As the scout troop breaks for lunch, Alex wonders why they have not made as much progress as they should have. He thinks he might make the hikers more efficient by trimming their individual capacity so that they’ll each maintain the two mile per hour hiking speed. He wants to test this. Alex notices a kid rolling some dice around on a nearby picnic table and asks to borrow them. He finds a box of matches and a few aluminum bowls and arranges the bowls on a line as if they were the stages of a manufacturing line. The matches represent the pieces of product moving through each stage, and the dice represents the statistical fluctuation in each stage.
Alex’s assumption that the hikers’ speed should fluctuate up and down and average itself out implies that he believes the stages of his manufacturing process will do the same. Even when one operates at a slower than average speed, it should be able to compensate with a faster than average period as well. The fact that each match must move from one bowl to the next means that the bowls are a series of dependent events.
A few kids, including Dave, notice Alex and his matches and bowls. Alex tells them that he’s inventing a game and enlists them to play. He explains that each kid will sit in front of his bowl and roll the dice in turn to see how many matches he get to move from the prior kid’s bowl into their own—the goal for the whole group is to move as many matches as possible from one side of the table to the other. Because the dice can roll any number between one and six, Alex and the boys agree that the number of matches moved per roll should average out to three and a half. Alex decides that he’ll keep a tally of each boy’s match movements. Whoever keeps averages higher than three and a half wins the game and won’t have to do dishes in the evening.
Alex and the boys all agree that the system should hold its average of three and a half matches per turn, suggesting that the basic assumption Alex makes about statistical fluctuations is intuitive. Notably, even while Alex is hiking with his son, he is primarily thinking about work and using the hikers to help solve his own problems. This suggests that Alex considers his work to be the center of his world, superimposing itself even onto the time that he spends with his family.
Andy, the first boy, rolls a two, so he moves two matches from the matchbox into Ben’s bowl. Ben rolls a four, but because he only has two matches in his bowl, can only move two matches. The next boy, Chuck, rolls a five, but he still can only move the two matches that Ben gave him. Chuck thinks this is unfair, but Ben tells him they’ll roll better next round.
Ben and Chuck’s productivity (moving matches) are limited by Andy’s initial roll, suggesting that any delay in the early stages of a manufacturing system limits the progress of every subsequent stage.
As the boys continue rolling, Alex realizes that the further back in the line each boy is, the more each other boy’s low dice rolls affect him. Even if Dave and Evan, the last two boys in the line, roll high, they can never move more than two or three matches at a time and their average score plummets. Alex is both stunned and troubled. Although the match system should be balanced by the law of averages, the whole process can never maintain the predicted average for more than the first round. He glumly thinks about his plant and all of the orders that they are never able to deliver on time.
As Jonah said, the combination of dependent events and statistical fluctuations causes serious problems for a manufacturing system. If each boy was not dependent on the rolls of the boys before him, he would likely maintain a statistical average close to what Alex projected. However, since each boy is constrained by both his own roll and the rolls of those before him, low rolls create compounding delays and productivity losses.