But someone mentioned that there are a different number of selling days in a month. Maybe January, 1995 is really soft if you factor in the number of selling days. Figure 11 is a control chart of the average daily sales per month for the same time period. (January, 1994 to January, 1995) What a different tale this chart tells! January, 1995 is, again, very close to an average performing month. The actual time of interest here is January, 1994. The chart signals that January, 1994 was unusually high for average daily sales. What happened last year to result in such high sales? Of course, if the chart had been in place last year that question could have been asked. Now, a year latter, it’s harder to find the cause.
STATISTICAL THINKING - A PERSONAL APPLICATION (TOM POHLEN)
I was introduced to Statistical Thinking in October, 1988 when I attended Heero Hacquebord’s course on “Statistical Thinking for Leaders”. I went into the course thinking that I already knew everything I needed to know about SPC. I came out of the course with a whole new perspective on statistics, looking upon SPC and other statistical applications more as a way of thinking about processes so we can learn how to improve them. I also found that I could never again be satisfied with looking at numbers without graphical analysis. I immediately began to think of all sorts of ways to apply this new knowledge at work and at home. One of my first applications was to control chart my weight, and I have been doing so ever since. My enthusiasm, however wasn’t shared by my wife, Carolyn. She had been an insulin-dependent diabetic since Nov., 1976. I could see an obvious application of control charts to her blood glucose, which she was testing daily. No matter what my argument was, she wasn’t interested.
What could be more important than a person’shealth. Here we see Statistical Thinking applied to ease someones pain. This “operational level” case study powerfully demonstrates the broad applicability of Statistical Thinking. It is an example of the third principle of Statistical Thinking, “Understanding and reducing variation are keys to success.” Understanding the variation in the process was a vital step toward making progress. Once Tom and Carolyn had a better understanding of the variation in the process, they were able to apply techniques to reduce that variation. The results were heartwarming, “. . . I can tell you for sure I know it worked because I feel a lot better now than I did before we started!” Can there be any better reason for applying Statistical Thinking in every part of our lives?!
STATISTICAL THINKING
Then in June, 1994 something changed. Somewhere between being tired of pricking her finger up to four times a day to get blood, having laser surgery in Nov.,’93 to repair eye damage caused by diabetes, and having been sick so frequently during the winter of ‘93/’94, she finally said she was ready to be my guinea pig for applying Statistical Thinking
The Objectives
We started out with a few simple objectives. For Carolyn it was to reduce the pain and inconvenience of diabetes, in particular, to regain her health and reduce the blood testing to no more than once a day. My objective was to get her what she wanted. To do so I knew that we had to understand her “process” variation, gain control of it, and reduce that variation. It seemed like a simple problem; after all it should be just like a production process! It wasn’t!
“My objective was to get her what she wanted.”
The “Process”
Carolyn is a “brittle’ diabetic, due to the fact that she has little or no insulin production. In June 1994, her swings in blood glucose levels were high. The normal non-diabetic has blood glucose of 70-120 milligrams/deciliter. It was not uncommon for Carolyn to vary from over 300 mg/dl to under 70 mg/dl (usually accompanied by an insulin reaction) in a very short time, sometimes within 24 hours. I ran a regression analysis to try to determine the effect of insulin on her blood glucose and re-learned the futility of analyzing “production” records for correlations. The analysis indicated that “increasing insulin increased blood glucose”, an obvious error! What was actually happening was that we had to increase insulin because blood glucose was up.
The Goal
“We dug into books and magazines and learned much about diabetes, including some of the mechanisms and key causes of blood glucose variation (food types, exercise, illness, infections, emotional stress...)”
Our main goal early in the project was to reduce glucose variation with an emphasis on reducing the overcontrol that was occurring. This was not a simple task because with diabetes there is no choice but to eat (usually sugar) when blood glucose drops and there is very little choice but to take extra insulin when blood glucose gets high (> 250 mg/dl). There was no doubt that we were dealing with a truly “chaotic” process. This indicated that we needed to try to find a control condition for Carolyn’s diabetes that would make her “process” more robust (insensitive to sources of variation.)
Understanding Variation
In June ‘94 before we could really get going with our efforts to control her diabetes, Carolyn had a bout with high blood glucose that we could not contain and she ended up in intensive care. She came out of the hospital June 26th still not very healthy. She continued to have high blood glucose problems and by August was back in intensive care.
This second failure was a big let-down, but we recommitted ourselves and decided it had to be done and it could be done. Carolyn long ago had learned that she had to take control of her own sickness and learn as much as she could about it. We dug into books and magazines and learned much about diabetes, including some of the mechanisms and key causes of blood glucose variation (food types, exercise, illness, infections, emotional stress...) A key book (reference #4) identified a very important fact: “The effect of any insulin on BG (blood glucose) usually diminishes as BG rises.” This indicates blood glucose has a non-linear response to insulin, a characteristic of a chaotic process.
After Carolyn came out of the hospital August 24, 1994, we began to make progress. Around this time we shared our data with Carolyn’s physician, Dr. John Zenk, doctor of internal medicine. He was pleased to see our active interest in controlling Carolyn’s blood glucose and was particularly satisfied with our charting of her numbers. As we gained better control, Carolyn had more low blood glucose reactions, a very undesirable complication. Low glucose tends to cause severe headaches and the potential to go into an unconscious state. The latter never happened but the potential of some brain cell damage is very undesirable. Her reactions tended to occur when sleeping in the early morning.
STATISTICAL THINKING
To deal with this we developed a theoretical quadratic model of how her insulin levels would build-up during a normal day. She was taking multiple shots/day of two kinds of insulin, Ultralente (long-acting, typically over 24 hrs.) and Regular (short-acting, typically over 3-6 hours, taken to handle the immediate effect of meals). Of her total insulin about 65-75% was Ultralente (initially 36 total units of insulin.) Our graphical model indicated we could improve the overall uniformity of insulin if she delayed her last shot of Ultralente till about 8 p.m. rather than taking it at 6 p.m. with dinner. To coincide with the change we also delayed our dinner time. The result was a reduction in problems with early morning insulin reactions.
“The theory that seemed to fit best was that the blood glucose level is really trying to be at some average level based on all the competing factors (insulin level, stress,illness/health, food intake,...)”
Finding Solutions
Knowing that we could not eliminate the causes of high blood glucose, we realized we needed to develop an adequate control strategy to bring high blood glucose down when it occurred. In the spirit of Statistical Thinking our first action in case of an out-of-control signal was to ask “why?” and investigate. Then based on that investigation, if an increase in insulin was called for, we needed an adjustment plan. The theory that seemed to fit best was that the blood glucose level is really trying to be at some average level based on all the competing factors (insulin level, stress, illness/health, food intake,...)
Due to the dynamics of the situation all these factors were simultaneously either rising or falling in amount. At any moment in time no single value of either the insulin dose or blood glucose level really has meaning. Thus, it was decided to use 24-48 hour averages of each of these two key parameters for determining the amount of change to make in the insulin doses to bring down high blood glucose. An initial crude formula was developed that worked well in dealing with high blood glucose levels in Nov. ’94 and Feb. ‘94.
In Jan. ‘94 a more fundamental theory was developed using the concept that the effect of insulin on blood glucose is non-linear. This was combined with an approach to apply differential equations further theorizing that the problem was similar to a population growth model. The final theory adopted the idea that the derivative of blood glucose with respect to insulin dose was an exponential function of blood glucose.
Successful Result
The use of the equation was successful in dealing with high blood glucose levels that occurred in May ‘95, June ‘95, July ‘95, Aug. ‘95, Dec. ‘95. We learned that in applying the equation it was important to continue to keep the relative doses of Ultralente and Regular at about the same ratio (about 65-75% Ultralente.) Usually, more than one iteration of the formula was needed to counteract high blood glucose due to the dynamic nature of each