Online Program

Sampling the Unknown: A Multinomial Approach (304163)

Keywords: statistics, analytics, sampling, stratified, multinomial

In this presentation, I provide a real-world sampling methodology problem from the medical device industry. Specifically, suppose during a manufacturing process, devices are stratified into multiple groups, but there is a catch: the stratum for each finished device is unknown. What sample size must be taken to ensure, with 95% confidence, that every stratum is represented in the sample?

Theoretically, this question can be answered directly using the multinomial distribution. However, the solution quickly becomes computationally challenging as the number of strata grows. I have developed a programmatic solution that uses exact multinomial calculations and multinomial simulations to determine the required sample size. Through examples, I will demonstrate when direct calculations are possible and when simulations are necessary.

While this presentation details a problem faced by quality engineers in the manufacture of medical devices, this approach can be used in many industries. Furthermore, my solution can be generalized to accommodate any number of strata, any confidence level, and any combination of success probabilities when strata are not equally likely.