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Control Charts and a Visit With My Doctor - Part 2: It’s Important to Talk to Your Doctor About Overdispersion

I followed the nurse down the long beige hallway and had a seat. “The doctor will be with you shortly,” she said as she turned to leave.

It had been a month since my last visit. My doctor had prescribed me a statin drug to lower my cholesterol. I had prescribed him a P chart to monitor his wait times. I was anxious to find out how both had worked.

“Ah there he is,” said my doctor as he entered the room and began his obligatory hand sanitization ritual. “Well, I’ve got some good news and some bad news.”

“Let’s start with the good news,” I said.

“Certainly. Well your labs are back and your cholesterol is definitely in control.”

“That’s great. But what’s the bad news?” I asked, growing just a little nervous.

“The bad news is that the P chart you recommended is definitely NOT in control. There are almost more red points than black. Here, see for  yourself.”

He fiddled with his laptop a brief moment and turned the screen toward me so that I could see all the bright red dots on his P chart.

The P chart of Wait Times seems out of control.

“I see what you mean,” I said. "There are lots of points outside the control limits. That usually means there’s a problem. Have you looked into why the wait times for those days might be out of control?”

“That’s just it,” he said. “I’ve spoken with just about all 30 doctors at this practice and most of the receptionists. As far as we can tell, everything seems to be going great. And we’re not getting many complaints at all from patients.”

“Wait a minute, how many doctors did you say?”

“About 30,” he answered. “We see about 400 patients here each day.”

“Ah,” I said. “I’ll bet you are suffering from a classic case of overdispersion.”

“You bet I am! I mean I’ve always been busy, but lately it’s just plain crazy. In between patients, I’m running all around the building trying to figure out what’s going with this P chart thing, and I’m spending all kinds of time trying to reassure management that everything is fine, and …”

“No,” I interrupted,“ that’s not what I meant. 'Overdispersion' means your data contain more variation than a traditional P chart is designed to accommodate.”

“Indeed," he said as he stroked his chin, his eyebrows raising slightly.

”And you say the number of patients per subgroup is 400?”

“Yes, it varies, but I’d say we see about 400 patients here each day,” he replied.

“Well a traditional P chart assumes that your rate of defectives is constant.“

“We don’t talk about our valued patients that way.”

“What? No, I don’t mean the patients are defectives. A defective in this case is a wait time that is too long. The problem with a regular P chart is that it assumes the rate of defectives never changes. But in practice there is often some amount of variation due to factors like weather. That’s overdispersion,” I explained.

“Indeed.”

“Overdispersion can make a chart appear to be out of control even when the process is performing well. And large subgroups like yours exacerbate the problem by making the control limits very narrow, which causes a lot of points to fall outside the limits.”

“Oh, curse my misfortune!" he exclaimed. "That my wealth of great data is actually working against me! If only there was some way to adjust the control limits for this overdispersion so that my control chart would more accurately reflect my process."

“Actually,” I said, “there is. It’s called a Laney P' chart. (Pronounced ‘P Prime.') And as luck would have it, it just became available in Minitab this week.”

“Oh, bless my good fortune! That THIS VERY WEEK, Minitab would choose to release the latest update to their premiere statistical and quality improvement software!”

“Quite so. And Minitab also includes several other charts and tools that will be invaluable to practitioners like yourself in the healthcare industry, or any other industry for that matter,“ I explained.

“Indeed. How do I acquire this valuable upgrade?”

“If you are not already a Minitab user, just visit www.minitab.com. Let’s take a look.”

I quickly showed him that creating a Laney P’ chart was just as easy as creating a traditional P chart, you just choose Stat > Control Charts > Attributes Charts > Laney P’. An awed smile slowly spread across his previously weary face as he glanced at the results.

The P prime chart of Wait Times shows all is well.
 
“It’s so beautiful....” His eyes grew a little misty. I asked him if he needed a moment.

“No, no. It’s just allergies, just allergies,” he assured me as he struggled to compose himself. “But, but how…?”

“Well actually, you’re not the first person to have this problem. Back in the early 90’s, an inventive statistician and quality analyst by the name of David Laney was having a similar problem with a huge data set of 911 calls. ‘How is it possible for every point on the chart to be out of control?’ he asked himself. That question lead him on a voyage of discovery that ultimately led to the creation of the Laney P’ chart you see before you.”

“Indeed. Curse our misfortune that we will never know the whole story!”

“Well, actually you can know the whole story. A colleague and I had the good fortune to interview Dr. Laney about his experiences and inspirations. That interview is available for all to enjoy on the Minitab website. It’s an interesting read and it gives you some great insights into the world of control charts and the history of quality analysis."

“Oh, bless our collective good fortune that the dedicated professionals at Minitab have brought us not only the tools, but also the knowledge and the inspiration that we need to propel us forward as we pursue quality in our own disciplines! I don’t know how much they are paying you over there, Mr. Fox, but surely it could never be enough.”

“Indeed, good doctor," I said. "Indeed.”
 

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