Acceptance Limit Calculations

The 1/1000th method assumes that pharmaceuticals are often considered to be nonactive at 0.1% of their normally prescribed dosages.14 The following equation demonstrates how an acceptance limit is calculated utilizing the 1/1000th method  

Maximum daily no. of dosage units product B (units/day) 

The second method uses the 10 ppm limit historically used to calculate commercial manufacturing limits. This method allows the maximum carryover of product A to be calculated using lot sizes and shared equipment surface area, regardless of the potency of the prior lot. The formula below shows the method used to develop the 10 ppm acceptance limits  

The 10 ppm method delivers a somewhat conservative estimate in cases where the potency of product A is low and the lot size of product B is small. It is obvious from Eq. (15.2) that two variables drive the acceptance limit the lot size of product B and the shared surface area. Of importance to note is that the potency of lot A is not considered in this calculation. For example, if the shared equipment surface area is constant between two chug product manufactures and the lot size for product B is 50 kg as opposed to 100 kg, the acceptance limit would be calculated to be half of that of the 100 kg lot size. An important aspect of the 10 ppm method is that it is independent of the potency or number of dosage units of either product A or product B. This calculation merely limits the absolute amount of product in A that can carry over to product B and be distributed evenly throughout all of the dosage forms in the second manufacture. Again, the acceptance limit in the ppm method is driven by lot size (kg) and shared surface area of the equipment. 

In this equation ARL is the acceptable residue limit, ADI is the acceptable daily intake, SBS is the smallest batch size, SA is the swab surface area, CF is the conversion factor (1000), MDD is the maximum daily dose of product B, and SSA is the shared surface area. At first glance, this calculation has desirable attributes of both the 10 ppm method and the 1/1000 method. For example, the 1/1000th method and the TTC method take into account the maximum daily dose of product B. Likewise the 10 ppm method and the TTC method take into account the lot size of product B. The main difference between the calculations is that the ADI is justified 

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TABLE 15.1 Lot Size and Dose Strength Assumptions Used for Safety Acceptance Limit Calculations... 

Since the theory of operation is similar, with some subtle difference, for both instruments the absolute sensitivity (mass detected) for both instruments should be similar. The critical attribute where the two instruments vary, which drives the utility for swab determinations at extremely low levels is in sample introduction. To reach the submi-crogram/swab regime, direct swab analysis may be required. Recall the acceptance limits calculated in Table 15.2. Using the assumptions in Table 15.1, a 1 mg tablet will drive the acceptance limit to 2.0 xg/swab, a 0.1 mg tablet will drive the acceptance limit to 0.2 xg/swab and a 0.01 xg tablet will drive the acceptance limit to 0.02 p,g/ swab. With direct swab analysis, ion mobility should be able to attain the required sensitivity for most compounds with this limit as the absolute amount on the swab would be 20 ng. However, if a typical dilution is required and deposition of a small aliquot... 

To properly handle the changing composition relationships it is almost essential to utilize some electronic computer techniques if good accuracy is to be achieved. Even three component systems become tedious using desk size electronic calculators without significant internal memory. Computers can be well programmed to handle the complexities of trial and check for convergence to a preset acceptable limit. 

Abbreviations for the solvents used are as follows C = Chloroform, E = Ethanol Elemental (C,H,N) analysis indicated that the calculated and observed values were within the acceptable limits ( 0.4%)... 

These observations indicated that an intermolecular double condensation to give a bis N-(methylene-4-oxocoumarinyl)-l,4 aromatic diamine had occurred. Data from the elemental analysis indicated that the calculated and observed values were within the acceptable limits ( 0.4%) and in conformity with the assigned structure. In the addition of molar equivalents of 1,4-aromatic binucleophilic compounds to compound 72 we did not observe any heterocyclic compounds resulting from the further intermolecular nucleophilic attack on the single condensation product. Since the condensation of 3-(dimethylaminomethylene)-chromane-2,4-dione with aromatic binucleophilic compounds is the only route to the new coumarinic compounds, this represents a useful synthetic method. 

The cut and try method. The recycle stream flows can be estimated and the calculations continued to the point where the recycle is calculated. The estimated flows are then compared with the calculated and a better estimate made. The procedure is continued until the difference between the estimated and the calculated flows is within acceptable limits. 

The consolidation of individual values into an overall value is possible by a number of other methods. The geometric mean calculation has a particularly distinguishing characteristic that if any individual desirability factor is zero, indicating that a response is outside of its acceptable limits, the overall desirability is zero. An optimization procedure to maximize the overall desirability function will therefore seek to remain within the acceptable ranges of all responses even though individual maximization, minimization, or an acceptable range of response values are required. By these criteria, the values maximizing the overall desirability function... 

Figure 4.8 shows the comparison of three lots of loperamide hydrochloride, each obtained from a different supplier. The displayed thermograms represent normal behavior for this material, and while the figure shows the uniqueness of each source, the variations were within acceptable limits. Owing to the decomposition that followed on the end of the melting endotherm, specific heats of fusion were not calculated in this case. 

To determine the QL, it is necessary to agree on acceptable limits for precision and accuracy. Commonly, precision is given as a maximal acceptable RSD of the analytical result, RSDn,ax- Then the QL can be calculated using... 

The second problem is even more serious. The number of product molecules in a bond separation reaction increases with the size of the reactant, and (presumably) so too does the overall magnitude of error in the calculated bond separation energy. Whereas errors in bond separation energies (and in heats of formation derived from bond separation reactions) are close to acceptable limits ( 2 kcal/ mol) for small molecules (see discussion in Chapter 6), it is likely that will rapidly move outside of acceptable limits with increasing molecular size. 

The thiocyanate salt of the TTF radical cations exists as dark-purple needlelike crystals that are insoluble in nonpolar solvents and moderately soluble in warm polar solvents (e.g., acetonitrile, dichloromethane). Stoichiometries derived from elemental analysis for this and most salts of the TTF radical cations are not unequivocal since several calculated values come within the acceptable limits (i.e., 0.3% per element) of the percentages actually determined. For identification purposes we have called the thiocyanate (TTF)14(NCS)8, although, for example, (TTF) (NCS)6, (TTF)I2(NCS)7, and (TTF)ls(NCS)8 are also consistent with our results. The compressed pellet resistance is 2-6 ohms (see Table I). 

One of the most frustrating problems that you may encounter using the Transient Analysis is convergence problems. When PSpice is simulating a differential equation, it calculates a data point and estimates the error associated with the calculation. If the error is larger than a specified maximum, PSpice reduces the time step and recalculates the point and the error for the new point. Reducing the time step usually reduces the error. PSpice will continue reducing the time step until the error is within acceptable limits, or until PSpice reaches the limit on the number of times it is allowed to reduce the time step. 

Minimum Approach for Multiple Batches When the hypothesis for equality of slopes is rejected at the 0.25 significance level, the minimum approach should be implemented. This is because the degradation lines of individual batches cannot be considered the same since they have different degradation rates. In this situation the FDA guideline establishes that the overall expiration dating period has to ensure that the product will remain within acceptable limits regardless of the batch from which it comes. Thus, the shelf life for each batch is calculated and the expiration dating period is based on the lowest of all shelf lives. Mathematically, this can be expressed as... 

The calculated DE may be below the acceptable limit, but the color difference may not be acceptable visually. 

The nature of the primary contaminating product—The nature of the primary potentially contaminating product refers to how the product is administered to the patient. Is the product a finished pharmaceutical dosage form or is it a precursor or chemical intermediate that will be used as a starting material by other companies to manufacture finished products Are the products sterile or nonsterile What is the route of administration of the product (e.g., oral, topical, intravenous, ophthalmic) The answers to these questions will dictate the actual calculations to be used to determine acceptable limits. 

The calculated total concentration of component j T ) is then compared to the total analytical (input) concentration of component to calculate the residual in the mass balance. From this point an iterative algorithm based on the Newton-Rapshon method and Gausian elimination (to convert non-linear equations to linear) is used to refine the initial estimates of each component concentration. At each refinement the residual in the mass balance is reduced until some acceptable limit is reached. 

The raw data themselves. The calculations and assumptions must be absolutely correct and within the acceptable limits. 

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