ASN2 Function

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Functions

ASN2 Function

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

Syntax

ASN2(mode,a₁,r₁,a₂,n₁,n₂,p)

where

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

a₁ is the acceptance number for the first sample, where $a_{1}\geq0$ .

r₁ is the rejection number for the first sample, where r₁>a₁+1.

a₂ is the acceptance number for the second sample, where $a_{2}\geq a_{1}$ .

n₁ is the size of the first sample, where $n_{1}\geq1$ .

n₂ is the size of the second sample, where $n_{2}\geq1$ .

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

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

and for semicurtailed inspection, the average sample number is

${ASN}=n_{1}+ \sum_{d=a_{1}+1}^{r_{1}-1} f(d| n_{1}) ( n_{2}F(a_{2}-d| n_{2}) + \frac{r_{2}-d}p [1- F(r_{2}-d| n_{2}+1)] )$

where

$f(d| n) &= & (\stackrel{n}{_d})p^d(1-p)^{n-d} \ &= & {binomial probability that ... ...lity that the number of nonconforming items is less} \ & & {than or equal to a}$

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;

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mode	identifies whether sampling is under full inspection (mode is `'FULL'`) or semicurtailed inspection (mode is `'SEMI'`).
a₁	is the acceptance number for the first sample, where $a_{1}\geq0$ .
r₁	is the rejection number for the first sample, where r₁>a₁+1.
a₂	is the acceptance number for the second sample, where $a_{2}\geq a_{1}$ .
n₁	is the size of the first sample, where $n_{1}\geq1$ .
n₂	is the size of the second sample, where $n_{2}\geq1$ .
p	is the proportion of nonconforming items produced by the process, where 0<p<1.