Overview of the min2HalfFFD R Package

Introduction

Welcome to min2HalfFFD, an intuitive and powerful R package designed for statisticians, experimental scientists, and researchers working with factorial experiments. This package generates all possible minimally changed two-level half-fractional factorial designs along with various statistical criteria to measure the performance of these designs through a simple, user-friendly shiny app interface. It includes the function minimal.2halfFFD(), which launches the interactive application where you can explore, compare, and select suitable designs. This vignette provides a quick overview of how to use the package and its shiny app interface.

What are Minimally Changed Factorial and Fractional Factorial Designs?

In many agricultural, post-harvest, engineering, industrial, and processing experiments, changing factor levels between runs can be physically difficult, time-consuming, or costly. Such experiments often involve hard-to-change factors or require a normalization period before stable operating conditions are reached. Because of these constraints, experimenters prefer run orders that keep the number of factor level changes to a minimum.

Minimally changed factorial and fractional factorial designs are constructed to address this practical need. They arrange the sequence of runs so that total factor changes are minimized, helping reduce operational effort, conserve resources, and lower the overall cost of experimentation.

This idea applies to both full factorial designs and fractional factorial designs. When a full factorial design contains too many treatment combinations to be feasible, a fractional factorial design—a carefully selected subset of the full design—offers a practical alternative.

Minimally Changed Run Sequences in Half-Replicate of $2^k$ Fractional Factorial Designs

In Design of Experiments (DOE) theory, the two levels of a factor can be represented as integers, e.g., –1 for the low level and 1 for the high level. A half replicate of a $2^k$ Factorial Designs ($\tfrac{1}{2} , 2^{k}$) with the minimum possible number of changes can be constructed by first developing a $2^{,k-1}$ factorial with minimal level changes in its run orders, and then generating a new factor by taking the product of all the 𝑘−1 factors in the constructed $2^{,k-1}$ design with minimally changed run orders, where 𝑘 is the number of factors.

Statistical Criteria for Evaluating Minimally Changed Designs

Minimally changed designs can be compared and assessed using several quantitative criteria. These measures help identify designs that not only reduce factor level changes but also maintain desirable statistical properties for experimentation.

$\mathrm{D}$-optimality criterion: A $\mathrm{D}$-optimal design is obtained by maximizing the determinant of the information matrix, or equivalently, by minimizing the generalized variance

$\mathrm{D}_{t}$-optimality criterion: $\mathrm{D}_{t}$-optimality criterion is found by minimizing the generalized variance or equivalently maximizes the information in presence of trend effect

Trend Factor: The trend factor is defined as the ratio of the $\mathrm{D}_{t}$-value to the $\mathrm{D}$-value for a particular run order. For completely trend free design trend factor value will be 1 . However, if the trend factor value is 0, then the design is completely affected by time trend.

These three measures together help identify run orders that are not only minimally changed but also statistically efficient and robust to potential trend effects.

Using the min2HalfFFD Package

Install and Load the package

You can install min2HalfFFD from CRAN:

install.packages("min2HalfFFD")
# Load the package
library(min2HalfFFD)

Launch the Shiny app

The interactive shiny app is the easiest way to explore and inspect minimally changed designs.
To open it from an interactive R session use:

library(min2HalfFFD)
# Run the function
minimal.2halfFFD()

Exploring the Shiny Interface

Once you launch the Shiny app with minimal.2halfFFD(), the interface opens in your browser (or in the RStudio Viewer).
The layout is designed for clarity and ease of use.

1. Input Panel

On the left side, you will find the input controls:

• Enter Number of Factors
  Specify how many two-level factors your experiment has.
  The number must be greater than 2.

• Trend Factor Range
  Enter the acceptable range for the Trend Factor between 0 and 1.
  For example: lower = 0.56, upper = 0.65.
  The upper bound must be greater than the lower bound.

• Generate Button
  Click Generate to start the design generation process.

2. Result Display Panel

After clicking Generate, the right side of the app displays the results.
The dropdown selector “Select Result to Display” allows you to choose what to view:

• Total Change Displays the sum of per-factor level changes of a run order.

• Total Number of Minimally Changed Designs
  Displays total number of all the minimally changed two-level half-fractional factorial designs.

• All Minimally Changed Designs
  Shows all the minimally changed two-level half-fractional factorial designs.

• All Minimally Changed Designs with D, Dt, Trend Factor
  Presents designs with corresponding D, Dt and Trend Factor values.

• Maximum D Value
  Maximum D-value within the generated minimally changed designs.

• D-Optimal Designs
  Designs with the Maximum D-value within the generated minimally changed designs.

• Maximum Dt Value
  Maximum Dt-value within the generated minimally changed designs.

• Dt-Optimal Designs Designs with the Maximum Dt-value within the generated minimally changed designs.

• Maximum Trend Factor Displays the Maximum Trend Factor Value for the generated minimally changed designs.

• Number of Minimally Changed Designs with Maximum Trend Factor Value Shows Number of minimally changed designs with Maximum Trend Factor value

• Minimally Changed Designs in Trend Factor Range Shows Minimally changed designs within the specified range of trend factor

References

Bhowmik, A., Varghese, E., Jaggi, S., and Varghese, C. (2015).Factorial experiments with minimum changes in run sequences.Journal of the Indian Society of Agricultural Statistics, 69(3), 243–255.

Bhowmik, A., Varghese, E., Jaggi, S., and Varghese, C. (2017).Minimally changed run sequences in factorial experiments.Communications in Statistics – Theory and Methods, 46(15), 7444–7459.

Bhowmik, A., Varghese, E., Jaggi, S., and Varghese, C. (2020).On the generation of factorial designs with minimum level changes.Communications in Statistics – Simulation and Computation, 51(6), 3400–3409.

Chanda, B., Bhowmik, A., Jaggi, S., Varghese, E., Datta, A., Varghese, C.,Das Saha, N., Bhatia, A., and Chakrabarti, B. (2021). Minimal cost multifactor experiments for agricultural research involving hard-to-change factors.Indian Journal of Agricultural Sciences, 91(7), 97–100.

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