Pareto Plot Post Processing

Plot the effects of input variables on output responses in hierarchical order (highest to lowest).

Plot the Effects of Variables on Responses in Hierarchical Order

Rank the effects of input variables on output responses in hierarchical order (highest to lowest) in the Pareto Plot post processing tab.
  1. From the Post Processing step, click the Pareto Plot tab.
  2. Using the Channel selector, select the response to plot.
    Tip: Analyze multiple responses simultaneously by switching the Multiplot option to (multiple plots) and selecting the responses to plot using the Channel Selector.
  3. Analyze the pareto plot.

    The effect of input variables on output responses is indicated by bars. Hashed lines with a positive slope indicates a positive effect. If an input variable increases, the output response will also increase. Hashed lines with a negative slope indicates a negative effect. Increasing the input variable lowers the output response.

    A line represents the cumulative effect.

  4. From the Channel Selector, review the Ranked Inputs.

    For more information, see Ranked Inputs.



    Figure 1.

Configure the pareto plot's display settings by clicking (located in the top, right corner of the work area). For more information about these settings, refer to Pareto Plot Tab Settings.

Pareto Plot Tab Settings

Settings to configure the plots displayed in the Pareto Plot post processing tab.

Access settings from the menu that displays when you click (located above the Channel selector).
Effect curve
Show line to represent the cumulative effect.
# Top factors displayed
Specify the number of input variables (bars) displayed in the plot.
Note: This setting does not change the calculated effects.
Multivariate Effects
Calculate the effect using all input variables simultaneously.
Linear Effects
Calculate the effect using each input variable independently.
For more information about linear effects, refer to Linear Effects Post Processing.
Include Interactions
Include first order, two way interactions along with first order effects, and calculate interactions consistently with the choice of linear or multi-variate effects.
For more information about interactions, refer to Interactions Post Processing.
Exclude dependent/linked inputs
Only show the independent input variables.
Tip: Excluding dependent/link inputs reduces redundant information.

Multivariate Effects

Calculate the effect using all input variables simultaneously.

Multivariate effect of an input variable is the difference between the output response values when the variable is at its lower and upper values while the remaining variables are held constant. All calculations are based on a single linear regression model including all variables.

Example

A system with two variables, X and Y and the output response, F (X,Y).
Table 1. Design Matrix
Run X Y F (X, Y)
1 42.0 108.0 1385.4
2 54.0 156.0 2290.2
3 66.0 84.0 3421.2
4 78.0 132.0 4778.3
5 32.4 165.6 824.4
6 44.4 93.6 1548.3

F (X, Y) = A+B*X+C*Y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOraiaabc cacaqGOaGaaeiwaiaabYcacaqGGaGaaeywaiaabMcacaqGGaGaaeyp aiaabccacaqGbbGaae4kaiaabkeacaqGQaGaaeiwaiaabUcacaqGdb GaaeOkaiaabMfaaaa@4481@ is the reference regression model and intercept. A and coefficients, B and C, are calculated using the data set above.

A = - 2609.8

B = 88.6

C = 2.5

Regression equation: F (X, Y) = -2609 .8 + 88 .6*X + 2 .5*Y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOraiaabc cacaqGOaGaaeiwaiaabYcacaqGGaGaaeywaiaabMcacaqGGaGaaeyp aiaabccacaqGTaGaaeOmaiaabAdacaqGWaGaaeyoaiaab6cacaqG4a GaaeiiaiaabUcacaqGGaGaaeioaiaabIdacaqGUaGaaeOnaiaabQca caqGybGaaeiiaiaabUcacaqGGaGaaeOmaiaab6cacaqG1aGaaeOkai aabMfaaaa@4EB5@
  • Effect of X (lower = 32.4, upper = 78.0)

    Since we are investigating the effect of X only, Y is held constant. For this example, use the mean value ( Y ¯ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmywayaara aaaa@36E9@ = 123.2).

    X = 32.4, Y = 123.2
    F  32.4, 123.2  = 2609.7937+88.6056*32.4 +2.4841*123.2 = 567.0787 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbGaaeiia8aadaqadaqaa8qacaaIZaGaaGOmaiaac6cacaaI 0aGaaiilaiaabccacaaIXaGaaGOmaiaaiodacaGGUaGaaGOmaaWdai aawIcacaGLPaaapeGaaeiiaiabg2da9iabgkHiTiaabccacaaIYaGa aGOnaiaaicdacaaI5aGaaiOlaiaaiEdacaaI5aGaaG4maiaaiEdacq GHRaWkcaaI4aGaaGioaiaac6cacaaI2aGaaGimaiaaiwdacaaI2aGa aiOkaiaaiodacaaIYaGaaiOlaiaaisdacaqGGaGaey4kaSIaaGOmai aac6cacaaI0aGaaGioaiaaisdacaaIXaGaaiOkaiaaigdacaaIYaGa aG4maiaac6cacaaIYaGaaeiiaiabg2da9iaabccacaaI1aGaaGOnai aaiEdacaGGUaGaaGimaiaaiEdacaaI4aGaaG4naaaa@672C@
    X = 78, Y = 123.2
    F  78, 123.2  = 2609.7937+88.6056*78 +2.4841*123.2 = 4607.4948 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbGaaeiia8aadaqadaqaa8qacaaI3aGaaGioaiaacYcacaqG GaGaaGymaiaaikdacaaIZaGaaiOlaiaaikdaa8aacaGLOaGaayzkaa WdbiaabccacqGH9aqpcqGHsislcaqGGaGaaGOmaiaaiAdacaaIWaGa aGyoaiaac6cacaaI3aGaaGyoaiaaiodacaaI3aGaey4kaSIaaGioai aaiIdacaGGUaGaaGOnaiaaicdacaaI1aGaaGOnaiaacQcacaaI3aGa aGioaiaabccacqGHRaWkcaaIYaGaaiOlaiaaisdacaaI4aGaaGinai aaigdacaGGQaGaaGymaiaaikdacaaIZaGaaiOlaiaaikdacaqGGaGa eyypa0JaaeiiaiaaisdacaaI2aGaaGimaiaaiEdacaGGUaGaaGinai aaiMdacaaI0aGaaGioaaaa@651C@
    ΔF = 4607.4948  567.0787 =4040.4161 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqqHuoarcaWGgbGaaeiiaiabg2da9iaabccacaaI0aGaaGOnaiaa icdacaaI3aGaaiOlaiaaisdacaaI5aGaaGinaiaaiIdacaqGGaGaey OeI0IaaeiiaiaabwdacaqG2aGaae4naiaab6cacaqGWaGaae4naiaa bIdacaqG3aGaaeiiaiabg2da9iaahsdacaWHWaGaaCinaiaahcdaca GGUaGaaCinaiaahgdacaWH2aGaaCymaaaa@5164@
  • Effect of Y (lower = 84, upper = 165.6)

    Since we are investigating the effect of Y only, X is held constant. For this example, use the mean value ( X ¯ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmiwayaara aaaa@36E8@ = 52.8).

    X = 52.8, Y = 84
    F  52.8, 84  = 2609.7937+88.6056*52.8 +2.4841*84 = 2277.2536 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbGaaeiia8aadaqadaqaa8qacaaI1aGaaGOmaiaac6cacaaI 4aGaaiilaiaabccacaaI4aGaaGinaaWdaiaawIcacaGLPaaapeGaae iiaiabg2da9iabgkHiTiaabccacaaIYaGaaGOnaiaaicdacaaI5aGa aiOlaiaaiEdacaaI5aGaaG4maiaaiEdacqGHRaWkcaaI4aGaaGioai aac6cacaaI2aGaaGimaiaaiwdacaaI2aGaaiOkaiaaiwdacaaIYaGa aiOlaiaaiIdacaqGGaGaey4kaSIaaGOmaiaac6cacaaI0aGaaGioai aaisdacaaIXaGaaiOkaiaaiIdacaaI0aGaaeiiaiabg2da9iaabcca caaIYaGaaGOmaiaaiEdacaaI3aGaaiOlaiaaikdacaaI1aGaaG4mai aaiAdaaaa@63A8@
    X = 52.8, Y = 165.6
    F  52.8, 165.6  = 2609.7937+88.6056*52.8 +2.4841*165.6 = 2479.9623 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbGaaeiia8aadaqadaqaa8qacaaI1aGaaGOmaiaac6cacaaI 4aGaaiilaiaabccacaaIXaGaaGOnaiaaiwdacaGGUaGaaGOnaaWdai aawIcacaGLPaaapeGaaeiiaiabg2da9iabgkHiTiaabccacaaIYaGa aGOnaiaaicdacaaI5aGaaiOlaiaaiEdacaaI5aGaaG4maiaaiEdacq GHRaWkcaaI4aGaaGioaiaac6cacaaI2aGaaGimaiaaiwdacaaI2aGa aiOkaiaaiwdacaaIYaGaaiOlaiaaiIdacaqGGaGaey4kaSIaaGOmai aac6cacaaI0aGaaGioaiaaisdacaaIXaGaaiOkaiaaigdacaaI2aGa aGynaiaac6cacaaI2aGaaeiiaiabg2da9iaabccacaaIYaGaaGinai aaiEdacaaI5aGaaiOlaiaaiMdacaaI2aGaaGOmaiaaiodaaaa@6808@
    ΔF = 2479.9623  2277.2536 =202.7087 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqqHuoarcaWGgbGaaeiiaiabg2da9iaabccacaaIYaGaaGinaiaa iEdacaaI5aGaaiOlaiaaiMdacaaI2aGaaGOmaiaaiodacaqGGaGaey OeI0IaaeiiaiaaikdacaaIYaGaaG4naiaaiEdacaGGUaGaaGOmaiaa iwdacaaIZaGaaGOnaiaabccacqGH9aqpcaWHYaGaaCimaiaahkdaca GGUaGaaC4naiaahcdacaWH4aGaaC4naaaa@5197@
Input Variable Multivariate Effect
X 4040.4161
Y 202.7087

Global Sensitivity Analysis (GSA)

This sensitivity method is based upon probabilistic analysis framework, Sobol Indices. It decomposes the variance of each response into fractions which are later distributed to inputs. Final sensitivity values are a normalized version of Total Sobol Index, including both main and all order interaction effects across the whole input space. This sensitivity method is highly recommended for studies with nonlinearity.

Steps in GSA:
  1. A fit model via FAST based on the original DOE data.
  2. Large number of sample points are generated using the fit model.
  3. Decomposition of variance based on sample points and derivation of Total Sobol Indices.
Figure 2.