See also:

Understanding variation is key to interpret process behavior. 

This simple exercise can help to experience process variation and understand the difference between process change and inherent process variation. 

This understanding is key on management decisions to avoid both overreaction and lack of reaction.

Manual dice throwing

To run the exercise with actual dice download and print the form:    Manual.JPG


  1. You will need a printed form and 4 dice for each team
  2. Throw 4 dice and add the outcomes
  3. Record the result in the Run Chart
  4. Repeat 50 times
  5. Join the dots in the Run Chart with a line
  6. Build the Histogram by counting the total number of dots on each group of 3 values 

Run the exercise with the simulator

Download this Excel Simulator:   Variation.xls

Close all Excel sheets before you open this one and enable MACROS.

Press RESET in the DICE sheet and keep on pressing F9 to throw the dice. 

Results Interpretation:

Try to answer these questions on each team and then discuss all teams together:

  1. Does each outcome depend on the previous one?
  2. Are there any special trends or indication of process change in the run chart? Is this a stable process?
  3. Is there a special cause that explains the maximum and the minimum values? Did you do anything different to obtain them?
  4. Is the frequency distribution close to normal: maximum at the center, declining frequency on both sides, symmetrical?
  5. What distribution would result throwing one single die? Why?
  6. Is it possible to predict the outcome of one specific throw?
  7. Is it possible to predict the frequency  of one specific outcome for a large number of throws?
  8. Can two different run charts produce the same histogram?

 Is there a downward trend?              Is this an upward trend?

Neither are statistically significant trends. The conclusion is that this is a stable process: there are no significant trends.

This is what we would expect since we have not changed the way we throw the dice so the process will continue to behave this way until we do so.

Stability doesn't necessarily mean that the process is OK: it just means that the process is neither improving nor getting worse. 

This is a stable process following a normal distribution with average 14 and standard deviation around 3.

If we throw one single dice the distribution would not be normal: it would be a uniform distribution (flat) because all values have the same probability. Throwing 4 dice there is only one combination that gives a sum of 4 (all 1's) but there are many combinations that give a sum of 14. The distribution of sums of 4 throws follows a normal distribution in spite of the distribution of single values following a uniform distribution (Central limit theorem).

Alternative process

 Let's now analyse another process: Open Variation.xls sheet ALT, press RESET and keep pressing F9 to run the process.

Now try to answer these questions on each team and then discuss all teams together:

  1. Is it likely that this data comes from the previous process of throwing 4 dice? Why?
  2. Is this a stable process?  Why?
  3. What is the meaning of the frequency distribution histogram in this case?
  4. Can we use it to predict the process behavior?
  5. What is the probability that values 7 - 13 happen again? Can you conclude that by looking at the histogram?

Alternative Process Conclusions

We can clearly notice that this process has an upward trend, therefore it isn't a stable process: its average is shifting up. 

Therefore it is very unlikely that it comes from throwing dice (apart from the values above 24 impossible with 4 dice).

In this case of an unstable process, as shown by the Run Chart, the Histogram is completely misleading if we want to predict the process behavior. Indeed, the histogram predicts that values below 15 have a certain probability of occurring but from the Run Chart we see that this is very unlikely. 

We can conclude that the Run Chart and the Histogram are both necessary and they complement each other. 

First we must check that the process is stable with the Run Chart and only if it is we can use the Histogram to characterize the process behavior.

 The question is how do we know if the process is stable (apart from just our impression)? The answer is to use a statistical analysis program such as Minitab:

Both significant Clustering and Trends confirm that the process is not stable.

Defect Rate Comparisons

Open Variation.xls sheet Defects

This are the defect rates produced by the 6 operators during one week. 

The department manager should decide, based on this data, whether he/ she should take some action such as:

  1. Talk to Amparo to remind her of our zero defects commitment with the customer
  2. Congratulate Fernando for his results and, maybe, give him a prize
  3. Ask the process engineer to explain why Mondays produce more defects than Fridays
  4. Tell operators that anyone producing above 8% average weekly defects will be penalized

If you have decided on any of these actions you are wrong. If fact, they may be counter productive.

This is an example of overreaction on the part of management due to a lack of understanding of process variation.

To see this just press F9 to simulate another week with this same process. 

If we analyse the results of 4 weeks we notice that the differences among operators aren't that large 

How do we know if there is a statistically significant difference among the different operators or days of the week?

This analysis can be done with the Analysis Tools in Excel: 2 Way ANOVA

The conclusion is that neither the differences among operators or days of the week are statistically significant.

Management improvement actions, in this case, should be directed to improve the overall process to reduce the defect rate. The process owner may run a Design Of Experiments (DOE) to optimize the critical process parameters. 

 Process Control

Open Variation.xls sheet Control press Reset

  1. You are responsible to control a machine to insure the deviation from target is zero in every run
  2. You can set the adjustment value (+ or -) to be applied to the next run 
  3. Set the adjustment and press F9 for the next run
  4. Repeat for 25 runs

  1. Did you achieve your objectives of controlling the process to obtain zero deviation in every run?
  2. Why?
  3. What strategy did you follow?
  4. What could you have done differently?
  5. Can you be held responsible for these results?
  6. Why?

 These are the results of overreaction:

If we made no adjustments:

Before we start making adjustments we should have seen how the process behaves with no adjustments. We see that the process has random variation and it is well centered in zero: this means we can't improve it with our adjustments, in fact, we will increase the variation and make it worse. 

In this case the operator has been given an impossible task.


  1. An understanding of process variation is essential in order to take the right improvement decisions
  2. Decisions based on one single outcome can lead to overreaction and making the process worse
  3. Statistical analysis is required to distinguish between a change in the process and intrinsic process variation
  4. Statistical applications such as Excel Data Analysis Tools or an application such as Minitab can help in this analysis
  5. Six Sigma education for professionals and management can be useful to adopt this new way of thinking