Another approach to statistical control. Dice Experiment.

Variation of a process is not a positive aspect in financial terms. To prove this theory, let's take the example of dices. All of us know that a dice has 6 faces, each of them having a number from 1 to 6, arranged so that on opposite faces, the sum of those numbers is 7 (or the average of these two numbers is 3.5). OK, let's take the dice and roll it 20 times. Record each run of the dice (in our experiment, it's the first column in the table, namely Regular Dice). Now, let's alter the dice, so that to keep the same rule, but using the closest numbers to average value of two opposite faces of regular dice. These numbers will be 3 and 4. So, on each pair of two opposite faces of the dice, we will have the values 3 and 4. Now let's make the same number of runs as in the first case and record the values (second column in our experiment, namely Modified Dice).

Regular dice Modified dice 1 3 4 3 1 3 2 4 2 4 3 3 5 4 4 4 1 4 4 3 5 3 5 3 5 4 1 3 5 3 1 4 2 3 5 3 5 3 3 4

Let's analyze the performance of each trial. Computed statistics (the average of runs and the variation of them) are presented in the following table:

	Regular dice	Modified dice
Mean (average)	3.2	3.4
Variation (stDev)	1.673	0.503

Plots of I-charts for each series are presented below (left chart for Regular Dice, right chart for Modified Dice):

Analyzing the charts and computed statistics lead to following conclusions:

• the first impression when comparing the average of each dice is that they are close to each other, in term of means (averages). There is a 6.25% difference in favor of Modified Dice. In terms of variation, a highly one is observed for Regular Dice, while for the Modified Dive the variation is small.
• both of I-charts show a controlled process, because no observation fall outside the control limits;
• both charts were plotted on same scales, in order to present visually the differences for variation. Is crearly observed that modified dice have a much lower variation than regular dice. These charts underline the need of lowering the variation in the process, with gains in terms of efficiency (means comparison).

Now, let's try to apply the data to a real situation. A truck transporting company has two loaders, first of them is loading the truck with quantities described in column 1, and the second one with quantities described in column 2 (all of these because skills and qualification of loader operators. Transportation of product is made on the same length of road, with the same driver, under the same conditions. What are the benefits? Because of lower variation in loading provided by the second loader, the company makes benefits in terms of either duration, or costs, or profits. That difference of means of 6.25% is in the favor of the second alternative, where variation is smaller. Assuming that in one year of operation, the profit made by the company using the first loader is 100.000$, in the second alternative the profit is 106.250$. Is that good? Of course...

The basic rule learned from this example is: narrow the variation of the process and expect an increase of profits.

Some of you may say: it's possible that in twenty runs, with the first dive, fifteen times of get the number 6. Of course, the mean of the process will be higher than with Modified Dice, but this is pure luck. Every business should be run so that to make that product or service with as smaller variation of characteristics as possible. This way, high confidence will arrise meaning that established objectives will be achieved. With a higher variation, reaching planned objectives is more risky.