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  1. Optimization Goal/Multiple Output Metric: Minimize or Maximize Weighted Sum: minimize or maximize the weighted sum of statistic. Weights are specified for each output in the Output Response dialog. For example, if the selected statistic was the Mean, and there were two outputs, the objective function would be:

             Weight1Mean1 + Weight2Mean2


    Note, if there is a single output in the model, this simplifies to minimize or maximize the statistic value.


    Note that the Output Goal specified in the Output Response dialog is not used here. It is only used in Maximize Desirability.


  2. Optimization Goal/Multiple Output Metric: Minimize Deviation from Target: minimize the square root of weighted sum of deviations squared. A target must be specified for each output in the Output Response dialog. The only statistic available for this option is the mean. This is also known as the Taguchi or Quadratic Loss Function. If there were two outputs, the objective function would be:

            SQRT( Weight1(Mean1 – Target1)2 + Weight2(Mean2 – Target2)2)


  3. Optimization Goal/Multiple Output Metric: Maximize the weighted linear sum of the Desirability Function (Derringer and Suich, 1980). Each output must specify:

    • Weight (default = 1). This is also referred to as “Importance”. (Note, another factor, the desirability shape is sometimes called “weight”. In DiscoverSim, the desirability shape factor is fixed at 1.)


    • Output Goal (Target, Maximize or Minimize) – this is specific to an output. For example, if Output 1 is production rate, the goal would be set to maximize, and Output 2, cost, would have a minimize goal. However the specified overall objective function goal is to maximize desirability.

      • If the output goal is Target, then LSL, Target, and USL are required. LSL and USL are the lower and upper specification limits used for process capability and dpm calculations, but are also used as the lower and upper bounds for desirability.


      • If the output goal is Minimize, then Target and USL are required.


      • If the output goal is Maximize, then LSL and Target are required.


    The only statistic available for this option is the mean.


  4. For further details on Multiple Output Metrics see the Appendix: Formulas for Multiple Output Metrics.

  5. Statistic: The following tables give the Statistic options available depending on the selected Optimization Goal and Multiple Output Metric:

    Optimization Goal:

    Minimize

    Maximize

    Multiple Output Metric:

    Weighted Sum

    Deviation from Target

    Weighted Sum

    Desirability

    Statistic:

    Mean
    Median
    1st quartile
    3rd quartile
    Percentile (%)
    Minimum
    Maximum
    Standard Deviation
    Variance
    Mean Squared Error (requires Target)
    Skewness
    Kurtosis
    Range
    IQR (75-25)
    Span (95-5)
    Actual DPM (defects per million - requires LSL/USL)
    Actual DPMU (Upper – requires USL)
    Actual DPML (Lower – requires LSL)
    Calculated DPM (defects per million assuming normal distribution - requires LSL/USL)
    Calculated DPMU (Upper – requires USL)
    Calculated DPML (Lower – requires LSL)

    Mean (requires Target)

    Mean
    Median
    1st quartile
    3rd quartile
    Percentile (%)
    Minimum
    Maximum
    Standard Deviation
    Variance
    Mean Squared Error (requires Target)
    Skewness
    Kurtosis
    Range
    IQR (75-25)
    Span (95-5)
    Pp (requires LSL/USL)
    PpU (Upper – requires USL)
    PpL (Lower – requires LSL)
    Ppk (requires LSL/USL)
    Cpm (requires Target/LSL/USL)
    %Pp (Percentile Pp – requires LSL/USL)
    %PpU (Percentile PpU – requires USL)
    %PpL (Percentile PpL – requires LSL)
    %Ppk (Percentile Ppk – requires LSL/USL)

    Mean (requires Target and LSL, USL or LSL/USL)

     

  6. Formulas for general statistical measures are given in the DiscoverSim Workbook Appendix: Formulas for Statistical Measures.

  7. Formulas for Quality and Process Capability Indices are given in the DiscoverSim Workbook Appendix: Formulas for Quality and Process Capability Indices.

  8. DiscoverSim includes the following Global and Local optimization methods:


  9. Replications value sets the number of replications used in optimization to obtain the Statistic. The default value is 1000.

  10. Seed is set to Clock by default so that the starting seed of random number generation will be different with each run. If you want the optimization results to match every time (for example in a classroom setting where you want all students to obtain the same results), select Value and enter an integer number. Stochastic optimization requires a fixed seed in order to avoid “chatter” that would result in inconsistent comparisons. If the Seed is set to Clock, the initial seed value will be obtained from the system clock and then kept fixed throughout the optimization. Note that the results of a fixed seed for 32-bit Excel will be slightly different for 64-bit Excel.

  11. Select Monte Carlo (Random) for full randomization. Latin Hypercube Sampling is less random than Monte Carlo but enables more accurate simulations with fewer replications.

  12. Accelerated Mode uses DiscoverSim’s Excel Formula Interpreter to dramatically increase the speed of calculations for rapid optimization. If unchecked, the calculations are performed using native Excel. The interpreter supports the majority of all Excel numeric functions (for more details see the DiscoverSim Workbook Appendix: DiscoverSim Engine and Excel Formula Interpreter). If the DiscoverSim interpreter sees a function that it does not support, you will be prompted to use the Excel Native mode.

  13. Check Independence (Ignore Correlations) to run the optimization with all inputs independent of each other (zero correlation).

  14. Optimization in process may be interrupted/paused or stopped. Upon completion, the user can paste the optimum input control values in order to perform further simulation studies.

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