A quality engineer for a drug manufacturer wants to determine the shelf life for a medication. The concentration of the active ingredient in the medication decreases over time. The engineer wants to determine when the concentration reaches 90% of the intended concentration. The engineer randomly selects 8 batches of medication from a larger population of possible batches and tests one sample from each batch at nine different times.
In the example of a stability study with a random batch factor, the engineer determined that the shelf life for a medication was about 53.18 months. For this analysis, the shelf life is the time when the 95% confidence interval for 95% of the drug crosses the lower specification limit. The lower specification limit is 90. The engineer wants to predict the mean concentration of the pills at 53.18 months.
The prediction for a random batch is for any batch from the population. The predicted mean concentration for any batch at 53.18 months is about 92.7. The confidence interval indicates that you can be 95% confident that the mean concentration is between approximately 91.84 and 93.52. The prediction interval indicates that you can be 95% confident that the concentration of any single pill that you test from the population is between approximately 90.15 and 95.22. The 95% confidence interval for the mean is greater than the lower specification limit at 53.18 months. In this analysis, the shelf life uses the time when the confidence interval for 95% of the concentrations is greater than the lower specification limit, not the confidence interval for the mean concentration.