Highly regulated fields such as medical devices or pharmaceutical require that a statistical rationale for any design verification and validation activity is used.
If a variable is continuous, the sample size for tolerance interval is a calculation based on the type of interval (1 vs. 2 tails), confidence, population coverage and margin of error.
If a variable is an attribute, typically a count of conforming items, the calculation's output is an acceptance number (maximum number of non-conforming items that can be accepted in the experiment) and a sample size, based on confidence and population coverage.
Sometimes even the conformity of a product is defined on a such statistical basis, sometimes with numbers which are impossible to find in tables:
Les contrôles des leucocytes résiduels dans les PSL sont effectués dans un délai maximal de 24 heures après la déleucocytation. De plus, les contrôles de chaque type de PSL, dans chaque établissement de transfusion sanguine (ETS), doivent montrer que, pour un calcul fait avec un degré de confiance de 95 % et en utilisant un plan d'échantillonnage adapté, les contenus ci-dessus doivent être respectés au minimum dans :
97 % de la production des PSL cellulaires déleucocytés ;
95 % de la production des plasmas à usage thérapeutique déleucocytés.
(e.g. allowed white blood cells post filtration in France, 97% conformity with 95% confidence see link https://www.legifrance.gouv.fr/affichTexte.do?cidTexte=JORFTEXT000023140529 )
So these tools are common also in PCMF (post market clinical follow-up) activities or market monitoring.
It would be nice to see this topic covered in JMP.
Some links:
http://reliabilityanalyticstoolkit.appspot.com/sample_size
https://support.minitab.com/en-us/minitab/18/help-and-how-to/statistics/power-and-sample-size/how-to...
https://www.qualitymag.com/articles/91991-sample-sizes-how-many-do-i-need
http://www.cbinet.com/sites/default/files/files/Session12_Golden_Alan_pres.pdf
https://www.mddionline.com/sample-size-selection-using-margin-error-approach