JOP: Main function to minimize the risc function of a sequence of...
In JOP: Joint Optimization Plot

Description Usage Arguments Details Value References Examples

View source: R/JOP.R

JOP calculates optimal design parameters associated with a given sequence of cost matrices based on the minimization of a risk function introduced by Pignatiello (1993). Furthermore JOP visualizes the optimal design parameters and the appropriate predicted responses using the joint optimization plot introduced by Kuhnt and Erdbruegge (2004).

JOP(datax, datay, tau = "min", Wstart = -5, Wend = 5, numbW = 10, d = NULL, 
optreg = "sphere", Domain = NULL, form.mean = NULL, form.disp = NULL, 
family.mean = gaussian(), dlink = "log", mean.model = NULL, var.model = NULL,
joplot = FALSE, solver = "solnp")

`datax`	data set with parameter settings from an experimental design (data.frame). Columns have to be named.
`datay`	data set with responses resulting from an experimental design (data.frame). Columns have to be named.
`tau`	list of target values or single character value for the corresponding responses, where also "min" for minimization or "max" for maximization is possible. If `tau="min"` or `tau="max"`, then all responses are minimized or maximized.
`Wstart`	value to calculate the sequence of weight matrices (see Details)
`Wend`	value to calculate the sequence of weight matrices (see Details)
`numbW`	value to calculate the sequence of weight matrices (see Details)
`d`	a vector with values to calculate the sequence of weight matrices (see Details)
`optreg`	User can choose the Optimization region. `optreg="box"`: box constraints `optreg="sphere"`: sphere
`Domain`	box constraints. Column 1 for lower contraints and Column 2 for upper contraints. Row i corresponds to Parameter i.
`form.mean`	list of formulas for mean of each response
`form.disp`	list of formulas for dispersion of each response
`family.mean`	`family` for the mean
`dlink`	`list of names of link functions for the dispersion models`
`mean.model`	list of functions that model the mean for the corresponding response
`var.model`	list of functions that model the variance for the corresponding response
`joplot`	logical, if TRUE then the joint optimization plot is displayed.
`solver`	Default is "solnp" for three different starting points. Alternatively, "gosolnp" is especially recommended for complex programs.

The main function JOP is a package for multiresponse optimization which aims to minimize a risc function for a prespecified sequence of cost matrices. This sequence of cost matrices is specified by the arguments Wstart, Wend, numbW and d. The user can plug in target values for the responses or set to the target value to "min" or "max" in order to minimize or maximize the corresponding response.

JOP needs models for the mean and dispersion of each response which can be plugged in by means three different possibilities.

First, the user can pass the models for mean and dispersion as lists of functions in the parameter vector through the arguments var.model and mean.model.
Secondly, the user can plug in a list of formulas for each response for the mean and dispersion via the arguments form.mean and form.disp. Furthermore, a suitable link and distribution assumption can be specified both for the mean and dispersion
Finally, if the user does not plug in neither formulas nor models then JOP calculates automatically double generalized linear models by means of the function dglm from package dglm. Furthermore, JOP performs a backward selection, starting from the full model with main effects, interactions and quadratic terms, and afterwards dropping the least significant covariate in each step.

The data sets datax and datay are needed for model building. Both datax and datay have to be data frames where datax contains an experimental design with settings for each parameter columnwise and datay contains the experimental results columnwise for every response. Additionally, the columns of the data sets should be named, as exemplary demonstrated by data(datax) and data(datay). The optimization is performed by the procedure solnp out of the package Rsolnp. JOP returns an object of class "JOP" which can be visualized by means of plot.JOP. Details on the JOP method can be found in Erdbruegge et al. (2011).

JOP returns a list containing the following elements:

`Parameters`	The i-th row of this matrix contains the optimal Parameter setting appropriate to the i-th weight matrix
`Responses`	The i-th row of this matrix contains the predicted Responses appropriate to the i-th weight matrix
`StandardDeviation`	The i-th row of this matrix contains the standard deviation value for each response
`OptimalValue`	This vector contains the optimal value of the risk function for each optimal parameter setting
`TargetValueJOP`	Contains the target values for the correspoding responses used internally by JOP
`TargetValueUSER`	Contains the target values for the correspoding responses specified by the user
`DGLM`	If no models assigned then the list DGLM contains the calculated models for the mean and dispersion for every response
`RiskminimalParameters`	Parameters that minimize the squared sum of single risks among all calculated Parameters
`RiskminimalResponses`	Responses for the risk minimal parameters
`ValW`	Values for Wstart and Wend
`d`	Slope vector
`numbW`	Number of weight matrices

Sonja Kuhnt and Martina Erdbruegge (2004). A strategy of robust paramater design for multiple responses, Statistical Modelling; 4: 249-264, TU Dortmund.

Martina Erdbruegge, Sonja Kuhnt and Nikolaus Rudak (2011). Joint optimization of independent multiple responses based on loss functions, Quality and Reliability Engineering International 27, doi: 10.1002/qre.1229.

Joseph J. Pignatiello (1993). Strategies for robust multiresponse quality engineering, IIE Transactions 25, 5-15, Texas A M University.

Alexios Ghalanos and Stefan Theussl (2012). Rsolnp: General Non-linear Optimization Using Augmented Lagrange Multiplier Method. R package version 1.12.

Peter K Dunn and Gordon K Smyth (2012). dglm: Double generalized linear models, R package version 1.6.2.

Sonja Kuhnt, Nikolaus Rudak (2013). Simultaneous Optimization of Multiple Responses with the R Package JOP, Journal of Statistical Software, 54(9), 1-23, URL http://www.jstatsoft.org/v54/i09/.

# Example: Sheet metal hydroforming process
# Run JOP without Model specification

outtest <- JOP(datax = datax, datay = datay, tau = list(0, 0.05), numbW = 5, joplot = TRUE)