Sampling refers to - ‘the process of selecting a portion or part to represent the whole’.

**SAMPLING :
PROBABILITY PROFILE**

**Sampling **refers to - **‘the process of selecting a portion or part to represent the whole’.**

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withdrawn from a relatively large batch containing **10% infected containers.** Thus, the **probability** of a *single* *item *taken at random* ***contracting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 : ***p*^{2}* *=* ***0.01**

(b) When **both items being non-infected : ***q*^{2}** **= (1 –** ***p*)^{2}** **= (0.9)^{2}** **=** 0.81**, and

(c) When **one item gets infected **and the other **one non-infected : **1 – (*p*^{2} + *q*^{2})

or = 1 –
(0.01 + 0.81) = 1 – (0.82)

or = 0.18

*i.e., ***= 2 pq**

**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 expres-sion :

*q ^{n} *= (1 –

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 em-phatically demonstrated that as
the **sample size enhances,** the **probability** component of the **batch** **being passed as sterile also gets decreased **accordingly.

**Table 8.4 : Sampling in Sterility Testing**

**1. A : First Sterility Test : **Calculated
from P = (1 –** ***p*)^{20}** **=** ***q*^{20}

**2. B : First Re-Test : **Calculated
from P = (1 –** ***p*)^{20}** **[2 – (1
–** ***p*)^{20}]

[Adapted
From : Hugo and Russell : **Pharmaceutical
Microbiology,** PG Publishing Pvt. Ltd., New Delhi, 3rd edn., 1984]

In actual
practice, however, the additional tests, recommended by **BP (1980),** enhances substan-tially 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 –

that
provides adequate chance in the **‘First
Re-Test’** of passing a batch comprising of a proportion or part ‘*p’* of the **infected containers.**

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