Part 6: Pharmaceutical Applications Hub

Step 1: Determine the acceptance criteria based on tablet weight

1. For tablets ≤130 mg: ±10% deviation allowed
2. For tablets 130-324 mg: ±7.5% deviation allowed
3. For tablets >324 mg: ±5% deviation allowed
4. Our tablets (250 mg) fall in category 2: ±7.5%

Step 2: Calculate percentage deviation for each tablet

1. % Deviation = |Individual Weight - Average Weight| / Average Weight × 100
2. Example: Tablet 1 = |248 - 250| / 250 × 100 = 0.8%
3. Example: Tablet 2 = |252 - 250| / 250 × 100 = 0.8%
4. Calculate for all 20 tablets

Step 3: Check compliance criteria

1. No individual tablet should exceed ±7.5% deviation
2. Count how many tablets (if any) exceed this limit
3. If ≤2 tablets exceed limit: PASS
4. If >2 tablets exceed limit: FAIL

Step 1: Understand the Acceptance Value formula

1. AV = |M - x̄| + ks
2. M = Reference value (usually 100% or label claim)
3. x̄ = Sample mean (%)
4. k = Acceptability constant (depends on sample size)
5. s = Sample standard deviation

Step 2: Determine k values based on sample size

1. For n = 10: k = 2.4
2. For n = 30: k = 2.0
3. Use appropriate k value for your sample size

Step 3: Calculate AV and interpret results

1. Calculate sample mean and standard deviation
2. Substitute values into AV formula
3. If AV ≤ 15.0: PASS
4. If AV > 15.0: Proceed to next stage or FAIL

Step 1: Calculate hardness statistics

1. Mean hardness = Σ(hardness values) / n
2. Standard deviation = √[Σ(x - x̄)² / (n-1)]
3. CV% = (Standard deviation / Mean) × 100
4. Typical acceptance: CV% < 15%

Step 2: Evaluate friability

1. % Friability = (Initial weight - Final weight) / Initial weight × 100
2. Typical acceptance: Friability < 1.0%
3. Document any capping or lamination

Step 1: Organize dissolution data by time points

1. Create matrix: Rows = tablets, Columns = time points
2. Calculate mean % dissolved at each time point
3. Calculate standard deviation at each time point
4. Calculate %RSD = (SD / Mean) × 100

Step 2: Assess variability

1. %RSD should typically be < 20% at early time points
2. %RSD should be < 10% at later time points
3. Identify any outlier tablets
4. Document minimum and maximum values

Stage 1 (S1): 6 tablets

1. Each tablet must dissolve ≥ (Q + 5)%
2. If Q = 80%, then each tablet ≥ 85%
3. If all 6 tablets pass: TEST PASSES
4. If any tablet fails: Proceed to S2

Stage 2 (S2): 6 additional tablets (12 total)

1. Average of 12 tablets ≥ Q%
2. No individual tablet < (Q - 15)%
3. If Q = 80%: Average ≥ 80%, no tablet < 65%
4. If criteria met: TEST PASSES, else proceed to S3

Stage 3 (S3): 12 additional tablets (24 total)

1. Average of 24 tablets ≥ Q%
2. No more than 2 tablets < (Q - 15)%
3. No tablet < (Q - 25)%
4. Complex criteria - if met: PASS, else: FAIL

Step 1: Set up linear regression model

1. Y = mx + b (where Y = potency, x = time)
2. Calculate slope (m) and intercept (b)
3. Determine correlation coefficient (R²)
4. R² > 0.95 indicates good linear fit

Step 2: Calculate 95% confidence intervals

1. Lower confidence bound = Y - t(α/2) × SE
2. Upper confidence bound = Y + t(α/2) × SE
3. SE = standard error of prediction
4. Use lower bound for shelf-life prediction

Step 3: Predict shelf-life

1. Find intersection of lower bound with specification limit
2. Example: 90% specification limit
3. Shelf-life = time when lower bound = 90%
4. Apply appropriate safety margins

Step 1: Key distribution parameters

1. D10: 10% of particles are smaller than this size
2. D50: Median particle size (50% smaller, 50% larger)
3. D90: 90% of particles are smaller than this size
4. These parameters describe distribution width

Step 2: Calculate Span (distribution width)

1. Span = (D90 - D10) / D50
2. Lower span = narrower distribution
3. Higher span = wider distribution
4. Typical range: 1.5 - 3.0 for pharmaceuticals

Step 3: Pharmaceutical applications

1. Milling efficiency assessment
2. Blend uniformity prediction
3. Dissolution rate correlation
4. Tablet compression behavior