Grouping index: A new quantitative criterion for goodness of block-diagonal forms in group technology

Group technology requires the block-diagonalisation of the machine-component incidence matrix as an essential first step towards implementation. The goodness of such block diagonal forms is usually evaluated by two measures known as grouping efficiency and grouping efficacy. The drawbacks of grouping efficiency have been exposed already in earlier studies. This study critically examines grouping efficacy and identifies its limitations. A new measure, grouping index, which overcomes the limitations of the earlier measures, is developed in this paper. The desirable properties of the existing measures have been retained. The properties of the proposed measure are analysed and compared with those of grouping efficacy for well-structured and ill-structured data sets.