AOQ2 Function

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Functions

AOQ2 Function

computes average outgoing quality for a double-sampling plan.

Syntax

AOQ2(replacement,N,a₁,r₁,a₂,n₁,n₂,p)

where

replacement has the value 'REP' or 'NOREP', respectively, depending on whether nonconforming items are replaced with conforming items.

N is the lot size, where $N\geq2$ .

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 $n_{1}\geq1$ and $n_{1}+n_{2}\leq N$ .

n₂ is the size of the second sample, where $n_{2}\geq1$ and $n_{1}+n_{2}\leq N$ .

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

Description

The AOQ2 function returns the average outgoing quality for a Type B double-sampling plan in which nonconforming items are replaced with conforming items (replacement is 'REP') or not replaced (replacement is 'NOREP'). For details on Type B double-sampling plans, see "Types of Sampling Plans".

For replacement, the average outgoing quality is

AOQ = [(pP_a₁(N-n₁) + pP_a₂(N-n₁-n₂) )/N]

and for no replacement, the average outgoing quality is

AOQ = [( pP_a₁(N-n₁) )/(N-n₁p )] + [( pP_a₂(N-n₁-n₂) )/(N-n₁p-n₂p )]

where, in both situations,

$P_{a_{1}} & = & \sum_{d=0}^{a_{1}} f(d| n) \ & = & {probability of acceptance fo... ...d| n_{1})F(a_{2}-d| n_{2}) \ & = & {probability of acceptance for second sample}$

and

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

Examples

The first set of statements results in a value of 0.0148099904. The second set of statements results in a value of 0.0144743043.

   data;
      aoq=aoq2('norep',120,0,2,1,13,13,0.18);
      put aoq;
   run;


   data;
      aoq=aoq2('rep',120,0,2,1,13,13,0.18);
      put aoq;
   run;

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replacement	has the value `'REP'` or `'NOREP'`, respectively, depending on whether nonconforming items are replaced with conforming items.
N	is the lot size, where $N\geq2$ .
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 $n_{1}\geq1$ and $n_{1}+n_{2}\leq N$ .
n₂	is the size of the second sample, where $n_{2}\geq1$ and $n_{1}+n_{2}\leq N$ .
p	is the proportion of nonconforming items produced by the process, where 0<p<1.