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Vishwadeep Khatri

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Sensitivity Analysis 


Sensitivity Analysis is a method used to quantify the impact of change in one or more input variables on the output variable. Its most common usage is in the financial sector in order to develop a financial model (predicting the outcome basis the inputs) and to optimize the model.


Root Cause Analysis (RCA)


Root Cause Analysis (RCA) - is a problem solving method which is used to identify the root causes for an issue or a problem. A cause is called a root cause if it is actionable and if actioned will prevent the recurrence of the issue. 5-Why, Fishbone Analysis and Affinity Diagrams are some of the common tools used in RCA.


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Prashanth Datta on 22nd March 2019.


Applause for all the respondents- Natwar Lal, Saounak L, Prashanth Datta, Arvindh Pradheep Shanmugam, Somsagar Karke, Tarun Gupta, Srinivas Sandepudi. 


Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.



Q. 144  How does Sensitivity Analysis relate with Root Cause Analysis?  



Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.


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As we have already seen and understood, Root Cause Analysis focuses on identification of all those independent variable X's (further narrowed to critical X's) deemed as input, which has an impact on the dependent output variable Y. In other words, identification of all causes which influences the effect.


In a Sensitivity Analysis, also referred to as "What-if" or "Simulation Analysis", we determine how the output-dependent variable (Y or effect) varies when each of the independent variable (X or causes) are varied under a predefined set of assumptions. Simply stating, how different values of each independent X, will have an impact on Y. 


Once we have the critical X's identified using the relevant Tools & Techniques of Root Cause Analysis, applying Sensitivity Analysis on these Critical X's will be extremely helpful to see how the focus metric Y, behaves by changing the values of each X under a set of predefined assumptions. This paves way to develop solutions in a more scientific method within the identified X's  and a combination of this approach across all input causes will help us with a more comprehensive solution that can be implemented during the Improve phase.

Let us now see an example.


I am running a small coffee shop and below are my financial workings as on date

  • Cost/Cup of Coffee - INR 12
  • Number of Cups of Coffee Sold per month - 4000
  • Operating Expense (incl. Rent, Salary, Milk, Sugar, Coffee power etc.,) = INR 40,000
  • Based on above workings my Monthly Income is INR 48,000 [12 per cup x 4000 cups per month].
  • My Profit after deducting the Operating Expense is INR 8,000 [Opex INR. 48,000 - Monthly Income 40,000].

I will now but a problem statement with a business case that I need to improve my Profits from this coffee shop


At an high level, if I want to put this in a mathematical format for my business case in Cause and Effect method Y=F(X), using Root Cause Analysis techniques, at an high level, we can say profits are influenced by price per cup, number of cups sold and the operating expenses.

  • Profits = f(Price per Cup, Number of Cups Sold, Operating Expense, ...)

I need to work on each of these levers either increase or decrease to improve my profits.

While at an high level, going by thumb rule, we always say to reduce the Opex and it in itself can lead to another root cause analysis on what we can vs what we cannot.


But looking at the other two levers of cost per cup and number of cups to be sold will form an interesting strategy to plan around and the Sensitivity Analysis will help me take a decision. With Sensitivity Analysis,  I can play around by increasing or decreasing the price or increasing or decreasing the number of cups sold and its impact on my profit.


As per the rules of Sensitivity Analysis, we make some assumptions and in this case we make an assumption that my Operating Expense will remain fairly at same price or allowed to go by not more than 10%. With this ground rule you can see the below table which helps you draw conclusion.  




I can now make some quick comparisons now. If I retain my current price of INR 12, but build strategies to increase sales to 5000 cups a month (increase in 1000 cups) I will make INR 20,000 profit vs my current profit of INR 8,000. Even an increase in Opex by 10% should still yield me INR 16,000 which is double my current scenario. Like wise if I want to retain the sale at 4000 cups and increase the price to INR 15 , I will have a similar story. 


In summary, with Sensitivity Analysis applied on Root Cause Analysis, it shows, how within each Inputs, you will have options to explore to arrive at a desired stable Output with Voice of Customer at crux. 

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Benchmark Six Sigma Expert View by Venugopal R


Sensitivity Analysis of “What-if” analysis is popularly used for financial studies to project the possible effect on any business outcome, with projected variations in the input factors that are expected to influence the outcome. It is a model built using the knowledge of current situation which is taken as a baseline and then by subjecting the inputs to assumed deviations from the base value, the effect on the outcome is estimated.


Though sensitivity analysis is more associated with financial projections to take decisions such as viability of a project outcome, it bears commonality with many of the techniques used for ‘root cause analysis’. The ‘Analyse’ phase of a Six Sigma project aims to establish the relationship between the input (x) factors and the output (y) factors, which is the intent of the sensitivity analysis model as well. However, in the case of root cause analysis, especially for finalizing the secondary causes, analysis of ‘actual’ data and validation of the effect of the input factors are necessary.


I have found situations where the sensitivity analysis has helped to set target for input factors. One such example is a project, where the objective is to make a particular branch of a bank profitable. Here there are several input factors to be considered such as Lending volume, Lending interest rates, Borrowing volumes, Borrowing interest rates, volumes of low interest deposits, mix proportion of other products, Fund Transfer pricing and so on. The existing values of all these input parameters and their effect on the overall profitability are taken as the baseline scenario and multiple future scenarios are modeled considering variations of the inputs. The inputs are also classified as ‘more controllable’ and ‘less / not controllable’. Based on these studies, the scenario is chosen and the ‘more controllable’ factors identified for improvement. This is followed by a more detailed ‘root cause analysis’ that cause the gap on those factors from the desired levels, which is supported by actual data.


Thus, Sensitivity Analysis helped in better depiction of the current situation with respect to the input / output factors and also helps to guide ourselves towards a desirable scenario, upon which the RCA can be carried out.


I will be eager to know about other experiences where this methodology relates to RCA.

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1 line answer - Sensitivity Analysis is the superset of all the data driven root cause analysis methods (non data driven methods like 5 Why and Fishbone Diagram etc. are not included)


All business problems can be expressed in the form of an equation Y = f(X), where Y is the dependent variable or the Output and X is the independent variable or the Input. A better way to represent the same equation is

Y = f(X1, X2, X3,.....................Xn), reason being an output is usually dependent on multiple inputs and seldom is a function of a single variable.

And we also know that if there is a problem with the Y, one has to identify the critical Xs in order to improve Y. Two most common tools to identify critical Xs are Hypothesis testing and Design of Experiments (DOE). In fact, both Hypothesis testing and DOE are also sensitivity analysis.


Technically speaking, Sensitivity Analysis is the study which determines how sensitive is the output to the input or in other words, it is the quantum of change in the output per unit of change in the input(s). Now in Hypothesis, we study the impact of changing one factor at a time (OFAT) on the output while in DOE, we study the impact of changing multiple factors at the same time. Also, in Regression, we get the Rsq value which explains the % variation in output attributed to the input (in case of linear regression) or how good is the model equation (in case of multiple regression).


Following are some of the ways in which Sensitivity analysis can be performed (all of these will lead to identification of root causes)

1. Hypothesis Testing (OFAT)

2. Multiple Regression

3. Scatter Plots

4. Simulations

5. Model Identification and Model reduction

6. Design of Experiments

7. Optimization Techniques

8. Reliability studies


Points where Sensitivity analysis scores over traditional root cause analysis

1. Some traditional RCA methods like Hypothesis Testing will only tell whether a particular input is critical for the output. It will not tell the extent of impact. Sensitivity analysis will provide the extent of impact as well

2. Sensitivity analysis can help build a new model. E.g. an analyst wants to understand how the share price of a share is dependent on 

a. Performance of a company (profit)

b. Earnings per share

c. Historical Performance

d. Debt-to-equity ratio

e. Performance of Competitors

f. Micro economic factors

g, Macro economic factors and so on

3. If an output is identified as highly sensitive to a particular input, it would prompt us to put more realistic control measures on it. E.g. we might choose to go for Control Prevention type Poka Yoke or do all tests for special causes on that particular X


Success of sensitivity analysis depends on how best you can identify and manage the following 

1. Correlated inputs

2. Assumptions for inputs


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Sensitivity analysis is done to undersrand the impact of inputs (potential x's) on the desired output. And root cause analysis is done to identify the potential root causes of faults. That is, what x's has caused y. Root cause is basically a problem solving tool however sensitivity analysis a mathematical tool to model best possible scenario for outputs and studying the impacts of inputs and rearranging them.

So basically in a way both these methods is used to understand the effects of inputs on outputs.

This is why both relates to each other.

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While Root Cause Analysis gives us the Risk Priority Number which is used for Risk Management,

Sensitivity Analysis is more of a predictive analysis to determine the least change in the severity of the risk which can bring about a definitive change in the outcome.  This done by calculating Marginal Risk Priority Number (MRPN = Risk Sensitive RPN-RPN).

 Therefore Sensitivity Analysis helps in better decision making by identifying and managing the most sensitve failure mode.

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Sensitivity Analysis are what-if analysis that are used to check for the most effective permutation of the independent variables, one that would yield the best possible impact on the dependent variable, under a certain set of assumptions. It is to test the behavior of Y for each change in X and arrive at the best scenario.


Now, one of most powerful tool for ‘Root Cause Analysis’ is FMEA. I call it most powerful by the simple virtue of being most proactive of the tools as opposed to a more reactive one, say ‘5 Whys’. Now while the experts are expected to take a lot of care in determining RPN while performing FMEA, and that involves active participation of the SMEs, inputs being provided on Severity, Occurrence and Detection need be independent of one another, use of actual data, et al, there is still subjectivity involved.


Sensitivity analysis could help to test the marginal relationship between the RPN and the independent variables (Severity, Occurrence, Detection), and see how a marginal change in one of these would impact the RPN, and thereby help to determine which failure modes are more sensitive than the others.

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Sensitivity Analysis is done to understand the marginal uncertainty caused in the output by the uncertainty in one of the inputs, while all other inputs are remained constant. This tool is used for prioritising potential causes (X's) to finalise the critical Xs. Sensitivity analysis is one of the tools used for prioritising the list of potential causes which are identified through a root cause analysis. 

Edited by Srinivas S
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