This paper discusses methods for computing sensitivity indices in sensitivity analysis, particularly for models with uncorrelated input factors. The author, Andrea Saltelli, presents two main theorems that allow for more efficient computation of sensitivity indices using fewer model evaluations. The first theorem reduces the computational cost from \( n(2k+2) \) to \( n(k+2) \), where \( n \) is the sample size and \( k \) is the number of input factors. This reduction is achieved by leveraging additional sampling matrices and re-sampling techniques. The second theorem extends this approach to obtain double estimates of sensitivity indices, providing more robust and accurate results. The paper also discusses the application of these methods to a complex model (PMOD) used in petroleum generation modeling, demonstrating their effectiveness in identifying influential factors and their interactions. The methods are particularly useful for computationally expensive models, helping to overcome the "curse of dimensionality."This paper discusses methods for computing sensitivity indices in sensitivity analysis, particularly for models with uncorrelated input factors. The author, Andrea Saltelli, presents two main theorems that allow for more efficient computation of sensitivity indices using fewer model evaluations. The first theorem reduces the computational cost from \( n(2k+2) \) to \( n(k+2) \), where \( n \) is the sample size and \( k \) is the number of input factors. This reduction is achieved by leveraging additional sampling matrices and re-sampling techniques. The second theorem extends this approach to obtain double estimates of sensitivity indices, providing more robust and accurate results. The paper also discusses the application of these methods to a complex model (PMOD) used in petroleum generation modeling, demonstrating their effectiveness in identifying influential factors and their interactions. The methods are particularly useful for computationally expensive models, helping to overcome the "curse of dimensionality."