Using RENO to Analyze the Risk of Allergic Reaction to Suntan Lotion

ReliaSoft > Software > RENO > Examples > Example RA-2

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Example RA-2 - Risk of Allergic Reaction to Suntan Lotion

Software Used:
RENO

Problem Statement:

Assume that chemical X is added to a suntan lotion. The manufacturing process contains some minor variability. The concentration of chemical X is normally distributed with a mean of 0.005 and a standard deviation of 0.0001 ml of chemical X per ml of lotion.

The amount of lotion applied by a person also varies and is known to be normally distributed with a mean of 100 ml and standard deviation of 20 ml.

It is suspected that 10% of the population may, depending on the amount used, have an allergic reaction to chemical X. From the 10% who are susceptible, the probability that someone will have an allergic reaction is a function of the amount of the chemical applied. This probability is given by a Weibull distribution with beta of 2.5 and eta of 1.8.

Determine the percentage of the population that is expected to experience an allergic reaction.

RENO Solution:

Define a Random Variable called “Concentration_Per_ml” to describe the concentration of chemical X in the suntan lotion.

Random Variable to describe the concentration of the chemical in the lotion

Define a Random Variable called “Application_ml” to describe the user’s application of the lotion.

Random Variable to describe the user's application of the lotion

Define an Equation Variable to calculate the amount of chemical X applied by the user, which is the amount of lotion applied multiplied by the concentration of chemical X in the lotion.

Equation Variable to calculate the amount of chemical applied

Define a Probability to describe the likelihood that a user will have a reaction to the chemical.

Probability to describe the likelihood of reaction

As you can see, this probability is based on the Weibull distribution and the amount of exposure calculated by the “Chemical_Applied” variable.

Construct the flowchart as follows:

Flowchart to model the problem

Step 1: Use a Block to calculate the percentage of the population affected based on the probability of a reaction.

Block to calculate the percentage of the population affected

Step 2: Use a Result Storage construct to store the average of the results.

Result Storage construct to store the average

After running 2,000 simulations (with a seed of 1 to provide repeatability), the results are displayed in the Simulation Results Explorer and in the flowchart, as shown next.

Flowchart with results displayed

.4203% percent of the population are expected to experience a reaction to the suntan lotion.

A RENO project with the solution for this example (called "Sun Tan.rnp") is shipped with the software and stored in the Examples\Reliability folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Risk Analysis\Sun Tan.rnp).

Questions?