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

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.

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.