In lean six sigma interventions, during the process improvement phase, we are often asked to build a resource allocation model (i.e. allocation of people to tasks and activities). In many instances, such model relies on a time standard that is a predetermined time/target in which an activity is expected to take to complete. The time standard is used with a forecast of the volume of work and any performance requirements to determine the work effort expected. The work effort is then used to determine the number of resources required to process work for a given period.

This blog discusses two statistical techniques that can be used to determine a representative time standard.

For illustration purposes, in the example provided in this blog, let’s assume that a series of tasks are completed within the generic activity type. The most complex case would have more than 200 tasks completed; while the simplest case would have between six and nine tasks conducted.

**Probability Plots**

In the development of a resource allocation an assessment of several representative time standards must be conducted. Averages and medians can often be skewed depending on the distribution of data; therefore, an examination of the type of distribution of various activity times, by type of work (e.g. processing simple versus complex transactions). The figure below shows how the data points for various activities/cases plot against a log normal probability plot.

Although the Normal, Exponential, Gamma and Weibull and Log-Normal distributions are typically examined, in the example used only the log normal distribution fit the data and therefore the log normal distribution is presented. Presentation of other distribution types is more complex and would need to be presented in an article on its own.

The Y axis for each graph measures the probability that a value will occur; while the X axis measures the processing time for the activity/case type. For example, the diagram above the last plot shows that 99% of all activities with 6-9 steps are processed in less than 10 minutes.

In the diagram above if most of the data points are close to the center line, then the data is expected to follow a log normal distribution. If the data tends to vary from the center line (i.e. beyond the 95% confidence intervals, which is also represented by the two lines to the right and left of the center line in some of the graphs), then the distribution follows a different distribution. The data in this example appears to follow a log normal distribution however we should do

As a result, it is expected that the mean of a log normal distribution should sufficiently represent the processing times of these activities however we will conduct one more test to be certain.

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**Histograms**

The histograms presented below show that the distribution of various processing times fitted against a log normal distribution.

The bar graphs show the actual percentage of records that were processed within a certain amount of time for a certain activity type. The solid line plotted on the same graph is the fitted log normal distribution. In cases at any given point where the bar graph is higher than the line graph, the log normal distribution under-estimates the true process value and vice versa. For instance, the log normal distribution over-estimates the actual processing time for cases in which more than 200 activities are conducted and under-estimates the true process value where the cases has 100-199 tasks.

Since the log normal distribution tends to under-estimate in some cases, it is more prudent to examine other central values, such as the mean excluding time under 1 minute, trimmed mean excluding the top and bottom 5% of the processing times, and the median values.

**Closing Thoughts**

In this blog I have presented two tests that can be used together to determine a time standard. Simply taking an average time is not sufficient and statistical techniques must be undertaken to determine a representative process value for an activity. I have personally seen instances in which an average value is used resulting in over or under allocation of resources. The next time you conduct a Lean Six Sigma project in which you are asked to come up with a time standard try uses these tests to ensure that the standard is accurate.

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**Valuable Resources**

The following URLs provide great additional information on Lean 6 Sigma

Toppazzini and Lee Consulting Lean 6 Sigma Consulting at -Lean Six Sigma Consulting

Linkedin Six Sigma Group at http://www.linkedin.com/groups?home=&gid=37987&trk=anet_ug_hm

ISixSigma web site at www.isixsigma.com

ASQ web site at www.asq.org