Cards and darts and XmR charts...

Improvement Insights Blog

Cards and darts and XmR charts…


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One great thing about the past few months – with in-person socializing limited, that means that you can connect with friends who live far away from you just as easily as those who live a mile away. Because of this, some friends of mine from our Midwestern high school re-started our weekly Euchre game from long ago, but this time via webcams and a forum where the card game can be hosted online.

I was preparing for just such an evening when I got a notification that the first of my friends had logged in to our online meetup space.

“Hey, Kokomo!” I greeted him as his face appeared via his webcam. “How’s the weather in Jersey?”

Kokomo’s real last name began with a K, ended in an O, and had more letters in the middle than the county post office, so we all took to just calling him Kokomo. More than 30 years later, the name still stuck.

“Miserable… just like your Euchre playing,” he responded. “Hey, I was hoping I’d be able to talk before the others get here. I need some chart help.”

“Really? Insult my fine Euchre playing and then ask for a favor?” I chided back. “I see how you are.” Kokomo laughed and I continued. “What do you need?”

“Okay, so let me share my screen…” after a moment, it switched to show his screen instead of his face and I saw this:

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“Okay, that’s an XmR chart,” I said. “I can see what I think you need help with, but tell me what you think you need help with.”

“We’ve got this new Quality Improvement thing at work, and I don’t get why there’s two charts here,” he said. “That’s I need help with.”

“Got it. Fortunately, I can explain this in terms that even YOU can understand.” I joked.

“Hey!” he responded. “How d’ya figure?”

“You fell asleep every day in Mr. Navin’s class, that’s how I figure!” We both laughed at the memory.

“Hey, you know as well as me that I got better grades in Physics than anyone in that class,” Kokomo replied. “It was right after lunch, I was full and tired… and I was bored.”

It was true, and we both knew it. Even Mr. Navin knew it back then, and after trying repeatedly to embarrass Kokomo (he tried waking him by surprise up to answer a question; Kokomo got the question right every single time), Mr. Navin gave up and just let him sleep. Sometimes it took Kokomo a minute to wrap his head around a concept, but when he did he grasped it fully.

“Yeah, well turn your bored attention to that chart. The chart on top is called the X chart. The chart on the bottom is called the R chart. Tell me what point the X chart starts on.”

“Uh… October 15.”

“Right. Now tell me what point the R chart starts on.”

“Uh… hey, wait… it doesn’t start until November 15,” Kokomo answered.

“Right. And see that the lowest point on the Y axis of the R chart is a 0? There’s a reason for that. The R chart tracks the DIFFERENCE between the last point and this point. Can’t do that on the first point, so that one’s left blank.”

“Ah! Got it.” said Kokomo. “And the Y axis goes to 0 because no matter if the difference is positive or negative, they just chart the absolute value?”

“Perfect,” I replied, tapping on my computer to search for photos.

“Okay, but how do you use it? What does the R chart tell you that the X chart doesn’t, and why is it all red when the other one’s not?” he asked, in rapid-fire succession.

“Patience… that’s why I’m looking for pictures of our last dart game… here you go.” I shared my screen, showing him this:

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“I can’t believe you kept those photos all this time just to embarrass me,” said Kokomo.

“Not at all; I kept those photos all this time just to prove a point… the fact that it embarrasses you is just a bonus.” We laughed. “Okay, so pretend that these aren’t our darts, and it’s just two random people. What would you tell the player throwing the red darts if they asked you for advice?” I asked.

“Oh… uh… well, maybe I’d tell them wherever they’re aiming, try aiming a little more to the right and a little more down,” he offered.

“Uh huh,” I agreed. “There’s two things about throwing darts: consistency and accuracy. The person on the left is very consistent, but not particularly accurate. Now tell me what advice you’d give the person throwing the blue darts?”

“Well… they’re all over the place. Just practice more and get better? Try not to be so all over the place?” he offered.

“Exactly. You really can’t offer any aiming advice, because they’re all over. Without consistency, it doesn’t matter that they got a couple really close to the bullseye, because they missed the whole board on a couple as well.” I explained.

“So what’s that got to do with…” Kokomo paused. “Oh, I get it! The R chart is the difference between points, so it’s charting consistency.”

“Exactly.” I replied. “That’s why in Quality Improvement, we look at the R chart before the X chart. The R chart measures how close the consecutive points are to each other – it is a measure how consistent your process is. If you have a process that’s consistent but not accurate, we can make changes to try to move the results to where they need to be, and we can be more certain that any change in results will be consistent as time goes on. If you don’t have a consistent process, you can try to implement changes but there’s no assurance that they will have any effect.”

“Got it,” said Kokomo.

“Now if we look at your XmR chart, you’ll see that none of the points of the X chart show as red: none are outside the control limits, none violate any trending or position rules… and yet the R chart shows how wildly inconsistent the measurements are. You need to first figure out why the same process results in such varied results, THEN look at identifying and implementing improvements.”

“I see,” said Kokomo confidently. “I get it now. Hey, you ARE pretty good at explaining this stuff.”

“Hey, that’s why I’m a multi-dozenaire!” I said, causing Kokomo to laugh at the joke. “So there’s one more thing that these dart patterns bring up.”

“Yeah? What’s that?” he asked, as the computer chimed to let us know that our other friends had joined the online forum for the card game.

“I seem to remember betting somebody on that dart game, and I just don’t remember anybody paying up on that bet.”

“Ohhhh… see, I was gonna be all nice and let you guys win the Euchre game tonight, but now it’s GAME ON!!!” Kowtko’s mock bluster made all four of us laugh.

“All right, hot shot,” I said as I pushed the button to deal the first hand. “Let’s see if you can play cards any better than you throw darts…”

If you’re interested in learning more about X charts and R charts, click HERE to view a video where Jay Arthur explains it far more effectively

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