## Wednesday, May 20, 2009

### Wednesday Math, Vol. 72: Dr. Deming

"Efficiency experts" were a common enough breed back in the 1940s and 1950s that they were mocked in popular culture, most famously in the play Desk Set, which was turned into a movie starring Spencer Tracy and Katherine Hepburn. Perhaps the most successful of this breed was W. Edwards Deming, though he wouldn't become famous in the United States until the late 1970s.

Deming was trained as a statistician, but he wasn't keen on a lot of the ideas in the field. He found little value in the concept of hypothesis testing, for example. The idea is to test samples from different populations to see if there is a significant difference in the measure of some similar aspect in the two populations. Deming was of the view that if there was a difference, eventually you should be able to find a large enough sample to show that difference to a convincing level.

Deming's great success as an efficiency expert came when he went to Japan after World War II. It might be hard for young people to believe, but in the middle of the century "Made In Japan" was just as much of a joke as "Made In China" is today, a sign that a product was made poorly so that it could sell cheaply. Deming and his system of continuous improvement is given much of the credit for turning things around.

In a mass production environment, Deming stated that quality was largely a matter of lack of variability. To reduce variability, he came up with a four step process.

Step 1: Measure everything. Take a sample of your product and carefully measure stuff. Say it's a car. Measure the length of the bolts in the transmission, the thickness of the windshields, the diameter of the intake valves, everything you can think of.

Step 2: Find the thing with the most variation. Here's where the math comes in. How can we fairly compare windshield thickness to intake valve diameter? Deming's idea was to use the coefficient of variation, the standard deviation divided by the average, usually written as a percentage. For example, the average height for men is 69.0 inches and the standard deviation is 2.8 inches. For women, the average is 63.6 inches and the standard deviation is 2.5 inches.

2.8/69.0 = .04057971... or about 4.1%
2.5/63.6 = .039308176... or about 3.9%

Notice that if I measure the heights in centimeters instead of inches, the raw numbers would change but the coefficient of variation would remain the same. Men are not only taller than women on average, but they have a little more variation in their heights.

Step 3: Reduce the variation of the most variable thing. Let's say that after all this measuring, we find that transmission bolts have the highest coefficient of variation at 5.1%. Deming says get that fixed. Go to your supplier and ask for the bolts to have less variation. If the supplier has trouble complying, this might be a process that needs to become internal to the company. However it gets done, bring down the variation of those transmission bolts.

Step 4: Go back to Step 1. This is what makes Deming's method continuous improvement. Once the bolt problem is fixed, measure again to find what the most pressing concern is now. There is a possible hitch in this method, where some factors negatively influence others in a feedback loop. Maybe fixing a problem with the bolt causes the thickness of the transmission wall to become more variable, and fixing the wall thickness problem causes the bolts to be more variable. If this shows up, where a couple of the things you measure are always causing the most trouble, it's time to completely redesign the product. Otherwise, over time the variability of everything should go down, and for a mass produced commodity, that should mean quality goes up.

Deming was highly respected in Japan, and companies gladly paid him to present his ideas. If he asked that the president of the company and the board of directors show up to make sure that everybody understood what his methods were about, the bigwigs would be in the front row. When Japanese quality was clearly better than American, and it probably happened in the sixties though we figured it out in the seventies, Deming, who was born in 1900, was invited to America to spread his ideas back in the good old U.S. of A. The thing is, when he invited the presidents and board of directors here, they sent secretaries. His message didn't get all the way to the top. Deming hated slogans. After he gave his talk at Ford, the company made a change.

Their new slogan was "Quality Is Job One."

Deming had little good to say about his experience in dealing with American industry. He passed away in 1993, but his ideas live on. There are many American companies now that have adopted the system of continuous improvement, and quality of many American made products is getting better. This, of course, assumes you can actually find American made products any more.

dguzman said...

Deming was a genius. Unfortunately, too many companies that preach "process improvement" end up focusing so much on the process that nothing gets improved.

Anonymous said...

You seem to pretty down on industry in the USA. Any data behind your implication that American manufacturing is low quality?

Matty Boy said...

My last paragraph gives some credit to American industry now. I was mainly ragging on Ford back in the 1980's.

Dr. Zaius said...

Jeepers! If I didn't have some variation in my transmission bolts, I wouldn't be able to tune in Jupiter, and Venus would come in all fuzzy.

Karen Zipdrive said...

We need a Deming now.
The Japanese appreciated him and now their manufacturing industry makes ours look like theirs did in the '50s.

namastenancy said...

Slightly off topic but still math related - excellent op ed piece on math at the NY Times:
http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/?em