equiBSPD (version 0.1.0)

equivalent_BSPD: Construct Equivalent Estimation Balanced Split Plot Designs

Description

The equivalent_BSPD() function constructs equivalent estimation balanced split plot designs for different experimental setups. The function takes inputs related to the number and levels of Whole Plot Factor(s) and Sub Plot Factor(s), the total number of experimental runs, and the bounds for a trend factor. Factor levels can be represented as integers, for example, -1 for low, 0 for medium, and 1 for high. A single whole plot factor or sub plot factor with levels 1 and -1 or 1,0 and -1 should be entered as list(c(1, -1)),list(c(1,0,-1)). If there are two whole plot factors or sub plot factors each with two levels, the input should be entered as list(c(1, -1), c(1, -1)), similarly for more number of factors. The trend factor value lies between 0 to 1. Higher the values, lesser the influence of trend effects on the run order. The function then generates equivalent estimation balanced split plot designs and evaluates them based on D-optimality and Dt-optimality criteria. Additionally, it explores the impact of trend effects and identifies the designs that maximize the trend factor value.

Usage

equivalent_BSPD(Number_of_whole_plot_factors, Whole_Plot_factors_levels,
                 Number_of_sub_plot_factors, Sub_Plot_factors_levels,
                 Total_number_of_runs_required, lower_bound, upper_bound)

Value

Returns a list with the following components:

Total_equivalent_estimation_designs

Total number of equivalent estimation balanced split plot designs for the given inputs.

Equivalent_Estimation_Designs

All the equivalent estimation balanced split plot designs for the given inputs.

All_equivalent_estimation_designs_with_D_Dt_Trend_Factor

All the equivalent estimation balanced split plot designs with D, Dt, and Trend Factor value for the given inputs.

Max_D_value

Maximum D-value within the generated equivalent estimation balanced split plot designs.

D_optimal_designs

Designs with the Maximum D-value within the generated equivalent estimation balanced split plot designs.

Max_Dt_value

Maximum Dt-value within the generated equivalent estimation balanced split plot designs.

Dt_optimal_designs

Designs with the Maximum Dt-value within the generated equivalent estimation balanced split plot designs.

Max_Trend_factor_value

Maximum Trend Factor Value for the generated equivalent estimation balanced split plot designs.

Number_of_Designs_Max_Trend_Factor

Number of equivalent estimation balanced split plot designs with Maximum Trend Factor value.

Equivalent_Estimation_designs_in_trend_factor_range

Equivalent estimation balanced split plot designs within the specified range of trend factor.

Arguments

Number_of_whole_plot_factors

Number of Whole Plot Factor(s)

Whole_Plot_factors_levels

Levels of Whole Plot Factor(s)

Number_of_sub_plot_factors

Number of Sub Plot Factor(s)

Sub_Plot_factors_levels

Levels of Sub Plot Factor(s)

Total_number_of_runs_required

Total Number of Runs Required

lower_bound

Lower bound of Trend Factor Value

upper_bound

Upper bound of Trend Factor Value

References

Bijoy Chanda, Arpan Bhowmik, Cini Varghese, Seema Jaggi, Anindita Datta, Baidya Nath Mandal and Soumen Pal (2024). Incomplete equivalent estimation split plot designs. Journal of Community Mobilization and Sustainable Development, 19(2), 357-360.

Harrison Macharia and Peter Goos (2010). D-optimal and D-efficient equivalent-estimation second order split-plot designs. Journal of Quality Technology, 42(4), 358-372.

Lieven Tack and Martina Vandebroek (2001). (Dt,C)-optimal run orders. Journal of Statistical Planning and Inference, 98, 293-310.

Examples

# One whole plot factor at two levels and one sub plot factor at three levels in four runs
Result1 <- equivalent_BSPD(1, list(c(1, -1)), 1, list(c(1,0,-1)), 4, 0.1, 0.9)

# One whole plot factor at three levels and one sub plot factor at three levels in six runs
Result2 <- equivalent_BSPD(1, list(c(1, 0, -1)), 1, list(c(1, 0, -1)), 6, 0.5, 0.95)

# One whole plot factor at three levels and two sub plot factors each at two levels in six runs
Result3 <- equivalent_BSPD(1, list(c(1, 0, -1)), 2, list(c(1, -1), c(1, -1)), 6, 0.6, 0.9)

# Accessing results
Result1$Total_equivalent_estimation_designs
Result1$Equivalent_Estimation_Designs
Result1$All_equivalent_estimation_designs_with_D_Dt_Trend_Factor
Result1$Max_D_value
Result1$D_optimal_designs
Result1$Max_Dt_value
Result1$Dt_optimal_designs
Result1$Max_Trend_factor_value
Result1$Number_of_Designs_Max_Trend_Factor
Result1$Equivalent_Estimation_designs_in_trend_factor_range