: PROBACC2 Function

PROBACC2 Function

computes the acceptance probability for a double-sampling plan.

Syntax

PROBACC2 $\text{[math]}$

where

$\text{[math]}$	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 number of nonconforming items in the lot, where $\text{[math]}$ .
$\text{[math]}$	is the lot size, where $\text{[math]}$ .
$\text{[math]}$	is the proportion of nonconforming items produced by the process, where $\text{[math]}$ .

Description

The PROBACC2 function returns the acceptance probability for a double-sampling plan of Type A if you specify the parameters $\text{[math]}$ and $\text{[math]}$ , and it returns the acceptance probability for a double-sampling plan of Type B if you specify the parameter $\text{[math]}$ . For details on Type A and Type B double-sampling plans, see Types of Sampling Plans.

For either type of sampling plan, the acceptance probability is calculated as

$\text{[math]}$

where

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

and

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

These probabilities are determined from either the hypergeometric distribution (Type A sampling) or the binomial distribution (Type B sampling).

Examples

The first set of statements results in a value of 0.2396723824. The second set of statements results in a value of 0.0921738126.

data;
   prob=probacc2(1,4,3,50,100,10,200);
   put prob;
run;

data;
   prob=probacc2(0,2,1,13,13,0.18);
   put prob;
run;