# (692b) Statistical Algorithm for Sustainability Measurement and Decision Making

Authors:
VRI-CUSTOM
Texas A&M Engineering Experiment Station
National Risk Management Research Lab, US EPA

Statistical Algorithm for Sustainability Measurement and Decision Making

Rajib Mukherjee1, Debalina Sengupta2, Subhas K Sikdar3

1. Vishwamitra Research Institute, Crystal Lake, IL
2. Texas A&M University, College Station, TX
3. NRMRL, US EPA, Cincinnati, OH

Abstract

Sustainability of process, product or supply chain is generally assessed with metrics or indicators that covers all three areas of sustainability: environmental, economic and societal. These indicators are not represented in any absolute scale. In fact there is no such thing as absolute sustainability. In order to assess sustainability of product, process or supply chain, we have to use a relative scale. To compare two or multiple competing systems in a relative scale, the systems may be assumed as points in a vector space and they are compared with reference to each other. In this case, each system will act as a vector and the indicators will act as the components of the vector. In case of multiple systems to be compared, it is convenient to create an artificial reference state and compare the competing systems with reference to the hypothetical state. The hypothetical reference state may be created in various ways. In some case, the reference state can be created with the minimum value of each and every components of the vector. In some other cases, it could be the average of the components. The origin of the vector space where all components are zero can also be used as a reference state. All these methods of finding the reference state has their own merits and demerits in evaluating the relative sustainability of the competing systems. Once a suitable reference state is identified for the competing systems, the actual comparison can be done using an aggregate method where all the indicators are aggregated into a single index.  Several alternative aggregate indices can be derived statistically from the indicator data.  In the simplest form, the aggregation can be performed using the geometric mean of the indicators. Other than normal geometric mean, aggregate indices based on Euclidean distance, Mahalonabis distance, Canberra metrics, vector norm have also been proposed by various researchers with varied applications. Aggregation of the indicators in any of the methods requires the vectors to be normalized. This is to retain the variability of the component of the vectors but reduce the variability among the components. Normalization can be performed in various ways. Each method of normalization has its own significance in the evaluation of the aggregate.

In this work we will show different ways of reference selection, normalization and aggregation of sustainability indices and make relative assessment of different methods with examples. We will present what can we learn about a system from an aggregate reading that we cannot learn by comparing individual indicator values. We will also present statistical methods of identifying which indicators are necessary and sufficient for sustainability evaluation of specific system. This in turn will also determine which indicators are insignificant or redundant.  Furthermore, we will also show the sensitivity of the system sustainability to changes in any one of the indicators and rank the indicators in order of their contribution to sustainability of the system. With our method of sustainability analysis with aggregated index and important indicator selection and their sensitivity, it would be easier to determine which indicators require attention in order to improve the product or process from sustainability viewpoint.