- defects per day could be a c chart, but an XmR chart works just as well
- defects/samplesize could be np, p or u chart, but XmR chart works just as well using the ratio

Almost two decades ago, Tom Pyzdek said: X chart provides an excellent approximation to the p chart.

More recently, Donald Wheeler noted that XmR chart limits will be very close to c, np, p or u chart limits if the underlying distribution is correct. Wheel close with: You can guarantee that you have the right limits for your count-based data by simply using the *XmR* chart to begin with.

If you have some c, np, p and u data, you could create different charts for each type of data or you could convert it into ratios and use the QI Macros XmR Dashboard to monitor all of the charts.

I have also found that varying limits in p and u charts cause confusion in the audience. Then I have to explain why they go up and down. They lose track of what the data is telling them and get bogged down in trying to understand how the limits are calculated. Not so with the XmR. I just have to explain that the R chart shows the difference between each two data points.

Consider using the XmR chart for attribute data. It will simplify your life.

]]>Then I realized that since QI Macros templates (e.g., XmR chart) calculate the average and sigma estimator, the LSL/USL for Cp = 1.0 would be:

LSL = Average – 3*SigEst USL = Average+ 3*SigEst

For Cp = 1.33, just change the 3 to a 4; Cp = 1.66, change the 3 to a 5. Here’s an XmR chart template with some sample data and calculations to reverse engineer spec limits:

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Later in the day another customer asked why Cpk is calculated as the minimum of the upper or lower Cpk? Because you use the one closest to the average. I think that customer may have had the same problem, confusing a hard limit with a specification limit.

If you have cycle time data, there is no lower specification. Zero is a hard limit, not a specification. If you specify an LSL, you will get a high Cp, but a Cpk less than one.

In healthcare, for example, time to thrombolytics should be less than 90 minutes. There is no LSL. Use a USL of 90 to get a proper Cpk.

]]>They had too many menu items, so they decide to simplify down to burgers, fries and soft drinks. (Think Lean inventory.)

They go to a tennis court and use chalk to lay out a possible floor plan to deliver service fast. One brother stands on a ladder watching while the employees pantomime cooking burgers, fries and soft drinks.

They go through several iterations to converge on their final design. (Think value stream mapping and spaghetti diagramming.)

I think they might have done it faster with cardboard boxes, but I wasn’t there. I was 3.

They understood it then, it’s still true now:

Speed is the killer app!

How would you mistake-proof this design? What are the possible failure modes and effects (FMEA)?

]]>In *The Math Gene*, Author Keith Devlin explores “why so many people find mathematics impossibly hard.” He says: *mathematics is the science of patterns*. Isn’t that what we’re trying to do in Six Sigma, separate the wheat from the chaff, separate the signal from the noise and detect the underlying patterns of performance?

Devlin also differentiates between arithmetic and mathematics. He argues that our brains aren’t well designed for arithmetic, but we are all good a math. My wife, for example, is dyslexic when it comes to numbers. Give her a phone number and she will often transpose numbers (arithmetic). But she can write software that involves algorithms (math).

Devlin also says that mathematics help *make the invisible, visible.* Again, isn’t that what we’re trying to do with Six Sigma? That’s why I always talk about the *invisible low hanging fruit*. You can’t see it, but it’s there.

Devlin’s metaphor of math is interesting; it’s construction: “Learning new mathematics is like constructing a mental house in my mind. Understanding new mathematics is like exploring the interior of the house. Working a math problem is like rearranging the furniture. Thinking mathematics is like living in the house.”

Devlin lists the following mental attributes as key to mathematical ability:

- A number sense (1, 2, 3)
- Numerical ability
- Algorithmic ability
- Abstraction
- Cause and effect (e.g., root cause analysis)
- The ability to
*construct*and follow a causal chain of facts or events (e.g., an improvement project) - Logical reasoning ability
- Relational reasoning ability
- Spatial reasoning ability (e.g., spaghetti diagram)

Notice, he never says *formulas*.

**Implications for Six Sigma**

In Six Sigma, we can let QI Macros calculate the formulas and give us control charts, Pareto charts and histograms that show the underlying *patterns of performance*. Then we can do some root cause analysis to find and fix those performance problems.

I realize that most Six Sigma books and courses are filled with formulas and manual calculations, but all that does is traumatize students and waste time. *You don’t need to know formulas to do Six Sigma*, but you do need to understand the patterns revealed in the charts.

Why do Six Sigma books and course insist that everyone learn the formulas behind the charts and statistics? Here’s my short answers: Because it fills up the curriculum (I get paid more if I teach longer). Because that’s how I learned it (I went through this hell; so should you). Because you need it to get by (no you don’t).

I want to make Six Sigma edible by the masses. Devlin says: “What a few individuals may be trained to do doesn’t matter. Only what an entire species does easily, naturally and by inclination is significant.”

Stop worrying about formulas. Start drawing control charts, Pareto charts and histograms that illustrate the underlying patterns of performance. Then start moving those charts in the right direction—fewer defects and less variation. That’s all you need to know to succeed a Six Sigma.

]]>Solution: Go on a Raw Data Diet

]]>They moved in a bunch of equipment one week. Then over a week later they jumped into action to install part of a new pipeline just before a big snow storm.

Then it was cold for a week. Then they did another day’s work. Not working today.

Not exactly one-piece flow.

There are two dump trucks and three backhoes and bulldozers sitting around while all this is going on. Couldn’t this equipment be useful somewhere? Seems like a lot of inventory sitting idle.

Meanwhile the neighborhood traffic has to snake through one lane.

Isn’t there a way to lean this kind of construction work?

]]>How can healthcare hope to achieve and sustain improvements without control charts?

There were over 500 posters, but too many had no charts at all.

I was there in 2006 when Don Berwick asked every attendee to commit to using science and evidence. I was there in 2015 when he repeated the request, asking for control charts, Pareto charts and histograms of performance improvement. Sadly, few attendees have gotten the message, or they aren’t putting charts in their posters.

]]>As I have written before, I call these folks “Stat Bastards” because they belittle others rather than help them.

As a member of the American Statistical Association, almost every statistician I meet is incredibly kind, generous and helpful. The few that flaunt their training rather than helping are impeding the forward progress of their organization.

I say, if they have better data, bring it. If they have better analysis, bring it. If they have better tools, bring it. But if not, shut up. Yo’re not helping.

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