PROBACC2 Function

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Functions

PROBACC2 Function

computes the acceptance probability for a double-sampling plan.

Syntax

PROBACC2(a₁,r₁,a₂,n₁,n₂,D,N)

PROBACC2(a₁,r₁,a₂,n₁,n₂,p)

where

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 a₂ > a₁.

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

D is the number of nonconforming items in the lot, where $0\leq D\leq N$ .

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

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

Description

The PROBACC2 function returns the acceptance probability for a double-sampling plan of Type A if you specify the parameters D and N, and it returns the acceptance probability for a double-sampling plan of Type B if you specify the parameter p. 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

P_a₁ + P_a₂

where

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

and

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

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;

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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 a₂ > a₁.
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 $n_{1}+n_{2}\leq N$ .
D	is the number of nonconforming items in the lot, where $0\leq D\leq N$ .
N	is the lot size, where $N\geq2$ .
p	is the proportion of nonconforming items produced by the process, where 0<p<1.