Page 170 - Six Sigma Demystified

Chapter 7 i m p r o v e S tag e 151

• Determining variables’ interactions
• Studying effects of change without risk, cost, and time of experimentation
• Teaching

Simulations can be used to investigate alternative process scenarios for a
given improvement strategy, allowing estimation of the solution’s robustness to
variation in input parameters. Proposed changes in resources, such as afforded
by cross- training or staff reallocation, can be analyzed quickly with respect to
cycle time. The effects of task prioritization, task order, and multitasking also
can be measured.
The input parameters for the simulation include a model of the process and
a suitable probability distribution (with parameters such as the mean and stan-
dard deviation) for each random variable. In some cases, it will be more conve-
nient to approximate the distribution with an alternate distribution. For
example, the normal distribution provides a reasonable approximation to the
binomial distribution for large samples.
The simulation, sometimes referred to as a Monte Carlo simulation, will gen-
erate a frequency distribution for the resulting process response. In a Monte
Carlo simulation, a large number of trials (5,000 or more) are run. Each time a
trial is run, a random number is generated for the response. The result is calcu-
lated and stored as the forecast of the result. After generating a large number of
forecasts, the distributional parameters of the response may be estimated.
Of course, the outcome is only as good as the prediction model, so actual
data should be used to verify the model either at the onset (if the model is
based on the current conditions) or at deployment of the improvements (if the
model is developed to predict performance of a new process).

A number of software tools are available for process simulations. Minitab
provides for random number generation in its Calc menu. Microsoft Excel pro-
vides its random number generation feature in the Tools/Data Analysis menu.
These random number generators form the basis for process simulations. The
common distributions and their properties and uses are shown in the “Distribu-
tions” section of Part 3.
An example simulation may be modeled for the four steps of the critical path
shown in Table 7.1. The model in this case is a simple addition of the cycle times
for each of the four steps in the process. Excel or Minitab may be used to gener-
ate a set of data of the appropriate distribution for each of steps 1 through 4.
(Note that in Excel the exponential data for step 4 are generated from a separate
set of uniform data, as described in the “Distributions” section of Part 3.)