Sampling
In usual practice, a
‘sterility test’ attempts to infer and ascertain the state (sterile or non-sterile)
of a particular batch ; and, therefore, it designates predominantly a
‘statistical operation’.
Let us consider that ‘
p’ duly refers to the proportion of infected containers in a batch, and ‘q’
the proportion of corresponding non-infected containers. Then, we may have :
p
+ q = 1
or
q = 1 – p
Further, we may assume that a specific
‘sample’ comprising of two items is duly withdrawn
from a relatively large batch containing
10% infected containers. Thus, the probability of a singleitem taken at random contracting infection is usually given by the following expression :
p
= 0.1 [i.e., 10% = 0.1]
whereas, the probability of such an item
being non-infected is invariably represented by the following
expression :
q
= 1 – p = 1 – 0.1 = 0.9
Probability Status
—The probability status of the said two items may be obtained virtually in
three
different forms, such as :
(
a) When both items get infected : p2 = 0.01
(
b) When both items being non-infected : q2 = (1 – p)2 = (0.9)2 = 0.81, and
(
c) When one item gets infected and the other one non-infected : 1 – (p2 + q2)
or = 1 – (0.01 + 0.81) = 1 – (0.82)
or = 0.18
i.e.,
= 2pq
Assumption :
In a particular ‘sterility test’ having a ‘sample’ size of ‘n’ containers, the ensuing
probability
p of duly accomplishing ‘n’ consecutive ‘steriles’ is represented by the following expression
:
q
n = (1 – p)n
Consequently, the ensuing values for various levels of ‘
p’* having essentially a constant sample
size
are as provided in the following. Table 8 : 4A, that evidently illustrates that the ‘sterility test’ fails
to detect rather
low levels of contamination contracted/present in the ‘sample’.
Likewise, in a situation whereby
different sample sizes were actually used**, it may be emphatically
demonstrated that as the
sample size enhances, the probability component of the batchbeing passed as sterile also gets decreased accordingly.
1.
A : First Sterility Test : Calculated from P = (1 – p)20 = q202. B : First Re-Test : Calculated from P = (1 – p)20 [2 – (1 – p)20]
In actual practice, however, the additional tests, recommended by
BP (1980), enhances substantially
the very
chances of passing a specific batch essentially comprising of a proportion or part of the
infected items
(see Table : 8.4B). Nevertheless, it may be safely deduced by making use of the following
mathematical formula :
(1 –
p)n [2 – (1 – p)n]
that provides adequate chance in the
‘First Re-Test’ of passing a batch comprising of a proportion orpart ‘p’ of the infected containers.