The Histogram is one of the 7 Quality Tools. In this article, we provide a link where you can get a Histogram Template Download – but it’s no ordinary template – what you get is a histogram generator – it automates most of the process in creating a histogram. But first, let me show you what you’ll get with this download. Watch the video below. Beneath the video will be a link where you can get your histogram template for free.

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This Countermeasure Worksheet Template Download is Free and simple to use. Use this worksheet after you’ve performed effective root cause analysis and then this worksheet will help you identify the countermeasures, owners, and timeline to implement solutions to root causes. Watch the video below to learn more and download the template today.

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This free Takt Time Calculator Download is an excel spreadsheet where you can easily plugin a few numbers and the worksheet does all the calculations for you to figure out what you Takt Time needs to be in order to meet customer demand. Check out the video below to learn more, then download the calculator by using the download link below the video.

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 At first glance, there’s no relationship between Kaizen and Shaving. But, like most things, it takes creativity and insight to recognize that a well planned and executed Kaizen that yields positive results is no different than a well executed and planned shave, where the outcome is a close, clean, and a razor burn free shave. Let me explain.

1. I Have Folliculitis

Yes, I’m laying it all out there. Totally vulnerable now. You see, Folliculitis – though it sounds cool and smoothly rolls off the tongue when said s l o w l y – is actually not a good thing. Folliculitis is having your facial hair declare war on its own skin. It hurts.

To help me out, my wife thoughtfully bought me a special shaving kit. Indeed, she bought me The Art of Shaving.

And, just like there’s a science and art to shaving, there’s also a science and art to Kaizen. Let’s explore the similarities and further investigate what the heck shaving has to do with Kaizen.

2. The Art of Kaizen

Kaizen, or changing for the better, has both an aspect of art and an aspect of science. Both are really part and parcel of each other for the most effective application of Kaizen. The Art of Kaizen has at its core the importance of people. The focus of Kaizen is in improving both the process, but also in developing people. It is an art to develop others and in the context of Kaizen, it is art to be able to do so.

3. The Science of Kaizen

The other side of Kaizen is the science of Kaizen. This means that the practice and application of Kaizen is systematic and ordered. Let’s take, for example, Kaizen Training.

In training groups and individuals in the principles of lean and in the practice of Kaizen, there must be order for it be most effective. This means that Kaizen follows a process and that systematic process is the vehicle for both developing people and also in improving the process – the art and science of making things better and changing for good.

Now let’s dig into my new Art of Shaving to see what it teaches us about what might the key elements in Kaizen should be.

4. The Steps to Proper Kaizen

When I first open up my Art of Shaving Kit, I’m immediately introduced to the steps to a proper shave. As I looked at this instruction sheet, it immediately dawned on me: the 4 elements to the perfect shave are the same elements to the perfect Kaizen.

A. Prepare Your Face, Prepare Your Kaizen

In order to have the perfect shave, it all begins with the Pre-Shave. In their words: “Always shave during or after a hot shower to deliver heat to the beard hair. Next, apply the Art of Shaving Pre-Shave Oil before shaving in order to soften beard hair and promote razor glide.”

Wow. I was blown away. So, I gave it a shot. I took a hot shower then I put on the Art of Shaving Pre-Shave Oil. The Oil is really a mix of sandlewood, olive oil, and nice smelly perfumes. No big deal – or so I thought.

It turns out that the Pre-Shave is a step that sets the rest of the shaving experience up for success. To my surprise, the Pre-Shave oil massively softened the hair on my face, which later helped make the actual shave super easy.

Which brings us to Pre-Kaizen or Planning. The work done prior to a Kaizen Event is critically important. Depending on the problem being solved, this might mean having the following done prior to the actual Kaizen Event:

• Date, Time, and Location reserved.
• Problem Statement and Scope of Event completed and agreed-to by team and stakeholders.
• Baseline metric is documented.
• Deliverables agreed to and Key Metrics identified.
• Targets agreed to.
• Team members are identified and are invited to the event.
• Lunch or Dinner is provided – this is not a trivial detail – this is very important in order to maintain energy and focus. And, it’s a thoughtful gesture for those involved. Remember – people first.
• Data Collection completed.
• Have resources ready – machines, electricians, carpenters, etc. – have the resources ready so countermeasures can be put in place THAT day, and not wait for to have the problem solved later.
• Buy-in from critical stakeholders – this means having your boss involved, or his boss, or his boss’s boss involved. Having decision makers’ support prior to the actual event and the their implicit and explicit support for the action items after the event is a must-have.

If any of the Pre-Kaizen items above (these are just some, there are others I’m not mentioning), the overall effectiveness of the Kaizen event will be diminished.

So, just as the Pre-Shave helps the rest of the shaving experience go well, the Pre-Kaizen items are critical in order for the rest of the Kaizen Event to hum nicely and effectively.

B. Lather Up, Promote the Kaizen

After the Pre-Shave, the instruction tells me to use the Art of Shaving Lather, which is made with Glycerin and Coconut Oil. Something immediately stood out to me as I tried their Lather versus the store-bought shaving cream: The Art of Shaving Lather is about 1000 times thicker than the shaving cream at your convenient store. WoW.

“Why so thick?”, I wondered.

As it turns out, the thick shaving cream really helped my skin and really softened the hair for shaving. The razor glided across my face like no other razor has every glided epidermis before.

Lather up is an extension of Prepare and is a necessary step in both shaving and in Kaizen.

C. Shave and Execute the Kaizen

To execute the Kaizen means that you’re running the actual event. Here are some steps to keep in mind as you do so and we’ll frame it in the Plan-Do-Study-Act framework (PDSA):

i. Plan

• Understand the current state
• Conduct root cause analysis
• Brainstorm possible countermeasures

ii. Do

• Design and implement countermeasures

iii. Study

• Pilot test the countermeasure. Observe results. Improve.

iv. Act

• Improve the countermeasures.
• Standardize.
• Train workforce.
• Establish leader standard work.
• Complete Kaizen report-out or Kaizen Newspaper.
• Report to stakeholders.
• Create A3 Report.
• Take team photo.
• Celebrate.

D. After Shave, Post Kaizen

When you’re done shaving, the people at the Art of Shaving suggest to use their aftershave. And, wow. Their aftershave is pretty amazing. It comes in a small bottle, but, man, does it make my face feel nice and smooth. In many ways, the aftershave is similar to the Post Kaizen activities.

Post-Kaizen, it’s important that the achievements and the lessons the team learned are documented and then disseminated to the broader group. Doing this is important because it allows the team to receive praise, but also allows the broader organization to learn.

Like aftershave and how it lessens the irritation from shaving, Post-Kaizen heightens the ability of the organization to learn from the efforts of the Kaizen team.

5. Free Point Kaizen Event Guide

There you have it.

And, to help solidify it even more, you can download a free point kaizen event guide here!

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Graphical methods includes boxplots, stem and leaf plots scatter diagrams, pattern and trend analysis, histograms, normal probability distributions and Weibull distributions. This premium article for members only describes each of the effective ways to graphically represent data, maximizing it for information. Toward the end of this article, you’ll be able to download a handy guide/flowchart that provides helpful tips on what type of chart will be helpful, given the type of data that you have.

The Boxplot

The boxplot is a number summary of the data. The data median is a line dividing the box. The upper and lower quartiles of the data define the ends of the box. The minimum and maximum data points are drawn as points at the end of lines (whiskers) extending from the box. Notches indicate variability of the median, and widths are proportional to the log of the sample size.

Stem and Leaf Diagram

The stem-and-leaf diagram is a convenient, manual method for plotting data sets. The diagram consists of grouping the data by class intervals, as stems, and the smaller data increments as leaves.

View this example of a stem and leaf diagram.

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This article will show you how to Prove Process Improvement with Paired T Test.

In you process improvement projects, you will almost – no, inevitably – make process changes. At times, you will be challenged on whether the process change made any difference at all. Sound familiar?

To statistically show whether there was a difference in the Before/After of a process change, the statistical test that can help is what’s called the Paired-T Test.

What’s the Paired T-Test?

A paired t-test compares two samples in cases where each value in one sample has a natural partner in the other.

What does a Paired T-Test Measure?

A paired t-test looks at the difference between paired values in two samples, takes into account the variation of values within each sample, and produces a single number known as a t-value.

You can find out how likely it is that two samples from the same population (i.e where there should be no difference) would produce a t-value as big, or bigger, than yours. This value is called a p-value. So, a t-test measures how different two samples are (the t-value) and tells you how likely it is that such a difference would appear in two samples from the same population (the p-value).

Some examples where a paired t-test makes sense to use are:

• Comparing the weight of people dieting after a controlled diet
• Comparing the performance of order pickers before and after a change to the picking process or pick path
• Comparing the level of defects before and after a process change

You get the point.

So, enjoy the free excel calculator and be sure to use it in your projects. And, if the calculator doesn’t do what you need it to do, then feel free to improve upon it.

Check out the video I made below of what the paired t-test calculator looks like and what it can do for you.

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Don’t you hate it when you attempt to get a fork from a condiment stand, but end up picking up a spoon? Has that ever happened to you? I hope I’m not alone in this one. Well, at a recent hotel stay, I experienced simple and powerful visual management that completely prevented me from making this common error.

I’ve been staying at many hotels recently. At one recent stay at a Hilton Hotel (The Hampton Brand), I noticed something refreshing, instructive, and actually helpful: simple visual management in the breakfast lobby.

The Hampton is nice because they provide a good breakfast, so I can quickly go in there, grab something, then head to work. During one of those hectic mornings, I quickly went in, looked for the oatmeal, grabbed my bowl, grabbed a spoon, then began eating.

Then, it dawned on me: I knew exactly where to go for my bowl and spoon, even though this was the first time I had stayed at this hotel. And, instead of picking up a fork or a knife, I actually picked the utensil I meant to get – a spoon!

That’s the power of visual management.

So, what’s the beauty of this?

Principles of Visual Management

The benefits of visual management are the following:

• Visual Management allows us to self-order and self-organize
• Visual Management is self-explanatory – that is, a human doesn’t need to be present in the workplace to explain what’s going on.
• Visual Management allows for obvious and self-improvement.

The example from the Hilton satisfies all 3 criteria above. So simple and so effective.

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There are many customer satisfaction models in the marketplace. One very important model is the Kano Model, which we’ll discuss today. In this article, we’ll discuss the following:

• The origins of the Kano Model
• Key Elements of Kano
• Methodology
• Applications of Kano
• Examples of how to use Kano Analysis

Origins of the Kano Model

The Kano Model concept was derived by Noriaki Kano in his article entitled “Kano, N., Takahshi, F & Tsuji, S. (1984). Attractive quality and must-be quality. The Journal of the Japanese Society for Quality Control, April, pp. 39-48.” Noriaki Kano was a professor at Tokyo Rika University and focused his research on how to satisfy customers. The prevailing idea at the time was that give the customers more would make them happy.

He didn’t believe that.

So, he challenged the prevalent customer satisfaction models of “more is better” and proposed a new line of thinking based on the following ideas:

• Performance on product and service attributes is not equal in the eyes of the customer.
• Performance on certain category attributes produces higher levels of satisfaction than others.

In other words, there are product and service attributes for which “more” doesn’t equal satisfaction.

Key Elements of Kano

The Kano Model is not difficult to understand. It is based on a few key elements:

• Identify the voice of the customer (VoC)
• Translate the voice of the customer into critical to quality characteristics (CTQ)
• Rank the CTQ’s into three categories:
  • Dissatisfier: “Must be” / Cost of Entry
  • Satisfier: “More is better” / Competitive
  • Delighter: “Latent Need” / Differentiator
• Evaluate current performance of the process, product, or service

To obtain the voice of the customer, often Surveys, Interviews, Focus Groups, Observation, and Customer Complaints are the most common ways to obtain customer data.

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Kaizen Leaders – this article is for you.

For those that have led and facilitated Point Kaizen Events, you have undoubtedly experience many emotions as you led a group through the steps of Plan-Do-Check-Act. Especially early in your career. But even more experienced veterans, there’s still some element of nervousness.

You will surely relate to and understand these emotions. For those new to Lean, this is what you have to look forward to.

1. Leading Kaizen Events is a roller coaster of emotions.

2. You’ve prepared and done a lot of pre-work.

3. But then . . . you forgot to invite the Kaizen Event Sponsor – Your BOSS!

4. Nevertheless, you are mostly feeling confident right now.

5. But, wait, right before the event begins, you all of a sudden get nervous.

6. What if you get tongue tied?

7. What if you mess up and look like a fool?

8. Whatever happens, happens. Let’s rock this.

9. Then, it turns out that you freaked out for no reason. You finish facilitating the Kaizen Event and it went awesome!

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We know that 5S is an important foundation in any implementation of Lean. Within 5S, there are many ways to apply its principles. In this manner, it’s helpful to see examples of visual management within the context of 5S. One example I saw recently that I found both funny and helpful was a 5S Shadow Board Example – Rasta Style.

5S Refresher

Let’s first review really quickly the steps of 5S:

• Sort. Clearly distinguish what is necessary to do the job from what is not. Eliminate the unnecessary.
• Set in order. Put needed items in their correct place to allow for easy accessibility and retrieval.
• Shine. Keep the workplace clean and clear of clutter. This promotes safety as well as efficiency.
• Standardized cleanup. Develop an approach to maintaining a clean and orderly work environment that works.
• Sustain. Make a habit of maintaining your workplace.

5S is foundational in Lean because it allows us to visually see what is normal from abnormal. If we can do that with physical clutter, then it enables us to see much better when there’s abnormality in the performance of our processes.

A better visualization of 5S is viewing it as a cycle like this:

5S Shadow Board Rasta Style

Given our treatment of 5S, one example of 5S in action is this shadow board:

Now, if we walked by this and noticed that Bob Marley was bald, I think that would strike most of us as “there’s something wrong here”. In other words, it’s an abnormal condition that Bob Marley is bald – so, that must mean that his hair “wires and cables” are missing.

It’s a fun example of a 5S Shadow board.

And who says Lean can’t be fun?

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In the introduction to the Measure Phase, I mentioned that our focus is in the practical use of data. In that spirit, by the end of this module on Data Types in Six Sigma,

• You’ll understand the role of data in Six Sigma
• Know the difference between discrete and continuous data
• Know how to collect data

In six sigma, data helps us to:

• Identify gaps between “what is” and “what should be”
• Find significance
• Understand frequency or how often something happens
• Verify whether the changes we made produced the effects we predicted
• And Compare processes

Watch the premium video (5:24 minutes) below to learn more.

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In Lean, there is plenty of talk about pretty diagrams, data, charts, etc. But at the end of the day, Taiichi Ohno was concerned more with actual changes – he always emphasized that Lean was practice over theory. To help us focus on making actual improvements to our process, one template that can help is the Kaizen Newspaper.

In my Lean training, I’ve spent a lot of time in both System Kaizen and Point Kaizen. But, one element of Point Kaizen that I’ve especially enjoyed is what I’ve come to call Daily Kaizen. But, regardless of the type of Kaizen you are running, keep in mind that classifications of Kaizen really do not matter. The most important item to remember is that Kaizen should be everyday and the most important Kaizen is what you are doing today – this moment – right now. But, if you’re still interested in classifying the types of Kaizen, go read about them here.

So, let me get back to the Kaizen Newspaper and Daily Kaizen.

The Kaizen Newspaper is really designed to help us in implementing many, many, small daily improvements. The template has a few items to help us do just that:

• The Problem or Opportunity
• Who owns it?
• The Root Cause(s)
• The Countermeasure(s)
• Estimated Completion Date
• The Status
• and the Actual Completion Date

The cool thing about Daily Kaizen and the Kaizen Newspaper is that is can be quick to do and implement immediately. Check this actual Daily Kaizen sheet from one company I was involved with:

And the way the above would work is that during daily standup, the team leader would go through the daily kaizen’s that happened the previous shift. Simple, yet it works.

Go download your free Kaizen Newspaper template by clicking on the button below.

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Continuing our series on the 7 quality tools, today we’ll discuss the Scatter Plot. The 4:27 minute video explains the Scatterplot in Six Sigma projects and the article below shows examples that you can apply in your own projects.

So, what is a scatter plot? The scatter plot is a chart that helps us visualize points relative to other variables. We would typically use a scatter plot to:

1. Understand the behavior of a process
2. See if two factors have a relationship
3. And To visually show correlation between two factors

We’ll be going through a data set together so we can better understand scatter plots through a practical example. The example we’ll be going through is a data set on the age of cars and their miles per gallon. Before we go to the data set, let’s discuss the steps to creating a scatter plot. You can follow these steps to create a basic scatter plot:

• First, identify the purpose. In this step, clarify what you are trying to achieve with a scatter plot. In other words, be clear about the problem you are solving.
• Determine the two factors to compare. This is important and by determining the two factors, you will keep your analysis tight and focused.
• Identify the measures. In this step, you want to find the pairs of values and their measurement. The factors must be variables – that is, they must be measurements on a continuous scale.
• Collect the data. We won’t go into sample statistics here, but you need to collect the data.
• Then plot the data.
• Interpret the data. Is there a relationship?
• Take action

Watch the movie below to learn more.

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There, I said it.

As a lean practitioner, we are involved in probably many lean workshops, training sessions and, dare I say, Kaizen events. But, guys, even though some of this is necessary, I’m afraid that we’re incorrectly depicting Lean to the world by doing so.

Let me explain.

When I began my Lean journey 14 years ago at Toyota’s Supply Parts Distribution facility in Kentucky, we didn’t use the word Lean, value stream mapping, or really any other word that has become so common place in Lean circles. Honestly, we were taught a new approach, we applied it, we were corrected and sometimes yelled at, then we tried it again, over, and over, and over again. It was part of work. I do not remember even 1 time where I was part of some workshop during my time there.

So, why is it that Lean has become about extra and added activities - it’s being depicted as added workshops, graphs, charts, and a bunch of maps?

Again, some of that is necessary, but there is too much focus on the wrong things.

As a result, organizations and others have come to view Lean as additive, when exactly the opposite is true: Lean should be about subtraction, not addition.

No, I’m not talking about subtracting people or the “lean is mean” mentality. I’m talking about eliminating waste.

What are your thoughts? Can we get back to the true essence of Lean? How should we do it?

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There’s quite a bit of confusion between the use PDCA Cycle versus PDSA Cycle. For those unfamiliar with the acronym, PDCA stands for Plan-Do-Check-Act and PDSA stands for Plan-Do-Study-Act. To some, the change of “check” to “study” might be trivial, but to Dr. Deming and his teacher, Dr. Walter Shewhart, there is a difference between “check” and “study”.

The PDCA or PDSA Cycle began as a series of steps within the world of product development. It wasn’t until much later did it become a method for process improvement. Let’s go through the history together.

1. The Shewhart Cycle

Dr. Walter Shewhart is best known for his development of statistical control. Back in 1939, Dr. Shewhart struggled with the current view of his time regarding quality and product development. He didn’t believe it was a linear model, but rather a cycle. In his words,

These three steps must go in a circle instead of in a straight line, as shown . . . It may be helpful to think of the three steps in the mass production process as steps in the scientific method. In this sense, specification, production, and inspection correspond respectively to making a hypothesis, carrying out an experiment, and testing the hypothesis. The three steps constitute a dynamic scientific process of acquiring knowledge. ¹

In his mind, it looked like this:

2. The Deming Wheel

Dr. Walter Shewhart’s student at the time was Dr. W. Edwards Deming. It was Deming who took the Shewhart Cycle and modified it. In 1950, while speaking to the Japanese Union of Scientists and Engineers (JUSE) regarding statistical quality control, Dr. Deming modified the Shewhart Cycle by adding a 4th step that he called – at the time – “redesign through marketing research”. Historians believe that it was at that meeting the term “Deming Wheel” was born ².

At that meeting, Dr. W. Edwards Deming discussed these steps:

1. Design the product
2. Make it and test in lab and production line
3. Launch the product
4. Test it in service via market research and user interviews
5. Redesign and improve the product given customer’s feedback

3. PDCA Cycle is Born

According to Misaki Imai, Japanese executives took the Deming Wheel from that 1950 seminar and called it PDCA and took Deming’s steps (1-4) and codified it as Plan-Do-Check-Act ³.

According to Imai, in the 1960′s, the what was initially the Deming Wheel was called PDCA by the Japanese. It evolved from a method to describe product development to become a method for process improvement.

4. PDSA Cycle is Reborn

In 1986, Dr. W. Edwards Deming reintroduces the Shewhart Cycle and warned his audience that Plan-Do-Check-Act (PDCA) version is not accurate because the English definition for “check” means to “hold back”. Deming continues by encouraging his audience to use Plan-Do-Study-Act (PDSA) and not the “corruption PDCA” ⁴.

5. PDCA or PDSA?

I’m not picking sides. I’ve always used PDCA. In fact, at Toyota PDCA is the recognized and approved framework, not PDSA. I’m not sure if that matters. I think in the grand scheme of things, in practice it really doesn’t matter. But, to theoreticians and academics, they will likely continue to quibble over PDCA versus PDSA. But for practitioners like you and me, we’ll be busy making things better.

What’s your opinion? Does it matter to you? ⁵

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I’ve been traveling a lot lately. I’ve had a lot of opportunity to think and observe airline operations and one thing is abundantly clear: the airline industry is a very mature industry but, man, is it incredibly inefficient and full of waste. Take my experience a few weeks ago traveling from Nashville to Salt Lake City: my flight was delayed for over an hour because the crew hadn’t yet arrived! Really?

I know some of my colleagues within the Lean community will be disappointed in what I’m about to say, but I’ve actually enjoyed Mckinsey’s recent series on Lean Manufacturing. I like them because they are written by Mckinsey consultants who used to work in industry – primarily operations and manufacturing. So, they feel more authentic than if they had just graduated from business school. In one recent series on lean manufacturing, Mckinsey describes an assignment where they were able to reduce delays for an airline. I found this article to be perfect, given my recent experience with flying ¹.

Look at the chart below, taken from that Mckinsey article. The chart shows the difference in turnaround times between flights and the changes they did to reduce the average turnaround time from 52:18 to 33:11, a substantial reduction given that idle planes represents a significant drain on both costs and revenue.

In another example, Mckinsey shows the difference that Lean can make in improving the deplaning process. They look at each step such as Unload Passengers, Wait for cleaning crew to board aircraft, clean airplane, etc and show the reduction in time that they were able to reduce through the use of lean methods.

Here’s the really interesting thing about their results: They made many small changes and yielded big improvements overall.

That’s the beauty of Lean – small changes – many of them can produce big, big positive results.

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In the world, tools can operate independently. Take a hammer. If there’s a nail, a hammer is a great tool to use to either hammer the nail in or pull the nail out. But, within the context of, say, building a house, the hammer is just one tool amidst an army of tools, each having its own purpose and use. The system in this case is really the operation to build a house. Is it the same way with Lean? Can picking and choosing lean tools lead to success?

You can pick a tool here and there, but you’ll have very little understanding of how all of the tools in lean operate as a whole and within the system.

This observation was made recently by Deryl Sturdevant, the former president of Canadian Autoparts Toyota. In a recent interview, he shared some of his thoughts as he’s advised companies through their lean transformation. At one manufacturer: ¹

A common characteristic of companies struggling to achieve continuous improvement is that they pick and choose the lean tools they want to use, without necessarily understanding how these tools operate as a system. (Whenever I hear executives say “we did kaizen,” which in fact is an entire philosophy, I know they don’t get it.) For example, the manufacturer I mentioned earlier had recently put in an andon system, to alert management about problems on the line.1 Featuring plasma-screen monitors at every workstation, the system had required a considerable development and programming effort to implement. To my mind, it represented a knee-buckling amount of investment compared with systems I’d seen at Toyota, where a new tool might rely on sticky notes and signature cards until its merits were proved.

An executive was explaining to me how successful the implementation had been and how well the company was doing with lean. I had been visiting the plant for a week or so. My back was to the monitor out on the shop floor, and the executive was looking toward it, facing me, when I surprised him by quoting a series of figures from the display. When he asked how I’d done so, I pointed out that the tool was broken; the numbers weren’t updating and hadn’t since Monday. This was no secret to the system’s operators and to the frontline workers. The executive probably hadn’t been visiting with them enough to know what was happening and why. Quite possibly, the new system receiving such praise was itself a monument to waste.

Let me underscore his message: A common characteristic of companies struggling to achieve continuous improvement is that they pick and choose the lean tools they want to use, without necessarily understanding how these tools operate as a system.

What’s your experience? Have you observed the same thing happening at companies?

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In this module, we’ll discuss the following various statistical approached utilized in Six Sigma.

1. The Purpose of Basic Statistics

The purpose for statistics in Six Sigma are the following:

• Provide a numerical summary of the data being analyzed.
• Provide the basis for making inferences about the future.
• Provide the foundation for assessing process capability.
• Provide a common language to be used throughout the organization.

Statistics is the basic language of Six Sigma. A good understanding of statistics is the foundation upon which many of the subsequent tools will be used.

1.2 Statistical Notation Cheat Sheet

Don’t bother memorizing any of this, but refer to this as needed.

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In the previous module, we learned Basic Statistics as used in Six Sigma. We learned that statistics is the language of Six Sigma and saw several real world examples from projects of how statistics can be used to improve operations and processes.

In this module, we learn how to use Z Values or the Z Score. It’s a rather obscure topic, but it’ll be helpful as you’ll see. At least some background or rudimentary understanding will help you. In practical terms, Minitab and Excel can help you with many calculations, but knowing what’s happening under the hood may help. This module is helpful, for example, in answering the question “What is the probability of a defect happening?” Learning how to calculate the Z Score will help you answer that question.

Before you read on, it’ll be helpful to review the section on Distributions.

1. Normal Curves

As we learned in the section on Distributions, the normal curve is actually a theoretical one, truly symmetrical about its mean and precisely defined by the mean and the standard deviation.  Consequently, if you change either one of these factors, you change the shape of the curve. The area under the theoretical normal curve can be divided into six zones, three on each side of the mean.  Each zone is one standard deviation in width.  99.73% of the values will lie between limits set by +3 standard deviations and -3 standard deviations.  This has been proven by theory and has been confirmed by practice over history.

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In the previous module, we learned to how to calculate the Z Score to estimate the probability of an event. You’ll need to know the basics of the Z Score in order to help you in this module.

In this module, we learn how to calculate sample size selection for Six Sigma projects.

Why Use Sample Sizes?

Data collection could take a long time and can become expensive. Instead of measuring an entire population, we instead take a sample from the population. Using statistics, we can ensure that the sample we obtain from the population is representative.

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