Christiana Edmunds runs a small pharmaceurical compounding business. FDA regulat

Question

Christiana Edmunds runs a small pharmaceurical compounding business. FDA regulations require that her flagship product contain no more than 4mg of active ingredient per dose (with an acceptable rate of out of spec of 99.7%, which is equivalent to six total standard deviations or C=1). The manufacturing process is an automate production line, in which the active ingredient is added through a finely tuned dosing mechanism that is amazingly reliable (it does not suffer from abnormal variation) that delivers a mean amount of acitve ingredient of 3.3mg/dose with a population/process standard deviation of 0.25 mg/dose.
You have exained the R- charts for her production line and have found that the R-charts show that the process is in control.
a.) Is the current process capable of meeting the FDA's standards? (compute the appropriate capability index to show this)
b.) With her current prcess, how many doses (measured as percentage) will Christina produce that contains greater than 4mg active ingredint? Hint: use z-scores and the normal distribution table. Round or interpolate as needed.

Explanation / Answer

a) Process mean 3.3 mg/dose Process std dev 0.25 mg/dose Specification limit 4 mg/dose Acceptable rate 99.70% within specs Z score 2.8 (4-3.3)/0.25 % of samples inside specs 99.74% So the current process is capable of meeting FDA standards b) % of doses that greater than 4mg active ingredient 0.26%

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