rawford Pharmaceuticals has developed a new drug, Vaxidene. The target amount fo

Question

rawford Pharmaceuticals has developed a new drug, Vaxidene. The target amount for a single dose of Vaxidene is 9191 mg. Patients can receive as little as 8888 mg or as much as 9494 mg without experiencing any ill effects. Because of potential liability issues, Crawford has determined that it is imperative that manufacturing be able to provide Six Sigma quality levels. At present, the manufacturing process has a process mean of 9191 mg and a standard deviation of 8.158.15 mg

. A. what are the upper and lower tolerance limits for vaxidene?

B. is crawfords's manufacturing process currently able to meet the dosage specifications at least 99.7% of the time? show work.

Explanation / Answer

The Upper Tolerance limit for Vaxidence = USL = 94 mg

Lower Tolerance limit for Vaxidence = LSL = 88 mg

Given are following data :

Process mean = m = 91 mg

Process standard deviation = Sd = 8.15 mg

Let Z value corresponding to probability that process value will be maximum USL of 94 mg. is Z1

Therefore ,

M + Z1 x Sd = 94

Or, 91 + 8.15.Z1 = 94

Or, 8.15.Z1 = 3

Or, Z1 = 3/8.15

Or, Z1 = 0.37 ( rounded to 2 decimal places )

Corresponding value of probability for Z1 = 0.37 as derived from standard normal table will be 0.64431

Similarly,

Let Z value corresponding to probability that process value will be maximum LSL of 88 mg. is Z2

Therefore ,

M + Z2 x Sd = 94

Or, 91 + 8.15.Z2 = 88

Or, 8.15.Z2 = - 3

Or, Z1 = - 3/8.15

Or, Z1 = - 0.37 ( rounded to 2 decimal places )

Corresponding value of probability for Z2 = - 0.37 as derived from standard normal table will be 0.64431 is 0.35569

Therefore,

Probability that current manufacturing process is able to meet dosage specification limits

= Probability that process value will be maximum 94 mg – Probability that process value will be maximum 88 mg

= 0.64431 – 0.35569

= 0.28862

Therefore Crawford’s manufacturing process is currently able to meet dosage specification only 28.86 % of time

CRAWFORD’S MANUFACTURING PROCESS IS CURRENTLY NOT ABLE TO MEET DOSAGE SPECIFICATION LIMIT 99.7 % OF TIME

CRAWFORD’S MANUFACTURING PROCESS IS CURRENTLY NOT ABLE TO MEET DOSAGE SPECIFICATION LIMIT 99.7 % OF TIME

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