6.
Process or Product Monitoring and Control
6.2. Test Product for Acceptability: Lot Acceptance Sampling


Skip Lot Sampling  Skip Lot sampling means that only a fraction of the submitted lots are inspected. This mode of sampling is of the costsaving variety in terms of time and effort. However skiplot sampling should only be used when it has been demonstrated that the quality of the submitted product is very good.  
Implementation of skiplot sampling plan 
A skiplot sampling plan is implemented as follows:


The \(f\) and \(i\) parameters 
The parameters \(f\) and \(i\)
are essential to calculating
the probability of acceptance for a skiplot sampling plan.
In this scheme, \(i\),
called the clearance number, is
a positive integer and the sampling fraction \(f\)
is such that \(0 < f < 1\).
Hence, when \(f=1\)
there is no longer skiplot sampling. The calculation of the
acceptance probability for the skiplot sampling plan is performed
via the following formula
$$ P_a(f,i) = \frac{fP + (1f)P^i}{f + (1f)P^i} \, ,$$
where \(P\)
is the probability of accepting a lot with a given
proportion of incoming defectives \(p\),
from the
OC curve
of the single sampling plan.
The following relationships hold: for a given \(i\), the smaller is \(f\) the greater is \(P_a\), 

Illustration of a skip lot sampling plan 
An illustration of a a skiplot sampling plan is given below.


ASN of skiplot sampling plan 
An important property of skiplot sampling plans is the average
sample number
(ASN).
The ASN
of a skiplot sampling plan is
$$ \mbox{ASN}_{skiplot} = (F)(\mbox{ASN}_{reference}) \, , $$
where \(F\)
is defined by
$$ F = \frac{f}{(1f)P_i + f} \, .$$
Therefore, since \(0 < F < 1\), it follows that the ASN of skiplot sampling is smaller than the ASN of the reference sampling plan. In summary, skiplot sampling is preferred when the quality of the submitted lots is excellent and the supplier can demonstrate a proven track record. 