macro that runs the KS-Test.

Now go "get all Tukey" on your data and evaluate it first without assuming a distribution.

John

PMAPs and Value Stream Maps – Which is Better?

noreply@blogger.com (John Borneman) — Fri, 11 Jul 2014 14:17:00 +0000

Those of you who have worked with me in the past know the answer to this question. "The better tool depends on the problem you are trying to solve."

General PMAP Thoughts:

For me, the PMAP is the basis of all problem solving. It is quite simply, a diagram that you create to show the inputs and outputs to any process. And yes, everything is a process, so everything can have a PMAP -- from a librarian cataloging books, to a golfer analyzing their swing, to building a car.

Are you trying to reduce the costs in a call center? The output is a correctly answered question (quality), done in a reasonable time (cost). The inputs could include (and I am not a call center expert), computers, phone connections, software to help guide answers, the operator, their training, etc.

Are you improving the first time quality of an assembly process? The output is quality measured by FTQ. The Inputs could include, equipment, operators, procedures, materials, etc.

PMAPS can take several forms. The classic linear flow model and the 'swim-lane' model are two commonly used formats for a PMAP.

Classic PMAP

All PMAPs show the sequence of tasks which represent the series of steps in your project’s process. A process map includes steps that are needed to transform any activity’s inputs into outputs. The classic PMAP shows the process steps in a linear fashion, from beginning of your process to the end.

For example; Process 1 (place part in fixture) --> Process 2 (lower holding clamp) --> Process 3 (form part). Each of these individual steps will have inputs (fixture, part, operator, method, electricity) and outputs (part in fixture, part held secure, part formed to specification).

From the PMAP one can analyze how failure of the outputs directly relate to failure of one or more of the inputs. Using a combination of process experts, DOEs and Failure Mode Effects analysis, we can quickly begin to focus on "where to work" to improve our process.

See an example of a linear PMAP here (credit DMAIC Tools) → http://www.dmaictools.com/wp-content/uploads/2009/11/flowcharting0002.PNG

Swim Lane

Swim Lane Process Maps are practically the same as the classic PMAP, but it orders the process into "lanes." The Swim Lane shows the flow of your project through functional groups instead of just time based. My first step is "specify product" done by sales or a program team, the second process step is 'design product' done by Engineering, the third step is "Build Product" done by Operations, etc.

They use the same format for showing the Steps, Inputs, and Outputs as regular PMAPs. They differ only because they arrange the map so the rows indicate “who” does the process step, e.g., Engineering, Finance, Purchasing, etc.

See example here → https://www.dropbox.com/s/xsup109y6uf6rfo/swim%20lane%20pmap.png

What is amzing to me is the number of poor examples of process maps and swim lane PMAPs is seen when one does a Google search. The all show simple diagrams of process steps, but almost none of them show the inputs and outputs. No wonder some firms place higher value to Value Stream mapping over PMAPs. It appears that not many people understand the power of the PMAP.

Value Stream Maps

It is my contention that a Value Stream Map is a sub-set of the Process Map. As the swim lane PMAP allows us to focus on the cross functional hand-offs throughout the process, the VSM allows us to focus on flow. By showing the process in a rough approximation of the actual plant (or office) layout, our inputs become flow oriented information (time to perform an operation, time sitting between operations, information/data flow patterns, materials flow patterns, and others. The outputs of the VSM are time related data, value added time and non-value added time. Of course one can also identify other areas of waste and search for ways to improve the process flow, reduce WIP, and other items.

See an example of a VSM here (credit velaction.com ) → http://www.velaction.com/lean-information/wp-content/uploads/2009/10/value-stream-map-sample.jpg

Summary

If you are a Six Sigma Black Belt, don't let the question "Are you familiar with Kaizen events and Value Stream mapping?" throw you off your game. A Kaizen event is just a term for continuous improvement, but usually focused on process flow and waste improvement --often through the use of the specialized PMAP called the Value Stream Map. Of course you should still study this tool and work to create VSMs. They are different and demand some specialized learning.

However, the most important thing for a Black Belt to understand is that everything is a process and everything has inputs and outputs. Also that failures in the inputs directly lead to failures of the outputs and these are the clues we need to solve the problem.

Coming up soon -- my favorite topic. Comparing data sets that may not be normal.

Are you enjoying this blog? Does it seem to have worth? Then pass this link to your Black Belt friends. Also please post comments below. I am always looking to improve.

Thanks,

John

Defining the Problem

noreply@blogger.com (John Borneman) — Mon, 07 Jul 2014 16:50:00 +0000

"A problem clearly stated is a problem half solved." - Dorothea Brande (1893 - 1948), American Writer and Editor

Define the Problem. Sound easy doesn't it? I often have people come to me with a problem statement that looks like some variant of the following, “Improve process efficiency by reducing downtime due to PM”

For the Six Sigma problem solver, there is something very wrong with this problem statement. Do you know what it is?

I guess this may be a trick question. The answer is the classic Black Belt answer. “It depends”

Unless you as the problem solver are almost ready to leave the “Define” phase of your project, a problem statement should never include an assumption of the solution. In the statement above we are directing our work exclusively to PM downtime.

Never forget that we, as Black Belts, are data-driven problem solvers. We need to make sure that the right questions were asked before PM was identified as the best area to work on. Why PM? What does the pareto (or pie chart) of total downtime for the plant look like? Plot these charts by hours down, and by cost of downtime. Is there a difference. Do these two charts give you any clues? Does the downtime pareto change when you break it down to look at department to department, line to line, shift to shift, process to process?

Often these type of assumptions are made by managers -- not from data -- but from listening to apocryphal stories told to them during their visits to the lines or plants. But don't blame them! That is why they have you as their Black Belt. To question. To explore. To “DEFINE” a problem. *

Alternately, even if PM is the largest piece of the plant's downtime, your delving into the data may uncover that one area (for instance, molding processes) comprise 90% of the downtime, and that this PM is fully justified and needed. So, does that mean you are done with your project? If you've done your homework and have all the other data, you may decide that value can be found in looking into the second highest level of downtime.

In the initial stages of defining a problem, we need to keep our problem statements simple. Think if them as only having a verb and a noun. For instance, Reduce Downtime, Increase FTQ, Decrease Variation.

Oh, go ahead and add an adjective or two at this phase, just be careful that you don't narrow your scope too much at this initial stage of 'Define'.

Reduce Molding Downtime (if you are only assigned to help that department). Increase FTQ at Electrical Test (but be wary that you don't mistake Test FTQ as reality unless you've done your MSE!) Decrease Variation in Length of Molded Parts (this amount of focus often occurs with a customer complaint).

Let the data lead you to the problem statement. When you leave the Define Phase, your statements may very well include some details of how the task will be accomplished. But those details won't be assumptions. They will be data driven!

"If you do not ask the right questions, you do not get the right answers. A question asked in the right way often points to its own answer." - Edward Hodnett (1871 - 1962), British Poet

Did you enjoy this article? Come back again to see more. And feel free to send this blog link to your problem solving colleagues. I will post something new about once per week.

John

* - of course if you're told directly by your manager to work on PM, then work on PM. But have keep the detailed data in your CYA file.

Lean versus Six Sigma

noreply@blogger.com (John Borneman) — Thu, 03 Jul 2014 12:55:00 +0000

For the past few years the job search market for problem solvers has shifted from employers looking for “Six Sigma” experts to a search for “Lean Six Sigma” experts. But what is the difference, really?

Some say (Ultimus Blog) that Six Sigma focuses on reducing errors by identifying and controlling variation, while Lean focuses on speed and reducing time and waste. They assert that Lean Six Sigma is a methodology that combines increasing process speed with reducing quality.

I wholeheartedly agree with this definition, but I do feel that too much emphasis has been placed on labeling our problem solving tools. Potential employers seem to want to hire a label. Why hire a Six Sigma Black Belt when you can hire a “Lean” Six Sigma Black Belt.

Ultimately, the goal of a Black Belt (or any problem solver for that matter) is to improve the system they are responsible for. No proper Black Belt focuses only on reducing variation. In DMAIC, we first must define our problem. Six Sigma teaches us to listen to the customer in order to identify what to work on. That may be reducing errors, controlling variation, finding root cause of a defect, or eliminating waste. Good Black Belts don't care what the label of a problem is, they only care that the problem is well defined and that they can select the proper tools to solve that problem.

These tools my be classic Six Sigma tools (PMAP, FMEA, DOE, Control Charts, etc), they may be via problem definition and sorting tools ala Shainin (r), or they may be waste identification and reduction tools as used in Lean.

A good Black Belt can use the tools they learned to reduce variation and defects. A GREAT Black Belt continues his or her education and learns whatever tools or techniques are required to do their job and to solve problems in any area of the plant or office.

One way to keep learning is to follow this Blog. I will periodically post small articles highlighting thoughts on problem solving, new tools for the practicing Black Belt, or new uses of old tools. Stay tuned!

Next time - “Problem Definition: Well Defined, Half Solved”

Coming soon – “PMAPs and Value Stream Maps – Which is Better?”

Umwelt

noreply@blogger.com (John Borneman) — Tue, 03 Apr 2012 11:34:00 +0000

This cartoon led me to looking into the biological concept of Umwelt. To paraphrase wiki, Umwelt, in this case, is translated as '"self-centered world" It is theorized that organisms can have different umwelten, even though they share the same environment.

In other words, an organism shapes and re-shapes its world based on its interaction with that world. Per Jakob von Uexküll, the creator of the theory of Umwelt, a stem of a blooming flower is perceived differently by an ant, cicada-larva, and a cow and therfore all perceive the same world in vastly different fashions. Alexi Sharov states that, the main idea of Uexküll is that each component of Umwelt has a functional meaning for an organism; it may be food, shelter, enemy, or simply an object that is used for orientation. An organism actively creates its Umwelt through repeated interaction with the world. It simultaneously observes the world and changes it

But it the concept of Umwelt limited to simple organisms? Can it be extended to humans? Many argue that because we are reasoning beings we live in the welt (actual world) instead of in an Umwelt (personal world).
I know that I perceive my world (my 'welt') through different filters -- different ways in which I interact with my world. I am an engineer so I tend to look at things with respect to how they work, how they can be fixed. But I am also a poet, so my perception relies heavily on the color and shape of words and how they interact, I can be metaphor driven. I am also white, middle aged, middle class, and I could be in better shape.

Does all this cause me to create my own Umwelt? A world perceived through the filters of my personal perceptions and interactions? And do I change my Umwelt as I observe it?

Or, as the critics of Unwelt applied to humans argue, does my ability to reason overcome and allow me to see the same world that everyone else sees?

I wonder if it is a bit of both. My personal Unwelt would cause communication problems when I am faced with someone whose personal Umwelt is significantly different. For instance, I may see items with weaknesses that could be fixed, whereas someone else may see the same items not in terms of their weaknesses, but in terms of their unique strengths.

But our human reason, will allow us (should allow us) to break out and find commonality.

Most of the time....

Spirituality

noreply@blogger.com (John Borneman) — Wed, 21 Mar 2012 14:29:00 +0000

pale buds explode into
daylilly's bright delight--
nature winks at us. - Borneman

The common definition of spirituality relates to religion, or a religious feeling, or a belief in God. This is a foreshortened definition which in my opinion only reflects a deeper and more profound meaning.

The root of the word spirituality is the Latin word spiritus which comes from spirare: a breathing or breath. It is one of many words in many languages that originated from the sound of the item. spirare--the sound one makes when breathing. Its Greek counterpart for the word 'to breathe' is psukhe. Say both of them out loud now. Spirare. Psukhe. Hear it? The sound of our breath, captured in words.

Humans have always related our breath to something sacred inside of us. After all, before we really understood the mechanics of our bodies, we knew that when our breath left us, so did our life. And is it not such a stretch to decide that when our breath leaves us, it might be traveling on to some better place? Or to to rejoin our creator? Which is why the words spirit and spirituality came to be associated with our soul--our inner essence without which we would not be...us.

To me, spirituality is not a separated piece of God, waiting to rejoin for everlasting joy. It is not a state of belief in a formal system of religion. It is an essence. It is that which makes us unique. It is that which makes us feel, react, choose to be good, or choose not to.

It is God in Us.

As I mentioned earlier, the Greek version of spirare is psukhe. That word evolved into the word psyche. Besides the current definition of psyche as our center of thought or emotion, it is was also associated with the name of the ancient Greek goddess, Psyche. Psyche, Goddess of the Soul or Spirit, was the wife and lover of Cupid. Wise Greeks, eh? They understood the deep association between our personal soul and our love for another.

One person strengthens the other. And the love between two people is not just a sharing of space, or sex, or even laughter and hardship. It is a sharing of souls.

So next time you kiss your loved one, consider that your intermingled breath is also a intermingling of your souls.

And maybe some bright green day, when you lean over and inhale the sweet scent of a Day Lilly, for a brief moment, you are sharing souls with the flower as well.