Where k = 2.4 for n = 10; k = 2.0 for n = 30; s is the standard deviation of the observations.
Unless otherwise specified, all the measurements of dosage units and criteria values (such as L
1) are in percentage label claim.
Lower probability bound of passing USP
Notice that P(passing USP test)
Assume that the X
i
's follow a normal distribution denoted N (μ, σ). Then the values of P(S
1) and P(S
2) can be calculated as described in the following two subsections.
Computation of P(S
1)
Given the definition of AV, it can be seen that:
For T ≤ 101.5
The density function of Z
2 is a x2 distribution with n – 1 degrees of freedom and is denoted as x2 (n – 1).
The joint density function is f(z
1,Z
2) = f
1(z
1) f
2(Z
2),
Given the independence of z
1 and Z
2, P(S
1) can be rewritten in terms of z
1 and Z
2 as:
Computation of P(S
2)
There are two subcriteria in S
2, which are denoted as C
21 and C
22, respectively, as follows:
C
21 = AV of the 30 dosage units is less than or equal to L
1.
C
22 = no unit deviates from the calculated value of M by more than 25% of M.
|
