**Computing statistical tolerance intervals in JMP**

Jean-François Michiels^{1}, Sarah Janssen^{2}, Pierre Lebrun^{3}.

^{1 }Corresponding author, jean-francois.michiels@arlenda.com, Arlenda SA, Liège, Belgium (http://www.arlenda.com)

^{2} Janssen Biologics, Leiden, Netherlands

^{3} Arlenda SA, Liège, Belgium

Two kinds of statistical tolerance intervals exist. First, beta-expectation tolerance interval is a statistical interval within which a specified proportion (beta) of the population is expected to fall. The second kind is the beta-content gamma-confidence tolerance interval that is an interval within which a beta proportion of the population fall, with the confidence level gamma. Those intervals are widely used in the pharmaceutical industry. For example, in bridging studies a beta-content gamma-confidence tolerance interval is computed on data obtained with a reference process and beta-expectation tolerance interval is computed on data obtained with a modified process. If the latest is included within the first one, then the modification does not affect the process. Depending on the statistical models, tolerance intervals can be computed with exact formulas, asymptotic approximations or using simulations. For linear fixed effect models (e.g. fixed ANOVA 1, linear regression), tolerance intervals can already be easily computed in JMP using the distribution platform or the fit model platform. Formulas have been developed and published for models with one random factors. However, scientists still require the help of statisticians to compute them since those formulas are not implemented in user-friendly software like JMP. With the help of Janssen, a JMP add-in aiming at computing tolerance intervals for model with one random factor such as a one way random ANOVA model has been developed and validated by Arlenda. This add-in will help scientists to compute by themselves these tolerance intervals, while statisticians can focus on other complex analyses.