Tip: At this point use the SigmaXL tool (bundled with DiscoverSim) to obtain descriptive statistics to test for normality (SigmaXL > Statistical Tools > Descriptive Statistics). Quantity Sold has an Anderson Darling Normality test p-value = 0.83, so may be considered as a Normal Distribution, but since it is a count we will apply DiscoverSim’s distribution fitting using discrete distributions. Price and Variable Cost are non-normal with AD p-values less than .05, so we will use DiscoverSim’s distribution fitting for continuous data. SigmaXL’s correlation matrix should also be used to evaluate correlations (SigmaXL > Statistical Tools > Correlation Matrix). The Spearman Rank correlation for Quantity Sold versus Price is -0.8 (Note: DiscoverSim uses the more robust Spearman Rank correlation rather than Pearson’s correlation). SigmaXL’s graphical tools such as Histograms and Scatterplots should also be used to view the historical data.
Since these are discrete distributions, Chi-Square is the statistic used to determine goodness-of-fit. The distributions are sorted by Chi-Square in ascending order. The best fit distribution is Negative Binomial with Chi-Square = 35.4 and p-value = “> .5”. The parameters are Number of Required Events = 33 and Event Probability = 0.2534. (See Appendix for further details on distributions and distribution fitting).
Tip: If the best fit discrete distribution has a p-value less than < .05 indicating a poor goodness-of-fit, none of the discrete distributions are adequate for use in Monte-Carlo simulation. In this case you should redo the distribution fit using the Continuous option (Note that you can use the continuous option for discrete data, but you cannot use discrete distributions for continuous data). After creating a DiscoverSim input distribution with the best fit (or normal if applicable), use Excel’s ROUND(number, 0) function to obtain integer values from the continuous distribution.
From the histogram and detailed report we see that typically we should expect a positive daily profit, but the variation is large. The likelihood of profit loss is approximately 0.56% (see Actual Performance (Empirical): %Total (out of spec)). Note that the “expected” loss of 1.49% assumes a normal distribution, so that is not applicable here because the output distribution is not normal (Anderson-Darling p-value is much less than .05).
Note: If Seed is set to Clock, there will be slight differences in the reported values with every simulation run due to a different starting seed value derived from the system clock
Tip: Percentile Process Capability Indices for non-normal data can be calculated from the Percentile Report as follows:
Percentile Pp = (USL – LSL)/( 99.865 percentile – 0.135 percentile)
Percentile Ppu = (USL – 50th percentile)/(99.865 percentile – 50th percentile)
Percentile Ppl = (50th percentile – LSL)/(50th percentile – 0.135 percentile)
Percentile Ppk = min(Ppu, Ppl)
Since we only have a lower specification limit (LSL = 0), Percentile Ppl is calculated as:
Percentile Ppl = (389.33 - 0) / (389.33 - (-30.81)) = 0.93
Here we see the negative correlation that was specified between the inputs “Price” and “Quantity Sold”, as well as the strong negative correlation between “Variable Cost” and “Profit”.
DiscoverSim uses the robust Spearman Rank correlation but the Pearson is also reported here for reference purposes. The correlations highlighted in red are statistically significant (p-value < .05).
Here we see that “Variable Cost” is the dominant input factor affecting “Profit” with a negative correlation (lower variable cost means higher profit). The next step would then be to find ways to minimize the variable cost (and reduce the variation of variable cost). “Quantity Sold” is the second important input factor. It is interesting to note that “Price” is the least important factor in this Profit simulation model.
In this case the input factor prioritization remains the same, but “Price” shows a small positive correlation rather than negative.