Used to model linear degradation paths, or nonlinear paths that can be transformed to linear. For details, refer to Simple Linear Path.
Used to model nonlinear degradation paths, especially those that cannot be transformed to linear. For details, refer to Nonlinear Path.
To change between the two specifications, use the Degradation Path Style submenu from the platform red triangle menu.
To model linear degradation paths, select Degradation Path Style > Simple Linear Path from the platform red triangle menu.
Use the Simple Linear Path Model specification to specify the form of the linear model that you want to fit to the degradation path. You can model linear paths, or nonlinear paths that can be transformed to linear. See Simple Linear Path Model Specification.
Simple Linear Path Options describes the options for the Simple Linear Path specification.
If you need to perform a transformation that is not given, use the Custom option. For example, to transform the response variable using exp(x2), enter the transformation as shown in the Scale box in Custom Transformation Options. Also, enter the inverse transformation in the Inverse Scale box.
Name the transformation using the text box. When finished, click the Use & Save button to apply the transformation. Select a transformation from the menu if you have created multiple custom transformations. Click the Delete button to delete a custom transformation.
To model nonlinear degradation paths, select Degradation Path Style > Nonlinear Path from the platform red triangle menu. This is useful if a degradation path cannot be linearized using transformations, or if you have a custom nonlinear model that you want to fit to the data.
To facilitate explaining the Nonlinear Path Model Specification, open the Device B.jmp data table. The data consists of power decrease measurements taken on 34 units, across four levels of temperature. Follow these steps:
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Click OK.

Device B Overlay Plot shows the initial overlay plot of the data.
The degradation paths appear linear for the first several hundred hours, but then start to curve. To fit a nonlinear model, select Degradation Path Style > Nonlinear Path from the platform red triangle menu to show the Nonlinear Path Model Specification outline. See Initial Nonlinear Model Specification Outline.
Note: To view the Edit button displayed in Initial Nonlinear Model Specification Outline, you must have the interactive formula editor preference selected (File > Preferences > Platforms > Degradation > Use Interactive Formula Editor).
The first step to create a model is to select one of the options on the menu initially labeled Empty:
The Reaction Rate options are applicable when the degradation occurs from a single chemical reaction, and the reaction rate is a function of temperature only. Select Reaction Rate or Reaction Rate Type 1 from the menu shown in Initial Nonlinear Model Specification Outline. Although similar to the Reaction Rate model, the Reaction Rate Type 1 model contains an offset term that changes the basic assumption concerning the response value’s sign.
For this example, select Reaction Rate and then select Celsius as the Temperature Unit. Click OK to return to the report. For details about all the features for Model Specification, refer to Model Specification Details.
Select Constant Rate from the menu shown in Initial Nonlinear Model Specification Outline. The Constant Rate Model Settings window prompts you to enter transformations for the Path, Rate, and Time.
Once a selection is made for each transformation, the associated formula appears in the lower left corner as shown in Constant Rate Transformation.
After all selections are made, click OK to return to the report. For details about all the features for Model Specification, refer to Model Specification Details.
The Prediction Column option enables you to use a custom model that is stored in a data table column. The easiest approach is to create the model column before launching the Degradation platform. You can also create the model column from within the Degradation platform if you want to use one of the builtin models shown in Column Selection.
For details about how to create a model and store it as a column, refer to Fit a Custom Model or the Nonlinear Regression chapter of the Specialized Models book.
Select Prediction Column from the menu shown in Initial Nonlinear Model Specification Outline. The Model Specification outline changes to prompt you to select the column that contains the model.
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If the model that you want to use already exists in a column of the data table, select the column here, and then click OK. You are returned to the Nonlinear Path Model Specification. For details about all the features for that specification, refer to Model Specification Details.

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If the model that you want to use does not already exist in the data table, you can click the Model Library button to use one of the builtin models. For details about using the Model Library button, refer to Model Library or the Nonlinear Regression chapter of the Specialized Models book. After the model is created, relaunch the Degradation platform and return to the column selection shown in Column Selection. Select the column that contains the model, and then click OK. You are returned to the Nonlinear Path Model Specification. For details about all the features for that specification, refer to Model Specification Details.

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If the model that you want to use is not in the data table, and you do not want to use one of the builtin models, then you are not ready to use this model specification. First, create the model, relaunch the Degradation platform, and then return to the column selection (Column Selection). Select the column containing the model, and then click OK. You are returned to the Nonlinear Path Model Specification. For details about all the features for that specification, refer to Model Specification Details. For details about using the Model Library button, refer to Model Library or the Nonlinear Regression chapter of the Specialized Models book for additional information.

After you select one of the model types and supply the required information, you are returned to the Nonlinear Path Model Specification window. See Initial Model Specification for the Model Specification that you get after clicking OK in Unit and Baseline Selection.
Note: To view the Edit button displayed in Initial Model Specification and Model Specification, you must have the interactive formula editor preference selected (File > Preferences > Platforms > Degradation > Use Interactive Formula Editor).
A model is now shown in the script box that uses the Parameter statement. Initial values for the parameters are estimated from the data. For complete details about creating models that use parameters, refer to Fit a Custom Model or the Nonlinear Regression chapter in the Specialized Models book. A nicely formatted view of the model is shown below the row of buttons.
If desired, type in the text box to name the model. For this example, use the name “Device RR”. After that, click the Use & Save button to enter the model and activate the other buttons and features. See Model Specification.
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The Fit Model button is used to fit the model to the data.

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The optimization method menu provides three choices for the optimization method (Newton, QuasiNewton BFGS, and QuasiNewton SR1).

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Newton chooses whether GaussNewton (for regular least squares) or NewtonRaphson (for models with loss functions) is the optimization method.

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QuasiNewton SR1 chooses QuasiNewton SR1 as the optimization method.

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QuasiNewton BFGS chooses QuasiNewton BFGS as the optimization method.

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The Optimization Settings button is used to change the optimization settings.

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The Delete button is used to delete a model from the model menu.

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The Generate Report for Current Model button creates a report for the current model settings. See Model Reports.

The initial parameter values are shown at the bottom, along with sliders for visualizing how changes in the parameters affect the model. To do so, first select Graph Options > Show Fitted Lines from the platform redtriangle menu to show the fitted lines on the plot. Then move the parameter sliders to see how changes affect the fitted lines.
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Dinf (D)  asymptotic degradation level

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Ea (Ea)  reactionspecific activation energy

where RU is the reaction rate at use temperature tempU, RU x AF(temp) is the reaction rate at a general temperature temp, and for temp > tempU, AF(temp) > 1
To fix a value for a parameter, check the box under Fixed for the parameter. When fixed, that parameter is held constant in the model fitting process.
You can use the Formula Editor to enter a model. Click the Edit button to open the Formula Editor to enter parameters and the model. For details about entering parameters and formulas in the Formula Editor, see Using JMP.
Note: To view the Edit button displayed in Alternate Model Specification Report, you must have the interactive formula editor preference selected (File > Preferences > Platforms > Degradation > Use Interactive Formula Editor).
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Select Analyze > Modeling > Nonlinear.

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Assign the model column to the X, Predictor role.

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Click OK.

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Click Go on the Control Panel to fit the model.

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Select Parameters from the popup menu above the list of columns.

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Click New Parameter.

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Click OK.

In the formula editor, when you add a parameter, note the check box for Expand Into Categories, selecting column. This option is used to add several parameters (one for each level of a categorical variable for example) at once. When you select this option a window appears that enables you to select a column. After selection, a new parameter appears in the Parameters list with the name D_column, where D is the name that you gave the parameter. When you use this parameter in the formula, a Match expression is inserted, containing a separate parameter for each level of the grouping variable.
The Model Library can assist you in creating the formula column with parameters and initial values. Click Model Library on the window to open the library. Select a model in the list to see its formula in the Formula box.
Click Show Graph to show a 2D theoretical curve for oneparameter models and a 3D surface plot for twoparameter models. No graph is available for models with more than two explanatory (X) variables. On the graph window, change the default initial values of parameters using the slider, or clicking and entering values directly.
The Reset button sets the initial values of parameters back to their default values.
Click Show Points to overlay the actual data points to the plot. A window opens, asking you to assign columns into X and Y roles, and an optional Group role. The Group role allows for fitting the model to every level of a categorical variable. If you specify a Group role here, also specify the Group column on the platform launch window.
Clicking Make Formula at this point (after using Show Points) creates a new column in the data table. This column has the formula as a function of the latest parameter starting values.
Note: If you click Make Formula before using the Show Graph or Show Points buttons, you are asked to provide the X and Y roles, and an optional Group role. After that, you are brought back to the plot so that you have the opportunity to adjust the parameters starting values if desired. At that point click Make Formula again to create the new column.
The Model Library is created by a builtin script named NonlinLib.jsl, located in the Resources/Builtins folder in the folder that contains JMP (Windows) or in the Application Package (Macintosh). You can customize the nonlinear library script by modifying this script.
To add a model, you must add three lines to the list named Listofmodellist#. These three lines are actually a list themselves, which consists of the following three parts.
Add the following lines to the NonlinLib.jsl script
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There is a comma as the last character in the example above. If this is the final entry in the Listofmodellist# list, the comma can be omitted.

To delete a model, delete the corresponding threelined list from the Listofmodellist# list.