# How do you create an acceptance criteria range for multiple populations?

#### deshao

##### New Member
I am trying to create a quality control acceptance criteria range for my company's product.

So here is an example of my problem:

A car is traveling on a straight road and through scientific studies, I am able to predict the distance where the car will travel at a fixed time. From there, I am thinking of creating an acceptance criteria range with the predicted distance as the center line and if the car reaches a distance that is within the range the quality of the car is a pass but if the car reaches a distance that is outside the range the quality of the car fails.

Imagine each car has the capacity to have 13 people in it. And currently, there are only 10 types of people with different weights. Thus, there are 10^13 different permutations (Order matters) and each permutation is considered a single car type. One of the factors that affect the distance traveled is the weight of the car. With each different permutation, the weight of the car may be different and this can affect its distance traveled. This is why I need to treat each car type differently and create an acceptance criteria range that only caters for that car type. True enough, certain permutation will result in the same total weight of the car and theoretically, I can group these permutations together. But there are still other factors that can affect the distance traveled and this includes the complex interactions that occur between each person in the car ( Which has not been studied). So in summary, it is safer to treat each car type as a unique entity.

I found out that to create the acceptance criteria, you would have to use the method of generating a confidence interval and to do that, I can run a single car type multiple times to get the sample mean and s.d. However, this may not be applicable for up-scale because I have 10^13 different types of cars and for me to create the acceptance criteria for all of them using this method, it would be practically impossible.

In addition, the creation of the acceptance criteria range for each car type should make use of the predicted distance that is derived scientifically as this method of prediction is the result of my project. Without using the method of prediction to create the acceptance criteria, it will seem like my project is useless because all the company has to do theoretically is to run the car types multiple of times to get the data set and confidence interval (as mentioned, it is practically impossible).

So is there any method for me to create the acceptance criteria range for all 10^13 car types without the need to run a single car type multiple times to create a dataset?

I had thought of a method to do that and it is to create a constant +- margin of error from the predicted distance (generated scientifically) for every car type. But how do I prove this concept statistically and how do i determine what is my margin of error since there is no sample mean and sample s.d. for me to work on.

#### Miner

##### TS Contributor
My initial thought is that you should design a response surface DOE for the cars and people to develop a prediction model. Once you have the model, you can do a number of different analyses with it such as a Monte Carlo analysis for the combinations in which you are interested.

#### deshao

##### New Member
Hi ! Can you explain more on what is a response surface DOE and monte carlo analysis and how does it apply to the problem im facing with? I am a beginner at statistics sorry about that! I would greatly appreciate it if you could kindly give me some advice on how i can create the response surface model and do the monte carlo analysis ! Thank you!!!!! #### Miner

##### TS Contributor
A response surface is a special class of designed experiments. If you are a beginner in stats, it will be hard to explain as it is a more advanced statistical tool. It is an efficient means to develop a mathematical model of an unknown system by running a small fraction of all possible conditions. If you are confident that your system is linear, you can use 2^k fractional factorial designs instead. Response surface designs allow for polynomial models. Once you have a mathematical model, Monte Carlo simulation allows you to model the variation in the dependent variable by inducing variation in the independent variables.