: AOQ2 Function

AOQ2 Function

computes average outgoing quality for a double-sampling plan.

Syntax

AOQ2(replacement, $\text{[math]}$ )

where

replacement	has the value 'REP' or 'NOREP', respectively, depending on whether nonconforming items are replaced with conforming items.
$\text{[math]}$	is the lot size, where $\text{[math]}$ .
$\text{[math]}$	is the acceptance number for the first sample, where $\text{[math]}$ .
$\text{[math]}$	is the rejection number for the first sample, where $\text{[math]}$ .
$\text{[math]}$	is the acceptance number for the second sample, where $\text{[math]}$ .
$\text{[math]}$	is the size of the first sample, where $\text{[math]}$ and $\text{[math]}$ .
$\text{[math]}$	is the size of the second sample, where $\text{[math]}$ and $\text{[math]}$ .
$\text{[math]}$	is the proportion of nonconforming items produced by the process, where $\text{[math]}$ .

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

$\text{[math]}$

and for no replacement, the average outgoing quality is

$\text{[math]}$

where, in both situations,

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

and

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

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;