RCD: Program for Constructing Non-Resolvable Row-column Designs

  1. Introduction
  2. Using RCD
  3. Output
  4. Examples
  5. References

Introduction

A (non-resolvable) row-column design (RCD) is an arrangement of v treatments set out in kxb array such that each treatment is replicated r times (vr=kb). We say this RCD is of size (v,k,b). A recommended reference on the subject is Chapter 5 of John & Williams (1995).

RCD is a Gendex module for constructing optimal or near-optimal row-column designs. The approach adopted by RCD is to permute the treatments within the blocks of an optimal or near-optimal block design used as the column component of the RCD. The optimality criterion and the algorithm used in RCD are discussed in Nguyen (1997).

Using RCD

Let's assume all Gendex class files are in the directory c:\gendex and suppose you want to construct an RCD of size (r,k,s)=(2,3,3). The following is the file bib.txt in the working directory which contains an IBD of size (v,k,r)=(9,3,2) with blocks as columns:

5     6     3     4     8     5
0     7     7     8     1     1
4     0     2     3     6     2

At the working directory, type the following command at the Command Prompt (case is important):

java -cp c:\gendex rcd

The RCD window will pop up. Enter bib.txt at the File text field, the RCD window will become:

Click START, the OUTPUT window (not shown) displaying the derived RCD will pop up and the RCD window will become:

Note that the START button has been changed to the STOP one. If you close the pop-up window, the STOP button will become a RESET one. If you click this RESET button, the output will disappear and you can now start a new design problem. Also note that the default random seed is the one obtained from the system clock and the default number of tries is 100. You can change these default values if you wish to.

Output

The result of the best try is displayed in the OUTPUT window and is also saved in the file rcd.htm in the working directory. This file can be read by a browser such as IE or Firefox. Information for this try includes:

  1. Try number;
  2. The random seed used;
  3. The number of iterations;
  4. The objective function f.
  5. The row, column and row-column efficiency E of the constructed design and the ratio E/U where U is the upper bound of an RCD of size (v,k,b). The program automatically stops if this ratio reaches 1.
  6. The distribution of the concurrences of this design;
  7. The design plan;
  8. The time in seconds RCD used to construct the above design.

An additional output of an RCD session is the file form.htm. The following is the content of file form.htm of the above example:

Row   Col   Treat
1     1     4
1     2     0
1     3     2
1     4     3
1     5     6
1     6     1
2     1     5
2     2     6
2     3     7
2     4     4
2     5     8
2     6     2
3     1     0
3     2     7
3     3     3
3     4     8
3     5     1
3     6     5

Examples

  1. An RCD of size (v,k,b)=(4,6,6) (http://designcomputing.net/gendex/rcd/r1.html).
  2. An RCD of size (v,k,b)=(10,5,6) (http://designcomputing.net/gendex/rcd/r2.html).
  3. An RCD of size (v,k,b)=(8,4,4) (http://designcomputing.net/gendex/rcd/r3.html).
  4. An RCD of size (v,k,b)=(9,3,6) (http://designcomputing.net/gendex/rcd/r4.html).
  5. An RCD of size (v,k,b)=(12,4,6) (http://designcomputing.net/gendex/rcd/r5.html).
  6. An RCD of size (v,k,b)=(12,4,9) (http://designcomputing.net/gendex/rcd/r6.html).
  7. An RCD of size (v,k,b)=(16,4,12) (http://designcomputing.net/gendex/rcd/r7.html).
  8. An RCD of size (v,k,b)=(6,4,9) (http://designcomputing.net/gendex/rcd/r8.html).
  9. An RCD of size (v,k,b)=(9,6,6) (http://designcomputing.net/gendex/rcd/r9.html).
  10. An RCD of size (v,k,b)=(15,6,10) (http://designcomputing.net/gendex/rcd/r10.html).

Notes:

References

John, J.A. & Williams E.R. (1987) Cyclic designs and computer-generated designs. New York: Chapman & Hall.
Nguyen, N-K (1997) Construction of optimal row-column designs by computer. Computing Science & Statistics 28, 471-475.

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