sensitivity analysis of transmission.pptx

detailed discussion on sensitivity analysis

1. Sensitivity analysis A  sensitivity analysis  is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions It is also known as the what – if analysis. It helps in analyzing how sensitive the output is, by the changes in one input while keeping the other inputs constant.

2. Principle Sensitivity analysis works on the simple principle:  Change the model and observe the behavior. The parameters that one needs to note while doing the above are : A) Experimental design:  It includes combination of parameters that are to be varied. This includes a check on which and how many parameters need to vary at a given point in time, assigning values (maximum and minimum levels) before the experiment, B ) What to vary : The different parameters that can be chosen to vary in the model could be:  a) the number of activities b) the objective in relation to the risk assumed and the profits expected c) technical parameters d) number of constraints and its limits C) What to observe : a) value of the decision variables b) value of the objective function between two strategies adopted

3. Measurement of sensitivity analysis Steps used to conduct sensitivity analysis: Firstly the output is defined; say V1 a input value for which the sensitivity is to be measured. All the other inputs of the model  are kept constant. Then the value of the output at a new value of the input (V2) while keeping other inputs constant is calculated. Find the percentage change in the output and the percentage change in the input. The sensitivity is calculated by dividing the percentage change in output by the percentage change in input.

4. Example Suppose that Y is the fuel consumption of a particular model of car. Suppose that the predictors are 1. X1 — the weight of the car (min-max: 1800-2200 kg) 2. X2 — the horse power ( min-max: 150-160 ) 3. X3 — the no. of cylinders (min-max: 3:5) Model equation Y= 0.25 + 0.05 X1 - 0.8 X2 + 0.01 X1 X3

5. Example Definition of a factor effect: The change in the mean response when the factor is changed from low to high.

6. Calculation of Effects: Main effect The effect of a factor is defined to be the change in the response Y for a change in the level of that factor. This is called a main effect. Effect of A

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8. Sumamry

9. Methods of Sensitivity Analysis There are different methods to carry out the sensitivity analysis: Modeling and simulation techniques Scenario management tools through Microsoft excel There are mainly two approaches to analyzing sensitivity: Local Sensitivity Analysis Global Sensitivity Analysis

10. various techniques widely applied include: Differential sensitivity analysis:  It is also referred to the direct method. It involves solving simple partial derivatives to temporal sensitivity analysis. Although this method is computationally efficient, solving equations is intensive task to handle. One at a time sensitivity measures:  It is the most fundamental method with partial differentiation, in which varying parameters values are taken one at a time. It is also called as local analysis as it is an indicator only for the addressed point estimates and not the entire distribution. Factorial Analysis:  It involves the selection of given number of samples for a specific parameter and then running the model for the combinations. The outcome is then used to carry out parameter sensitivity. Through the sensitivity index one can calculate the output % difference when one input parameter varies from minimum to maximum value. Correlation analysis  helps in defining the relation between independent and dependent variables. Regression analysis  is a comprehensive method used to get responses for complex models. Subjective sensitivity analysis:  In this method the individual parameters are analyzed. This is a subjective method, simple, qualitative and an easy method to rule out input parameters.

11. Search techniques- univariate/multivariate Univariate - One variable is analyzed at a time. Objective is to describe the variable. Example- How many students are graduating with “Analytics“ degree ? Bivariate - Two variables are analyzed together for any possible association or empirical relationship. Example- What is the correlation between “Gender” and graduation with “Analytics” degree ? Multivariate - More than two variables are analyzed together for any possible association or interactions. Example – What is correlation between “Gender”, “Country of Residence” and graduation with “ Analytics” degree? Any statistical modeling exercise such as Regression, Decision Tree, Clustering are multivariate in nature