In the pharmaceutical industry. quality engineers are responsible for maintainin

Question

In the pharmaceutical industry. quality engineers are responsible for maintaining the quality of drug products produced in the manufacturing process. The key to quality is an assessment of product characteristics through repeated measurements of the variable of interest. When the variable is the concentration of a particular constituent in a mixture, the process is called an assay. For the purpose of this analysis, we focus on a chemical assay to determine how fast a solid-dosage pharmaceutical product e. g an aspirin tablet or capsule) dissolves. Since variation in the dissolution of the drug can have handful effects on the patient, quality inspectors require a test that accurately measures dissolution. Two statisticians Russel Reeve and Francis Giesbrecht explored the dissolution characteristics of anew immediate-release ding product manufactured by a well-known pharmaceutical company. An immediate-release product is designed to dissolve and enter the bloodstream as fast as possible. To test for dissolution of the solid dosage drug, the company uses an apparatus with six vessels or tubes, each tube containing a dissolving solution. Drug tablets or capsules are dropped and analyzed using high- performance liquid chromatography (HPLC). The HPLC device quantifies how much of the drug is in the solution: this value is expressed as percent of label strength (%LS). Dissolution test data for an analgesic in Tablet form conducted at two manufacturing sites (New Jersey and Puerto Rico) are provided in the following Table. Note that the %IS values were obtained at four different points in after 20 minutes, after 40 minutes, after 60 minutes, and after 120 minutes-for each of the six vessels. Razed on the sample data provided above, do the two sites produce equivalent assay results? (Apply test of hypotheses methods: eight-step procedure, P-value approach, and confidence interval approach to come up with your conclusions. State all the assumptions you make to perform this analysis. Verify that all the conditions for statistical analysis are fulfilled before performing the analysis).

Explanation / Answer

1. Descriptive statistics (overall ):

For region "New Jersy":

For region Procio Rico:

2. 2 WAY ANOVA (using excel data analysis add in):

Here based on p-values, we conclude that there is significant effect of each treatment of both the factors & intercation at 6% level.

20min 40 min 60 min 120 min Mean 6.75 71.83333 95.5 99 Standard Error 1.200536 1.341829 0.84835 0.460566 Median 6.5 71.5 95.5 99 Mode 5 72 99 100 Standard Deviation 4.15878 4.648232 2.938769 1.595448 Sample Variance 17.29545 21.60606 8.636364 2.545455 Kurtosis -0.58428 0.404878 -0.65573 0.441497 Skewness 0.175744 0.648364 -0.36105 -0.16117 Range 14 16 9 6 Minimum 0 65 90 96 Maximum 14 81 99 102 Sum 81 862 1146 1188 Count 12 12 12 12

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