Estimation & analysis the sensitivity of procedures partial and total productivity

Abstract

The Production index is described as a sufficient but inefficient measure in estimating productivity because it does not give an idea of the quantity and value of the inputs that contributed to the formation of this production, which include (labour, materials, machines, equipment, services, and capital). The production quantity may be large, and the inputs are also large; therefore, the production index is inefficient in explaining the facility's or organisation's productivity. Meanwhile, the productivity index (whether total or partial) links outputs (x) and inputs (y) (outputs & inputs).
Total productivity (P) = outputs/inputs, while partial productivity (Pi) = outputs/one of the inputs.
Total productivity (P) is not equal to the sum of partial productivity of the resources involved in the production process. In other words, total productivity is not equal to the sum of all (labour productivity, materials productivity, machinery, equipment, services productivity, and capital productivity). The researcher may sometimes face difficulties obtaining information regarding inputs or outputs. Or both, either because of its confidentiality or because the establishment does not want to give such information, but rather it suffices with giving the partial productivity of the contributing elements (inputs) in creating production.
The research aims to address this situation by finding a new method through which total productivity can be reached through partial productivity of factors contributing to production without using outputs or inputs, using the inverse of productivity, as follows: