Dynamic applied statistics trainer

BEST SimuLab is an application created to teach applied probability and statistics concepts in a dynamic environment where attendees can play with controllers (sliders, buttons, etc.) to observe in real-time the effect of the changes they inplement.  For example the two limits imposed on the normal distribution below (L, U) can be dynamically moved with the mouse to see how the Tail Probability changes.  In the case shown (gap ~ NormalDistribution (25, 4) ) 2.28% is the probability of one sample gap lying below 17.  Similarly, the parameters of the distribution can be changed, or even the type of distribution can be modified.

The user can compare two populations in the same plot.  This is useful to represent changes in process parameters.  In the example below the blue curve represents the "desired" population and the pink one represents a change in that disired population.  In this case, the changes simulated are such that the Normal distribution is not the best mathematical model but the Weibull distribution represents better the new population.  Obviously, the change could have only included parameters of the original distribution.  

Note that the the user can plot a simulated histogram of the sample mean for a given sample size.

Statistics

The user can define one or two populations and then simulate taking samples from the populations while the histograms of the selected sample statistic are drawn.

SPC

For a silulated change in process parameters a control chart for the sample mean can be simulated.  In the case shown below note that the control chart for the mean detects the change in all the 10 samples simulated, but the Sample Range control chart does not detect the change.

For a silulated change in a process as shown below note that the "Two-out-of-three rule" is does help detecting the change even for variable sample sizes.

Simulating discrete random variables is also possible.  Even SPC charts can be simulated to evaluate the detection capabilities of the charts for the changes displayed in the initial (blue) population.

DOE

The DOE tab creates the design matrix of fractional factorials experiments for a selected number of factors (k) and the desired fraction.  This application is designed for illustration purposes only and, for such purpose, it is particularly useful when the number of factors is high (k > 15).

The experimental fraction for the inputs above are shown below.