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Apogee: Sensitivity Analysis

Quickly examine the effects of variation on your designs

Apogee licenses start at $269
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Sensitivity analysis is a quick and easy way to assess the magnitude of response variation caused by the variation of the parameters, and it also identifies key drivers of response variation. The response mean and standard deviation are computed using the input parameter means and standard deviations and the function's low-order partial derivatives.


  • Identify tolerances that are too tight or too loose
  • Quantify risk of not meeting requirements
  • Easy-to-use and learn interface
  • Unlimited number of factors*
  • Advanced calculations for numerical derivatives
  • 2nd-order analysis
  • Nonlinearity test and warning
  • Pareto plots of contributors to response variability

*Constrained only by worksheet size/memory limits in MS Excel™


If the input parameters of a mathematical function have statistical variation, then the output response will also have variation. Sensitivity analysis is a quick and easy way to compute the mean and standard deviation of responses using the input parameter means and standard deviations and the function’s partial derivatives.

If the response has a defined Upper Specification Limit (USL) or Lower Specification Limit (LSL) then the probability of the response falling outside of these limits will be computed using the tail areas of the Normal distribution. This probability is called the Probability of Non-Compliance or PNC.

Pareto plots of the contributions of each parameter to the response are automatically created. This can be useful for identifying which parameters have the largest impact on response standard deviation and which parameters could be changed to reduce the response PNC.


  • Microsoft Windows 7, 8, or 10
  • Microsoft Excel 2007, 2010, 2013 (32 or 64 bit), or 2016 (32 or 64 bit)
  • Administrator rights required to install software


  • Define input parameters as: Continuous, Integer, Discrete, Noise, Constant


  • Probability distributions can be defined as: Normal, Uniform, Triangular, Lognormal, Exponential, Weibull, Beta, Gamma, Johnson, or Histogram.
  • Multiple distributions can be combined and/or truncated to create unique composite distributions.


  • Define the lower and/or upper specification limits for each output response.
  • Define the Probability of Non-Compliance (PNC) goal.


  • Define input parameters and output responses on Excel worksheets.
  • Define indicators of each cell type


  • Quickly modify the problem using the Formulation Editor.


This video shows Sensitivity Analysis and Monte Carlo using SDI Tools v3 in action. We will be updating this video to reflect changes to SDI Tools v4 soon.