Rank Order Clustering Algorithm

Starting with the initial part$-$machine incidence matrix, the algorithm consists of the following steps:

$1.$ In each row of the matrix, read the series of $1$ s and $0$ s $($blank entries $\backslash (=0\backslash$mathrm$\{$~s$\}\backslash ))$ from left to right as a binary number. Rank the rows in order of decreasing value. In case of a tie, rank the rows in the same order as they appear in the current matrix.

$2.$ Numbering from top to bottom, is the current order of rows the same as the rank order determined in the previous step? If yes, go to step $7.$ If no$,$ go to the following step.

$3.$ Reorder the rows in the part$-$machine incidence matrix by listing them in decreasing rank order, starting from the top.

$4.$ In each column of the matrix, read the series of $1$ s and $0$ s $($blank entries$=0$s$)$ from top to bottom as a binary number. Rank the columns in order of decreasing value. In case of a tie, rank the columns in the same order as they appear in the current matrix.

$5.$ Numbering from left to right, is the current order of columns the same as the rank order determined in the previous step? If yes, go to step $7.$ If no$,$ go to the following step.

$6.$ Reorder the columns in the part$-$machine incidence matrix by listing them in decreasing rank order, starting with the left column. Go to step $1.$

Binary values