Example RA-2 - Risk of Allergic Reaction to Suntan Lotion
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.
Define a Random Variable called "Application_ml" 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.
Define a Probability to describe the likelihood that a user will have a reaction to the chemical.
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:
Step 1: Use a Block to calculate the percentage of the population affected based on the probability of a reaction.
Step 2: Use a Result Storage construct to store the average of the results.
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.
.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).
