Critical Chain - Eliyahu M. Goldratt [17]
Judging by the students' expressions, I'd better explain. "Let's take it slowly. For every step in the project there is a time estimate; the length of time, we estimate, it will take from the start of that step until completion of that step. Mark, when you or your people are asked to estimate the time required for a step, how much safety do you embed in your time estimate?"
"No safety. We give realistic estimations. As much as we can." He is not playing games with me, he believes in what he is saying. I don't see any choice but to dive to a deeper level.
"You all learned about probability distributions," I start my explanation.
Knowing the extent to which students dislike statistics I decide to take it in very clear steps all to the point. "Consider a good marksman aiming to hit a bull's-eye and using a wellbalanced gun. What is the probability of the marksman hitting a specific point on the target?"
I draw the Gaussian distribution on the board.
"You've probably seen this bell shape more than once." Nevertheless, I explain, "The probability of our good marksman missing the target completely is very low. His probability of hitting the bull's-eye is not one hundred percent, but it's higher than the probability of hitting any other point on the target. And here is the probability distribution of an excellent marksman." And I draw a much thinner and taller Gaussian.
"Now let's consider another case. How much time will it take you to drive from the university to your house? Brian, would you volunteer?"
"About twenty-five minutes," he answers, not really knowing what I'm asking for.
"What do you mean by ‘about'?"
"About means about. Sometimes it may take thirty minutes, sometimes less. Depends on the traffic. Late at night, and with my radar detector on, I might do it in less than ten minutes. In rush hour on a bad day it might even take an hour." He starts to see what I mean, because he continues, "If I have a flat tire it would take more. If my friends persuade me to stop at a bar, it might take even longer."
"Precisely," I say, and draw the corresponding probability distribution. Five minutes has zero probability, twenty-five minutes has the highest, but even three hours has some non-zero probability.
"Mark, when you estimate the time it will take to do a step in a project, which one of these two probability distributions more closely resembles your situation?"
"The last one." Grinning, he adds, "Actually it is more like Brian, who loves to stop for a drink and talk for hours."
"The higher the uncertainty the longer the tail of the distribution," I remind them. "This is the median of the distribution," I draw the line on the graph. "It means that there is only a fifty percent chance of finishing at or before this time."
I wait for everyone to digest this fact before I turn back to Mark. "Mark, when Brian was asked to estimate, he gave an estimation that is close to the median. But when you or your people are asked to estimate the time required for a step in a project, what estimation do you usually give? Will you, please, come here and show it to us on Brian's probability distribution."
It takes him some time to reach the board. I hand him the chalk, and without hesitation he draws a vertical line, way to the right of the distribution curve.
"Why not the median?" I ask him.
"Because Murphy does exist," he laughs.
"It also exists for Brian."
"Come on," he says. "Only a suicidal, inexperienced person would choose the median."
"Makes sense," I comment. "It especially makes sense because in most environments there is little positive incentive, if any, to finish ahead of time, but there are plenty of explanations required when we are late. Under such conditions, I agree with Mark that almost nobody will choose an estimate they have a fifty percent chance of blowing. What probability