Function to generate a unit space for the Mahalanobis-Taguchi (MT) method

Description

MT generates a unit space for the Mahalanobis-Taguchi (MT) method. In general_MT, the inversed correlation matrix is used for A and the data are normalized based on unit_space_data.

Usage

MT(unit_space_data, includes_transformed_data = FALSE, ...)

Arguments

Value

MT returns an object of S3 class "MT". An object of class "MT" is a list containing the following components:

References

Taguchi, G. (1995). Pattern Recognition and Quality Engineering (1). Journal of Quality Engineering Society, 3(2), 2-5. (In Japanese)

Taguchi, G., Wu, Y., & Chodhury, S. (2000). Mahalanobis-Taguchi System. McGraw-Hill Professional.

Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.

Woodall, W. H., Koudelik, R., Tsui, K. L., Kim, S. B., Stoumbos, Z. G., & Carvounis, C. P. (2003). A review and analysis of the Mahalanobis-Taguchi system. Technometrics, 45(1), 1-15.

See Also

solve, general_MT, generates_normalization_function, and diagnosis.MT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_MT <- MT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE)

# The following tol is a parameter passed to solve function.
unit_space_MT <- MT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE,
                    tol = 1e-9)

(unit_space_MT$distance)

Function to generate a unit space for the Mahalanobis-Taguchi Adjoint (MTA) method

Description

MTA generates a unit space for the Mahalanobis-Taguchi Adjoint (MTA) method. In general_MT, cofactor matrix is used for A and the data are normalized based on unit_space_data.

Usage

MTA(unit_space_data, includes_transformed_data = FALSE)

Arguments

Value

MTA returns an object of S3 class "MTA". An object of class "MTA" is a list containing the following components:

References

Taguchi, G. & Kanetaka, T. (2002). Engineering Technical Development in MT System - Lecture on Applied Quality. Japanese Standards Association. (In Japanese)

Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.

See Also

calc_cofactor, general_MT, generates_normalization_function, and diagnosis.MT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_MTA <- MTA(unit_space_data = iris_versicolor,
                      includes_transformed_data = TRUE)

(unit_space_MTA$distance)

Function to generate a unit space for the Recognition-Taguchi (RT) method

Description

RT generates a unit space for the Recognition-Taguchi (RT) method. In general_MT, the inversed correlation matrix is used for A and the data are transformed by the function to be generated by generates_dimensionality_reduction_function based on unit_space_data. In the transformation, the p variables in unit_space_data are reduced into 2 synthetic variables.

Usage

RT(unit_space_data, includes_transformed_data = FALSE, ...)

Arguments

Value

RT returns an object of S3 class "RT". An object of class "RT" is a list containing the following components:

References

Taguchi, G. (2006). Objective Function and Generic Function (11). Journal of Quality Engineering Society, 14(2), 5-9. (In Japanese)

Huda, F., Kajiwara, I., Hosoya, N., & Kawamura, S. (2013). Bolt loosening analysis and diagnosis by non-contact laser excitation vibration tests. Mechanical systems and signal processing, 40(2), 589-604.

See Also

solve, general_MT, generates_dimensionality_reduction_function, and diagnosis.MT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_RT <- RT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE)

# The following "tol" is a parameter passed to the solve function.
unit_space_RT <- RT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE,
                    tol = 1e-9)

(unit_space_RT$distance)

Function to generate a prediction expression for the two-sided Taguchi (T1) method

Description

T1 generates a prediction expression for the two-sided Taguchi (T1) method. In general_T, the data are normalized by subtracting the mean and without scaling based on unit_space_data. The sample data should be divided into 2 datasets in advance. One is for the unit space and the other is for the signal space.

Usage

T1(unit_space_data, signal_space_data, subtracts_V_e = TRUE,
  includes_transformed_data = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Taguchi, G. (2006). Objective Function and Generic Function (12). Journal of Quality Engineering Society, 14(3), 5-9. (In Japanese)

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_T, generates_transformation_functions_T1, and forecasting.T1

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

model_T1 <- T1(unit_space_data = stackloss_center,
               signal_space_data = stackloss_signal,
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

(model_T1$M_hat)

Function to generate a prediction expression for the Ta method

Description

Ta generates a prediction expression for the Ta method. In general_T, the data are normalized by subtracting the mean and without scaling based on sample_data. The sample data are not divided into 2 datasets. All the sample data are used for both unit space and signal space.

Usage

Ta(sample_data, subtracts_V_e = TRUE, includes_transformed_data = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_T, generates_transformation_functions_T1, and forecasting.Ta

Examples

model_Ta <- Ta(sample_data = stackloss[-c(2, 12, 19), ],
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

(model_Ta$M_hat)

Function to generate a prediction expression for the Tb method

Description

Tb generates a prediction expression for the Tb method. In general_T, the data are normalized by subtracting the center and without scaling based on sample_data. The center is determined by the specific way for the Tb method. For details, please see generates_transformation_functions_Tb. All the sample data are used for both unit space and signal space.

Usage

Tb(sample_data, subtracts_V_e = TRUE, includes_transformed_data = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_T, generates_transformation_functions_Tb, and forecasting.Tb

Examples

model_Tb <- Tb(sample_data = stackloss[-c(2, 12, 19), ],
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

(model_Tb$M_hat)

Function to estimate M value (M hat) for a family of T methods.

Description

calc_M_hat estimates M values (M hat) for the T method.

Usage

calc_M_hat(X, beta_hat, eta_hat)

Arguments

Value

Vector with length n. Estimated M values (M hat).

See Also

general_T and general_forecasting.T

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

# The following settings are same as the T1 method.
model <- general_T(unit_space_data = stackloss_center,
                   signal_space_data = stackloss_signal,
                   generates_transform_functions =
                                       generates_transformation_functions_T1,
                   includes_transformed_data = TRUE)

modified_eta_hat <- model$eta_hat
modified_eta_hat[3] <- 0

(modified_M_hat <- calc_M_hat(model$X, model$beta_hat, modified_eta_hat))

Function to calculate a cofactor matrix

Description

calc_cofactor calculates a cofactor matrix.

Usage

calc_cofactor(data)

Arguments

Value

calc_cofactor returns a cofactor matrix of size p x p.

See Also

MTA

Examples

# 40 data for versicolor in the iris dataset                            
iris_versicolor <- iris[61:100, -5] 
                            
calc_cofactor(cov(iris_versicolor))
 

Function to calculate overall prediction eta for the T method

Description

calc_M_hat calculates the overall prediction eta for the T method.

Usage

calc_overall_predicton_eta(M, M_hat, subtracts_V_e = TRUE)

Arguments

Value

Numeric. Overall prediction eta which is used to measure the estimation accuracy.

See Also

general_T and general_forecasting.T

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

# The following settings are same as the T1 method.
model <- general_T(unit_space_data = stackloss_center,
                   signal_space_data = stackloss_signal,
                   generates_transform_functions =
                                       generates_transformation_functions_T1,
                   subtracts_V_e = TRUE,
                   includes_transformed_data = TRUE)

modified_eta_hat <- model$eta_hat
modified_eta_hat[3] <- 0

modified_M_hat <- calc_M_hat(model$X, model$beta_hat, modified_eta_hat)

(modified_overall_predicton_eta <-
                            calc_overall_predicton_eta(model$M,
                                                       modified_M_hat,
                                                       subtracts_V_e = TRUE))

Function to predict a diagnosis for a family of Mahalanobis-Taguchi (MT) methods

Description

diagnosis is a generic function. For details, see diagnosis.MT, diagnosis.MTA, diagnosis.RT or general_diagnosis.MT.

Usage

diagnosis(unit_space, newdata, threshold, includes_transformed_newdata)

Arguments

Value

A list containing the following components is returned.

See Also

diagnosis.MT, diagnosis.MTA, and diagnosis.RT

Diagnosis method for the Mahalanobis-Taguchi (MT) method

Description

diagnosis.MT (via diagnosis) calculates the mahalanobis distance based on the unit space generated by MT or generates_unit_space(..., method = "MT") and classifies each sample into positive (TRUE) or negative (FALSE) by comparing the values with the set threshold value.

Usage

## S3 method for class 'MT'
diagnosis(unit_space, newdata, threshold = 4,
  includes_transformed_newdata = FALSE)

Arguments

Value

diagnosis.MT (via diagnosis) returns a list containing the following components:

References

Taguchi, G. (1995). Pattern Recognition and Quality Engineering (1). Journal of Quality Engineering Society, 3(2), 2-5. (In Japanese)

Taguchi, G., Wu, Y., & Chodhury, S. (2000). Mahalanobis-Taguchi System. McGraw-Hill Professional.

Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.

Woodall, W. H., Koudelik, R., Tsui, K. L., Kim, S. B., Stoumbos, Z. G., & Carvounis, C. P. (2003). A review and analysis of the Mahalanobis-Taguchi system. Technometrics, 45(1), 1-15.

See Also

general_diagnosis.MT and MT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_MT <- MT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE)

# 10 data for each kind (setosa, versicolor, virginica) in the iris dataset
iris_test <- iris[c(1:10, 51:60, 101:111), -5]

diagnosis_MT <- diagnosis(unit_space = unit_space_MT,
                          newdata = iris_test,
                          threshold = 4,
                          includes_transformed_newdata = TRUE)

(diagnosis_MT$distance)
(diagnosis_MT$le_threshold)

Diagnosis method for the Mahalanobis-Taguchi Adjoint (MTA) method

Description

diagnosis.MTA (via diagnosis) calculates the distance based on the unit space generated by MTA or generates_unit_space(..., method = "MTA") and classifies each sample into positive (TRUE) or negative (FALSE) by comparing the values with the set threshold value.

Usage

## S3 method for class 'MTA'
diagnosis(unit_space, newdata, threshold,
  includes_transformed_newdata = FALSE)

Arguments

Value

diagnosis.MTA (via diagnosis) returns a list containing the following components:

References

Taguchi, G. & Kanetaka, T. (2002). Engineering Technical Development in MT System - Lecture on Applied Quality. Japanese Standards Association. (In Japanese)

Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.

See Also

general_diagnosis.MT and MTA

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_MTA <- MTA(unit_space_data = iris_versicolor,
                      includes_transformed_data = TRUE)

# 10 data for each kind (setosa, versicolor, virginica) in the iris dataset
iris_test <- iris[c(1:10, 51:60, 101:111), -5]

diagnosis_MTA <- diagnosis(unit_space = unit_space_MTA,
                           newdata = iris_test,
                           threshold = 0.5,
                           includes_transformed_newdata = TRUE)

(diagnosis_MTA$distance)
(diagnosis_MTA$le_threshold)

Diagnosis method for the Recognition-Taguchi (RT) method

Description

diagnosis.RT (via diagnosis) calculates the distance based on the unit space generated by RT or generates_unit_space(..., method = "RT") and classifies each sample into positive (TRUE) or negative (FALSE) by comparing the values with the set threshold value.

Usage

## S3 method for class 'RT'
diagnosis(unit_space, newdata, threshold,
  includes_transformed_newdata = FALSE)

Arguments

Value

diagnosis.RT (via diagnosis) returns a list containing the following components:

References

Taguchi, G. (2006). Objective Function and Generic Function (11). Journal of Quality Engineering Society, 14(2), 5-9. (In Japanese)

Huda, F., Kajiwara, I., Hosoya, N., & Kawamura, S. (2013). Bolt loosening analysis and diagnosis by non-contact laser excitation vibration tests. Mechanical systems and signal processing, 40(2), 589-604.

See Also

general_diagnosis.MT and RT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

unit_space_RT <- RT(unit_space_data = iris_versicolor,
                    includes_transformed_data = TRUE)

# 10 data for each kind (setosa, versicolor, virginica) in the iris dataset
iris_test <- iris[c(1:10, 51:60, 101:111), -5]

diagnosis_RT <- diagnosis(unit_space = unit_space_RT,
                          newdata = iris_test,
                          threshold = 0.2,
                          includes_transformed_newdata = TRUE)

(diagnosis_RT$distance)
(diagnosis_RT$le_threshold)

Function to predict a forecasting for a family of Taguchi (T) methods

Description

forecasting is a generic function. For details, see forecasting.T1, forecasting.Ta, forecasting.Tb or general_forecasting.T.

Usage

forecasting(model, newdata, includes_transformed_newdata)

Arguments

Value

A list containing the following components is returned.

See Also

forecasting.T1, forecasting.Ta, and forecasting.Tb

Forecasting method for the T1 method

Description

forecasting.T1 (via forecasting) estimates the dependent values based on the T1 model.

Usage

## S3 method for class 'T1'
forecasting(model, newdata, includes_transformed_newdata = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Taguchi, G. (2006). Objective Function and Generic Function (12). Journal of Quality Engineering Society, 14(3), 5-9. (In Japanese)

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_forecasting.T and T1

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

model_T1 <- T1(unit_space_data = stackloss_center,
               signal_space_data = stackloss_signal,
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

# The following test samples are chosen casually.
stackloss_test <- stackloss[c(2, 12, 19), -4]

forecasting_T1 <- forecasting(model = model_T1,
                              newdata = stackloss_test,
                              includes_transformed_newdata = TRUE)

(forecasting_T1$y_hat) # Estimated values
(stackloss[c(2, 12, 19), 4]) # True values

Forecasting method for the Ta method

Description

forecasting.Ta (via forecasting) estimates the dependent values based on the Ta model.

Usage

## S3 method for class 'Ta'
forecasting(model, newdata, includes_transformed_newdata = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_forecasting.T and Ta

Examples

model_Ta <- Ta(sample_data = stackloss[-c(2, 12, 19), ],
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

forecasting_Ta <- forecasting(model = model_Ta,
                              newdata = stackloss[c(2, 12, 19), -4],
                              includes_transformed_newdata = TRUE)

(forecasting_Ta$y_hat) # Estimated values
(stackloss[c(2, 12, 19), 4]) # True values

Forecasting method for the Tb method

Description

forecasting.Tb (via forecasting) estimates the dependent values based on the Tb model.

Usage

## S3 method for class 'Tb'
forecasting(model, newdata, includes_transformed_newdata = FALSE)

Arguments

Value

A list containing the following components is returned.

References

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_forecasting.T and Tb

Examples

model_Tb <- Tb(sample_data = stackloss[-c(2, 12, 19), ],
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

forecasting_Tb <- forecasting(model = model_Tb,
                              newdata = stackloss[c(2, 12, 19), -4],
                              includes_transformed_newdata = TRUE)

(forecasting_Tb$y_hat) # Estimated values
(stackloss[c(2, 12, 19), 4]) # True values

General function to generate a unit space for a family of Mahalanobis-Taguchi (MT) methods

Description

general_MT is a (higher-order) general function that generates a unit space for a family of Mahalanobis-Taguchi (MT) methods. Each MT method can be implemented by setting the parameters of this function appropriately.

Usage

general_MT(unit_space_data, calc_A, generates_transform_function,
  includes_transformed_data = FALSE)

Arguments

Value

A list containing the following components is returned.

See Also

MT, MTA and RT

Examples

# 40 data for versicolor in the iris dataset                            
iris_versicolor <- iris[61:100, -5] 

# The following settings are same as the MT method.                          
unit_space <- general_MT(unit_space_data = iris_versicolor, 
                         generates_transform_function = 
                                            generates_normalization_function,
                         calc_A = function(x) solve(cor(x)),  
                         includes_transformed_data = TRUE)
                         
(unit_space$distance)

General function to generate a prediction expression for a family of Taguchi (T) methods

Description

general_T is a (higher-order) general function that generates a prediction expression for a family of Taguchi (T) methods. Each T method can be implemented by setting the parameters of this function appropriately.

Usage

general_T(unit_space_data, signal_space_data, generates_transform_functions,
  subtracts_V_e = TRUE, includes_transformed_data = FALSE)

Arguments

Value

A list containing the following components is returned.

See Also

T1, Ta, and Tb

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

# The following settings are same as the T1 method.
model <- general_T(unit_space_data = stackloss_center,
                   signal_space_data = stackloss_signal,
                   generates_transform_functions =
                                       generates_transformation_functions_T1,
                   subtracts_V_e = TRUE,
                   includes_transformed_data = TRUE)

(model$M_hat)

General function to implement a diagnosis method for a family of Mahalanobis-Taguchi (MT) methods

Description

general_diagnosis.MT is the general function that implements a diagnosis method for a family of Mahalanobis-Taguchi (MT) methods. Each diagnosis method of a family of MT methods can be implemented by setting the parameters of this function appropriately.

Usage

general_diagnosis.MT(unit_space, newdata, threshold,
  includes_transformed_newdata = FALSE)

Arguments

Value

A list containing the following components is returned.

See Also

diagnosis.MT, diagnosis.MTA, and diagnosis.RT

Examples

                          
# 40 data for versicolor in the iris dataset                            
iris_versicolor <- iris[61:100, -5] 

# The following settings are same as the MT method.                          
unit_space <- general_MT(unit_space_data = iris_versicolor, 
                         generates_transform_function = 
                                            generates_normalization_function,
                         calc_A = function(x) solve(cor(x)),  
                         includes_transformed_data = TRUE)

# 10 data for each kind (setosa, versicolor, virginica) in the iris dataset                         
iris_test <- iris[c(1:10, 51:60, 101:111), -5]
                         
diagnosis <- general_diagnosis.MT(unit_space = unit_space, 
                                  newdata = iris_test, 
                                  threshold = 4,
                                  includes_transformed_newdata = TRUE)
                              
(diagnosis$distance)
(diagnosis$le_threshold)                          

General function to implement a forecasting method for a family of Taguchi (T) methods

Description

general_forecasting.T is the general function that implements a forecasting method for a family of Taguchi (T) methods. Each forecasting method of a family of T methods can be implemented by setting the parameters of this function appropriately.

Usage

general_forecasting.T(model, newdata, includes_transformed_newdata = FALSE)

Arguments

Value

A list containing the following components is returned.

See Also

forecasting.T1, forecasting.Ta, and forecasting.Tb

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

# The following settings are same as the T1 method.
model <- general_T(unit_space_data = stackloss_center,
                   signal_space_data = stackloss_signal,
                   generates_transform_functions =
                                       generates_transformation_functions_T1,
                   subtracts_V_e = TRUE,
                   includes_transformed_data = TRUE)

# The following test samples are chosen casually.
stackloss_test <- stackloss[c(2, 12, 19), -4]

forecasting <- general_forecasting.T(model = model,
                                     newdata = stackloss_test,
                                     includes_transformed_newdata = TRUE)

(forecasting$y_hat) # Estimated values
(stackloss[c(2, 12, 19), 4]) # True values

Function to generate a data transformation function for the Recognition-Taguchi (RT) method

Description

generates_dimensionality_reduction_function returns the data transformation function for the Recognition-Taguchi (RT) method based on the unit_space_data. The function reduces the dimensionality of data into 2 synthetic variables.

Usage

generates_dimensionality_reduction_function(unit_space_data)

Arguments

Value

Function is returned which takes an n x p matrix as an (only) argument and returns a dimensionality-reduced n x 2 data frame with named columns; Y_1 and Y_2.

References

Taguchi, G. (2006). Objective Function and Generic Function (11). Journal of Quality Engineering Society, 14(2), 5-9. (In Japanese)

Huda, F., Kajiwara, I., Hosoya, N., & Kawamura, S. (2013). Bolt loosening analysis and diagnosis by non-contact laser excitation vibration tests. Mechanical systems and signal processing, 40(2), 589-604.

See Also

RT

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

reduces_dimensionality <-
                 generates_dimensionality_reduction_function(iris_versicolor)

is.function(reduces_dimensionality) # TRUE

Wrapper function to generate a model for a family of Taguchi (T) methods

Description

generates_model generates a model for a family of Taguchi (MT) methods. The model of T1 method, Ta method or the Tb method can be generated by passing a method name (character) into a parameter method.

Usage

generates_model(unit_space_data, signal_space_data, sample_data,
  method = c("T1", "Ta", "Tb"), subtracts_V_e = TRUE,
  includes_transformed_data = FALSE)

Arguments

Value

A returned object depends on the selected method. See T1, Ta or Tb.

See Also

T1, Ta, Tb

Examples

# The value of the dependent variable of the following samples mediates
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ]

# The following samples are data other than the unit space data and the test
# data.
stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ]

# The following test samples are chosen casually.
stackloss_test <- stackloss[c(2, 12, 19), -4]

# T1 method
model_T1 <- generates_model(unit_space_data = stackloss_center,
                            signal_space_data = stackloss_signal,
                            method = "T1",
                            subtracts_V_e = TRUE)

forecasting_T1 <- forecasting(model = model_T1,
                              newdata = stackloss_test)

(forecasting_T1$y_hat)

# Ta method
model_Ta <- generates_model(sample_data =
                                   rbind(stackloss_center, stackloss_signal),
                            method = "Ta",
                            subtracts_V_e = TRUE)

forecasting_Ta <- forecasting(model = model_Ta,
                              newdata = stackloss_test)

(forecasting_Ta$y_hat)

# Tb method
model_Tb <- generates_model(sample_data =
                                   rbind(stackloss_center, stackloss_signal),
                            method = "Tb",
                            subtracts_V_e = TRUE)

forecasting_Tb <- forecasting(model = model_Tb,
                              newdata = stackloss_test)

(forecasting_Tb$y_hat)

Function to generate the data normalization function

Description

generates_normalization_function returns the data normalization function. The data normalization function is generated based on unit_space_data.

Usage

generates_normalization_function(unit_space_data, unit_space_center,
  unit_space_scale, is_scaled = TRUE)

Arguments

Value

Function is returned which takes an n x p matrix as an (only) argument and returns a normalized n x p matrix. The normalization is conducted based on unit_space_data.

See Also

MT and MTA

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

normalizes_data <- generates_normalization_function(iris_versicolor)

is.function(normalizes_data) # TRUE

Function to generate data transformation functions for the T1 methods

Description

generates_transformation_functions_T1 is the argument for the parameter generates_transform_functions in genera_T, which is used in the T1 method. In addtion, the Ta method also uses this function for the argument.

Usage

generates_transformation_functions_T1(unit_space_data)

Arguments

Value

generates_transformation_functions_T1 returns a list containing three functions. For the first component, the data transformation function for independent variables is a function that subtracts the mean of each independent variable. For the second component, the data transformation function for a dependent variable is a function that subtracts the mean of a dependent variable. For the third component, the inverse function of the data transformation function for a dependent variable is a function that adds the mean of a dependent variable. The mean used is the mean of the unit_space_data.

See Also

T1 and Ta

Examples

   
# The value of the dependent variable of the following samples mediates  
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ] 
      
tmp <- generates_transformation_functions_T1(stackloss_center)
mean_subtraction_function <- tmp[[1]]
subtracts_M_0 <- tmp[[2]]
adds_M_0 <- tmp[[3]] 

is.function(mean_subtraction_function) # TRUE
is.function(subtracts_M_0) # TRUE
is.function(adds_M_0) # TRUE

Function to generate data transformation functions for the Tb methods

Description

generates_transformation_functions_Tb is the argument for the parameter generates_transform_functions in genera_T, which is used in the Tb method.

Usage

generates_transformation_functions_Tb(sample_data)

Arguments

Value

generates_transformation_functions_Tb returns a list containing three functions. For the first component, the data transformation function for independent variables is a function that subtracts the center of each independent variable. The center is determined in a specific manner for the Tb method. The center consists of each sample value which maximizes the signal-to-noise ratio (S/N) per independent variable. The values are determined independently so that different samples may be selected for different variables. For the second component, the data transformation function for a dependent variable is a function that subtracts the dependent variable of the sample which maximizes the S/N per independent variable. For the third component, the inverse function of the data transformation function for a dependent variable is a function that adds the weighted mean of a dependent variable. The weighted mean is calculated based on the S/N and the frequency of being selected in independent variables.

References

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

Tb

Examples

# The value of the dependent variable of the following samples mediates  
# in the stackloss dataset.
stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ] 
    
tmp <- generates_transformation_functions_Tb(stackloss_center)
center_subtraction_function <- tmp[[1]]
subtracts_ys <- tmp[[2]]
adds_M_0 <- tmp[[3]] 

is.function(center_subtraction_function) # TRUE
is.function(subtracts_ys) # TRUE
is.function(adds_M_0) # TRUE

Wrapper function to generate a unit space for a family of Mahalanobis-Taguchi (MT) methods

Description

generates_unit_space generates a unit space for a family of Mahalanobis-Taguchi (MT) methods. The unit space of MT method, MTA method or RT method can be generated by passing a method name (character) into a parameter method.

Usage

generates_unit_space(unit_space_data, method = c("MT", "MTA", "RT"),
  includes_transformed_data = FALSE, ...)

Arguments

Value

A returned object depends on the selected method. See MT, MTA or RT.

See Also

MT, MTA, RT, and solve

Examples

# 40 data for versicolor in the iris dataset
iris_versicolor <- iris[61:100, -5]

# 10 data for each kind (setosa, versicolor, virginica) in the iris dataset
iris_test <- iris[c(1:10, 51:60, 101:111), -5]

# MT method
unit_space_MT <- generates_unit_space(unit_space_data = iris_versicolor,
                                      method = "MT")

diagnosis_MT <- diagnosis(unit_space = unit_space_MT,
                          newdata = iris_test,
                          threshold = 4)

(diagnosis_MT$distance)
(diagnosis_MT$le_threshold)

# MTA method
unit_space_MTA <- generates_unit_space(unit_space_data = iris_versicolor,
                                       method = "MTA")

diagnosis_MTA <- diagnosis(unit_space = unit_space_MTA,
                           newdata = iris_test,
                           threshold = 0.5)

(diagnosis_MTA$distance)
(diagnosis_MTA$le_threshold)

# RT method
unit_space_RT <- generates_unit_space(unit_space_data = iris_versicolor,
                                      method = "RT")

diagnosis_RT <- diagnosis(unit_space = unit_space_RT,
                          newdata = iris_test,
                          threshold = 0.2)

(diagnosis_RT$distance)
(diagnosis_RT$le_threshold)