Functions

ASN2 Function

Subsections:

computes the average sample number for a double-sampling plan.

Syntax

ASN2(mode,$a_{1},r_{1},a_{2},n_{1},n_{2},p$)

where

mode

identifies whether sampling is under full inspection (mode is 'FULL') or semicurtailed inspection (mode is 'SEMI').

$a_{1}$

is the acceptance number for the first sample, where $a_{1}\geq 0$.

$r_{1}$

is the rejection number for the first sample, where $r_{1}>a_{1}+1$.

$a_{2}$

is the acceptance number for the second sample, where $a_{2}\geq a_{1}$.

$n_{1}$

is the size of the first sample, where $n_{1}\geq 1$.

$n_{2}$

is the size of the second sample, where $n_{2}\geq 1$.

p

is the proportion of nonconforming items produced by the process, where 0 < p < 1.

Description

The ASN2 function returns the average sample number for a Type B double-sampling plan under full inspection (mode is 'FULL') or semicurtailed inspection (mode is 'SEMI'). For details on Type B double-sampling plans, see Types of Sampling Plans.

For full inspection, the average sample number is

\[ \mbox{ASN}=n_{1}+n_{2}[F(r_{1}-1|n_{1})- F(a_{1}|n_{1})] \]

and for semicurtailed inspection, the average sample number is

\[ \mbox{ASN}=n_{1}+ \sum _{d=a_{1}+1}^{r_{1}-1} f(d|n_{1}) \left( n_{2}F(a_{2}-d|n_{2}) + \frac{r_{2}-d}{p} [1- F(r_{2}-d|n_{2}+1)] \right) \]

where

\begin{eqnarray*} f(d|n) & = & (\stackrel{n}{_ d})p^{d}(1-p)^{n-d} \\ & = & \mbox{binomial probability that the number of nonconforming items }\\ & & \mbox{in a sample of size }n \mbox{ is exactly } d \\ F(a|n) & = & \sum _{d=0}^{a}f(d|n) \\ & = & \mbox{probability that the number of nonconforming items is less} \\ & & \mbox{than or equal to } a \end{eqnarray*}

Examples

The first set of statements results in a value of 15.811418112. The second set of statements results in a value of 14.110408695. 

data;
   asn=asn2('full',0,2,1,13,13,0.18);
   put asn;
run;

data;
   asn=asn2('semi',0,2,1,13,13,0.18);
   put asn;
run;