Why are DOE simulated values negative?

[#1]

I am struggling to find the reason of getting the negative numbers which comes from simulation in DOE. The input dataset has seven Cost Type variables (X) and response variable is Total Cost (Y). I have imputed the data in custom design (see screenshot “DEO Setup_1”). The Min and Max values of the variables are as follows.

	Min	Max
Cost Type 1	11.31	18.91
Cost Type 2	8.2	16.39
Cost Type 3	8.3	17.88
Cost Type 4	8.08	17.87
Cost Type 5	9.79	18.12
Cost Type 6	7.41	18
Cost Type 7	10.99	18.95
Total Cost	64.08	126.12

In the simulated data file (attached), I expected to see the data under Total Cost should be in between 64.08 (Min) and 126.12 (Max). However, it is actually in between -5.201 (Min) and 126.12 (Max).

Can anybody suggest why is this and how to get the simulated values in between 64.08 (Min) and 126.12 (Max)?

[#2]

The simulated data have nothing to do with the original Total Cost data. The simulated data depends entirely on your definition of the model parameters. Here are the definitions you used:

I would expect the simulated data based on your definitions.

[#3]

Thank you @Mark_Bailey OK. Why are some  Total Cost Data negative? I expected that they should between 64.08 (Min) and 126.12 (Max). These are the values I added in designing the DOE.

[#4]

Hi @Mark_Bailey 

I can deal with the simulated cost (see attached). However, why are some  Total Cost Data negative? I expected that they should between 64.08 (Min) and 126.12 (Max). These are the values I added in designing the DOE.

[#5]

Why would you expect the simulated Total Cost values to be between 64.08 and 126.12? The simulation parameters determine the simulated values in the data table column.

You entered those values in the definition of the response. They are saved as the Response Limits column property. The simulator does not use those values. The Prediction Profiler uses those values when you optimize the response using the fitted model. They represent the range of outcomes that are acceptable to you. You defined this Total Cost to minimize it. So if you achieve a response of 64.08 or lower, the desirability equals 1. If you achieve a response of 126.12 or higher, the desirability is 0. The desirability is between 0 and 1 when the response is between those two values. That is what your definition means.

[#6]

Have you read the chapter on Custom DOE in the JMP Design of Experiments Guide? It explains the design parameters and how to use them. 

[#7]

Hi @Mark_Bailey 

Thank you for your reply.

Yes, I understand that I shouldn’t expect the simulated Total Cost values to be between Min = 66.463 (sum of all minimum seven cost types) and Max = 116.636 (sum of all maximum seven cost types).

The simulation parameters determine the simulated values in the data table column.

This table shows that regression coefficients are all equal including the intercept.

I tempted to run the model by setting Intercept = 0 and changing the regression coefficients depending on my own choice of effects of independent variables on the dependent variable (where Regulatory Fines assumes to be largest impact on the response variable i.e., Total Cyber Cost).

I have shown it in the below figure (for example)

However, when I hit “Apply”, I do not see any output.

Question 1: What is the purpose of this window in the DOE exercise?

The response limits that I have entered on the Model Dialogue as below.

I understand that the simulator does not use those values. The Prediction Profiler uses those values when I optimize the response using the fitted model (see, Model 2).

Prediction Profiler

I have created a new column on your JMP Data File “Total Cyber Risk (Actual))” where I presented the sum of all seven cost types. (Right Click the Variable Name and See the Formula).  You can use this Variable as your response (Y) variable sand Run the regression (See Model 2)

Here Min = 66.463 and Max = 116.636

Objective: Minimize

Following your response, I can achieve a response of 66.463 or lower, the desirability equals 1. If you achieve a response of 116.636 or higher, the desirability is 0. The desirability is between 0 and 1 when the response is between those two values 66.463 (Min) and 116.636 (Max).

Response (Y): <= 66.463, Desirability = 1

Response (Y): >= 116.636, Desirability = 0

Response (Y): 66.463 <= Y <=116.636, 0<=D<=1

I understand all of them.

Question 2: However, I am still do not understand how are the values of three variables i.e., Total Cyber Cost, Total Cyber Cost Simulated and Y Simulated are created.

I read the chapter on Custom DOE in the JMP Design of Experiments Guide you suggested. However, I do not fine enough clue to answer the above two questions (red fonts) in the context of this exercise (see JMP file attached).

[#8]

Answer 1: The simulated responses appear in the data table you made. There is a data column for the response. You use this column to enter the actual experimental results for analysis. There is another column next to it populated by the Simulate Responses dialog. It is populated every time you click the Apply button. You can copy the values in the second column and paste them into the first response column for analysis.

Answer 2: The Total Cyber Cost column is populated by you as you run the experiment or initially by the simulator. When you click the Apply button, the Total Cyber Cost is populated by the Simulate Responses dialog. I don't know where the Y Simulated column came from. I would expect it only if you did not change the default name (Y) in the response definition in Custom Design.