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When we speak about the capability of processes we often refer to a couple indices called Cp and Cpk. These two indices, used together, can tell us how capable our process is and whether or not we have a centering issue.  For the math geeks out there here are the formulas for calculating Cp and Cpk.

Cp = (USL - LSL) / 6*Standard Deviation (within)

Cpk = Min (Cpl, Cpu); where:

Cpl = (mu - LSL) / 3*Standard Deviation (within)

Cpu = (USL - mu) / 3*Standard Deviation (within)
 

Golf Analogy

For the rest of us here is a nice golf analogy to help differentiate between Cp and Cpk.

OK, I admit I don’t play golf but work with me here.  For grins, let’s say you want to learn how to drive a golf ball like Tiger does.  Even I, a non golfer, would love to be able to do this!

Step 1: Hit it Consistently

Your first mission is to learn how to hit the ball consistently and to the same spot. When you have learned this fine art and are indeed able to hit the ball to the same spot over and over again you may say you have good Cp. This is to say that you have a very capable golf swing.

Step 2: Get it to the Hole!

This is all well and good. But there is one big issue. You now need to learn how to aim since you have not paid any attention to where the pin was when learning how to hit the ball to the same spot. You may say your process is “shifted” away from the target (i.e. the golf pin which is the center of the process). So your over paid golf instructor now teaches you how to shift your body and aim your now capable shot.

Assuming this process is successful you are now able to hit the ball to the same spot (good Cp) and you are now able to aim the ball toward the hole (good Cpk). Life is good… Tiger watch out!

Summary

In summary, Cp tells us how capable our process is. If there is tons of variation your process may not be very capable at all. In this case you will want to reduce variation which will improve your Cp.

When you are happy with Cp you can move onto to Cpk which tells us how centered our process is. If your process is capable (good Cp) but is hugging the upper customer specification limit your Cpk will be poor. In order to improve Cpk you will need to work on “shifting” the process back towards the mean of the process.

There are some rules to all this Cp and Cpk fun. One giant rule is that your data must follow the normal distribution.  Here is an excellent article from Keith Bower on this very topic.

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I love Design of Experiments (DOE). Over the years I have done my fair share of them – everything from simple 2^2 full factorial designs to your more complicated Response Surface Methodology designs.

Tonight I want to start by explaining what DOE’s are and what they are not. I will build on this topic of DOE over the coming months (and years). I don’t want to attempt a 3 part series or anything like this since this topic is monstrous.

OFAT - What is it?

OFAT stands for “one factor at a time” and many people confuse this with DOE. OFAT problem solving occurs when someone changes one thing in a process to see what it does. Let’s use a real life example to explain. I experienced this exact situation when visiting a supplier of my former company about 5 years ago. The names of the guilty will be omitted for obvious reasons.

When touring this supplier I came across an engineer who wanted to show me how he determined the optimal settings for his injection molding machine. He didn’t know I had a Six Sigma background and I guess I forgot to mention it. I did later train this man on DOE during one of our “Supply Chain” green belt training classes so the story did end up nicely.

Anyhow, before his training on DOE, the nice engineer started off by showing how he tested “parameter 1” at the high, medium, and low setting. When he found the best one he set it in place and did not change it. Then he tested “parameter 2” at the high, medium, and low setting. Once he found the best one he set that parameter in place. So now he had the “best” settings for both parameter 1 and 2. He continued on until he had set all his parameters to the “optimal” settings. In the end, I will grant him, he had a good part. But he did tell me he had lots of variation in the process and that their scrap rates were too high.

This engineer was using your traditional OFAT problem solving approach. The problem with this technique is that you cannot determine how the various parameters interact with one another. It is this interaction understanding that makes DOE so powerful.

Full Factorial Designs

A better approach to identifying the optimal parameters would be to design a simple full factorial experiment. Let’s assume a screening experiment (a topic for another day) had been completed and the engineer had determined that there were three key parameters he needed to optimize for this process. Let’s call them pressure, speed, and temperature for sake of simplicity. Let’s also assume he knows from process knowledge the realistic range each of these parameters operates at.

The picture is what this 2^3 (3 factors at 2 levels) full factorial designed experiment would look like. In this DOE all possible combinations are tested and thus any and all interactions would be seen. The output in this DOE may be something like the weight of the part. To be sure, much care must be taken in choosing the correct output. We also must be sure our measurement system is repeatable and reproducible or we are just wasting our time.

This full factorial approach is far more effective than the aforementioned OFAT approach. In many cases it is also quicker to complete!

In the future I will build on this DOE topic more explaining how to analyze them, etc. I have only begun to scratch the surface.

This evening we will wrap up our discussion of regression. So far we have discussed what regression is and a few ways to determine whether our model is significant.

Next up I want to discuss something called the least squares method and residuals. I will wrap it all up with a short discussion on the differences between correlation, causation, and extrapolation. Yikes, this sounds serious.

Least Squares Method

Our regression equation used to predict things is determined by a procedure known as the method of least squares. There is some math involved to sort this all out but the basic idea is simple. All we are doing is plotting the actual data points and drawing a line down the middle of them. This line is called the “best fit” line as it tries to minimize the distance of all the points to the best fit line (actually it is the total squared vertical distance for the statistics nerds out there).

So basically, we plot the actual data points and fit a line down the middle of them. That is the least squares method and I didn’t even need an entire book!

Residuals

I mentioned how the lack of a flip chart was slowing me down last night. Well I am trying out my scanner and while it is not the best it is better than nothing. As my nice little picture (compliments are very welcome by the way… hee hee) demonstrates, a residual is simply the distance between the actual data point and the predicted data point (also called the “fit”). Put another way, the residual is the leftover variation in Y after using X to predict it.

We like to look at our residuals when doing regression as it can help us spot any issues with data collection, variation issues, operator error, etc. There are a few assumptions we make with residuals, namely:

• They are not related to the inputs
• They don’t change over time – they are consistent
• They are normal (bell shaped)

A nice Black Belt can help you ensure these assumptions are in check. If they are not in check you need to proceed with much caution (i.e. don’t try to predict anything).

Correlation, Causation, and Extrapolation

Typing those three words made me cringe. They sound so serious. Well don’t sweat it I will do my best to bring it down to earth for us normal people. Yes, I am normal. I swear. I am!

Correlation means that two things seem to be varying in a similar manner. If raising the temperature on our injection molding machine seems to be impacting the weight of the part we may say there is correlation.

Taking it one step further, causation means that when we change one variable the other variable in question changes too. So, in our injection molding example we may be able to prove causation by predicting what our Y will be given a specific X and then testing the theory! The 11th commandment of Six Sigma is “Thou Shall Confirm.”

Finally, the term extrapolation means that we attempt to predict Y outside the range of what was tested. So if you only tested up to 500 degrees with your injection molding machine you should not try to predict what will happen at 600 degrees. We have no data and do not know if there is a linear relationship.

Summary 

Well that about sums things up for our regression discussion. I hope you found it useful. As with anything, the best way to learn something is to give it a shot! So go collect some variable data and fit a line through it. Until next time, I wish you all the best on your journey towards continuous improvement.

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One of my favorite statistical tools is hypothesis testing. We can use hypothesis testing for many purposes.  For example, we would use the popular 2-sample t-test when we have two samples of variable data and want to understand if they represent different populations, statistically speaking of course. 

State the Null and Alternate Hypothesis

The first order of business when completing hypothesis tests is to state the null hypothesis (Ho) and the alternative hypothesis (Ha). The null hypothesis is the statement of no change. I always remember it like this, “Ho hum… there is no difference here.” Conversely, the alternative hypothesis is the statement of change. Just remember, “a Ha, there is a change!”

In our 2-sample t-test example, Ho would be that the means are equal and Ha would be that the means are not equal. It’s as simple as that.

Collect Data and Run Test

Next, we need to carefully collect some data and run the actual hypothesis test. You can program spreadsheets to do this test or use a standard off the shelf software package to do it for you. Personally, I prefer Minitab but I suppose that is just because it is what I have always used.

We Never “Accept” Anything!

When we run the actual hypothesis test we will get a P value. We use this P value to determine whether enough evidence exists to REJECT the null hypothesis. I emphasize REJECT since the most common error I see people make is when they speak of “accepting” a null hypothesis. We never accept a null hypothesis for the same reason we never prove someone innocent in the US judicial system. Instead, we prove someone guilty or not guilty. So with hypothesis testing we either reject or fail to reject the null hypothesis.

If P is Low, Ho must Go!

Now then, the P value is the probability of incorrectly rejecting the null hypothesis. Since we are making important decisions with this P value we tend to error on the safe side. Typically, if the P value is less than 5% we reject the null hypothesis. If the P value is greater than 5% we fail to reject the null hypothesis.

If all this makes your head hurt no worries. Just remember this saying, “If P is low, Ho must go. If P is high, Ho can fly.”

Alpha Risk Explained

Why 5%? Because I said so… quit asking so many questions! Just kidding. The standard is usually to go with 5% since this the risk most people are willing to take at being wrong. This is also why you often hear about 95% confidence intervals. If you are sending people to the moon or testing something ultra serious you may consider tightening this “alpha value” as it is called to something like 1% or 2%. I will resort to the response any good Black Belt should give when asked what alpha value to use – it depends!

Until next time, I wish you all the best on your journey towards continuous improvement.

Hello friends! This is the 3rd and final installment of all you wanted to know about control charts but were afraid to ask.

In part 1 of the series we talked about the history and purpose of control charts. In part 2 we discussed three different control charts that are commonly used with attribute data. Tonight we will be discussing two different control charts that are commonly used when we are dealing with continuous data, also referred to as variable data.

Continuous Data

If you remember from last night, attribute data are either counted (Poisson) or categorized (Binomial). Data that can be measured on a continuum or scale (weight, distance, volume, height, etc.) are what we call continuous or variable data. This is the most powerful type of data available so do all you can in order to collect it instead of attribute data.

I MR Chart

The first type of continuous data control chart we will discuss is the Individuals and Moving Range chart, commonly referred to as an I MR chart.

Typically we see the Individuals chart, which is simply each data point graphed individually, in the upper portion of the graph. The Moving Range chart, which is simply the difference between two consecutive individual points, is seen below the Individuals chart.

Any off the shelf statistical software will calculate the control limits for you. However, if you want to construct your own I MR chart I will refer you to an excellent book entitled Understanding Variation – The Key to Managing Chaos by Donald J. Wheeler. The book is easy to read and offers an outstanding summary of all things related to control charts.

The I MR chart is very robust. You can use it to track anything from the number of home runs hit by your favorite baseball player to the OTD of your manufacturing plant. Now before you ask why you would use an I MR chart for OTD and not a p chart I will refer you back to Wheeler’s book for an excellent explanation (see page 138).

Xbar R Chart

The last type of control chart to discuss is the ever powerful Xbar R chart. The main difference with the Xbar R chart compared to the I MR chart deals with what we call subgroups.

Let’s assume you have a collected 1 continuous data point each day for one year. Let’s also assume there 250 working days (5 days x 50 weeks). This means we have 250 data points. Well plotting each of these data points individually may be a bit arduous so an alternative may be to use a subgroup of 5. All this means is data points 1 to 5 are averaged, then data points 6 – 10, etc. meaning we would have 50 points plotted instead of 250.

The Range portion of the chart is calculated by taking the difference between the highest and lowest value in each subgroup.

The Xbar portion of the graph is normally shown on top while the R portion of the graph is shown beneath it.

If you have access to a statistical software package like Minitab or JMP you are in luck as the software does the boring math (calculating control limits, etc.) for you. Most of these companies also offer trial versions of their software.

Summary

The whole point of using control charts is to add context and to visualize both the centering and variation of your data which enables us to determine if our process is in statistical control or not.

The hardest Six Sigma project is one where you asked to “move the mean” of a process that is in statistical control. The reason it is so hard is you must make a fundamental change to the process in order to succeed. If, on the other hand, you find some special causes via your initial control chart you can investigate them and find out the reason they occurred. If you can then Poka-Yoke (error proof) the process ensuring the problems don’t come back you may have a quick win!

Well that is about it for this series on control charts. I hope it was helpful. If you have any questions or want clarification on anything please post a comment or shoot me an email.

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One debate that often arises amongst my Six Sigma cohorts is when to use the standard deviation of a dataset and when we should use another measure of dispersion, namely the range.

Descriptive Statistics Overview

Let’s take a quick review from our descriptive statistics class. When we are looking at the dispersion or spread of a data set there are three primary methods at our disposal.

• Variance
• Standard Deviation
• Range

If you work for GE we can add a fourth – span. But let’s leave that for a future blog.

Am I Normal?

So the debate on when it is OK to use standard deviation versus the range deals with something called “normality.” And my, oh my, can statisticians get their under garments in an uproar over this!

The standard normal distribution has a mean of zero and a variance of one. When you look at a normally distributed data set on a graph it resembles that of a bell, thus the term bell curve.

However, sometimes data will not follow a normal distribution. Instead, the distribution may be skewed positively or negatively.

A good example here is cycle time with a natural boundary of 0. You can’t have less than 0 seconds, days, months, etc. which makes the whole bell curve tough to create! Thus, cycle time is often non-normal in nature. Below is how a graph of cycle time may look.

Some statisticians from world class Six Sigma companies will tell you to use standard deviation no matter what type of data you have.

Others will say that if your data are not normal you should not use standard deviation, instead you should use the range.

The rationale for using the range is that for non-normal distributions like cycle time or things like home prices using the standard deviation may be misleading.

It’s all about Central Tendency

The reason it could be misleading, they say, has to do with the “measure of central tendency” employed. We can either use the mean, median, or mode to describe the central tendency of data. For normally distributed data we generally use the mean.

However, as an example, in the case of home prices (non normal data) a millionaire’s home may skew the mean away from the general population making it a bit misleading. So, in these types of non-normal situations we generally use the median for the measure of central tendency and not the mean.

This is significant for the simple reason that in order to calculate standard deviation we depend on the mean (it is part of the formula). So if you cannot trust the mean how can you trust standard deviation?

What to Do?

So what is a well balanced Six Sigma practitioner to do?

Personally, I usually state both the standard deviation and range when my data are not normal. After all, we are talking about variation and I know I want to kill it no matter what it is called!

I have seen people go to blows over this topic… no kidding. So, if you have a hot sports opinion on this topic please do share!

If someone walked up to your this morning at the coffee machine and asked you, “is process mapping a Lean or Six Sigma tool?” what would you say? This may seem like a trivial question but I dare say it is not.

Poka-Yoke is a Six Sigma Tool?

I remember reading Michael Georges’ book “Lean Six Sigma” and being taken aback a bit when he said Poka-Yoke was a Six Sigma tool. I thought, “Huh, are you crazy man?” Then I stopped for a second and realized I had first learned about Poka-Yoke in a Six Sigma training class many moons ago. So is Michael George, arguably one of the leading Lean Six Sigma experts in the world, wrong?

This gets right to the point of this blog which is which tool bag do certain tools belong? Let us begin with Process Mapping.

Types of Process Maps

Most of us have drawn up process maps. My favorites are the ones drawn up over lunch on a napkin. There are many different kinds of process maps such as:

• SIPOC
• Detailed Process Maps
• Swim Lane
• Brown Paper
• Value Stream Maps

Each of these process maps help us in different ways and at varying degrees of detail but they all have one thing in common – they help us better understand how something works.

Both Lean and Six Sigma rely upon this basic understanding in order to get on with more advanced things like deciding if a step is muda (Lean approach) or determining which inputs are controllable, noise, or SOP (Six Sigma approach).

Value Stream Maps

What about Value Stream Maps, also referred to as ‘Material and Information Flow Maps’ by Toyota? Surely this is a Lean tool, right? I mean Toyota invented it! Well, out of respect for Toyota and the sensei that first drew them I would say that VSM’s officially belong in the Lean tool kit. But it doesn’t mean a Six Sigma practitioner cannot use them!

Process Maps Unite!

For example, a favorite trick of mine is to start with a SIPOC to get a better understanding of the process and who should be on my team (I use the supplier and customer columns and pick team members accordingly). I then usually move to a VSM where I “learn to see” the process. Next, depending on the situation I may decide to drill into a process step with a swim lane process map in order to really understand this process step. Now I am in position to decide if my problem is more of defects/variation (Six Sigma approach) or waste/speed (Lean approach). But you see I don’t discriminate and I use all the tools I have at my disposal in the beginning of any improvement initiative.

Summary

So, to answer my own question of whether of a process map is a Lean or Six Sigma tool I will respond with the obvious answer – yes!