ATI2 Function

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Functions

ATI2 Function

computes the average total inspection for a double-sampling plan.

Syntax

ATI2(N,a₁,r₁,a₂,n₁,n₂,p)

where

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 ATI2 function returns the average total inspection for a Type B double-sampling plan. For details on Type B double-sampling plans, see "Types of Sampling Plans".

The average total inspection is

ATI = n₁P_a₁+(n₁+n₂)P_a₂+N(1-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

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

Examples

The following statements result in a value of 110.35046381:

   data;
      ati=ati2(120,0,2,1,13,13,0.18);
      put ati;
   run;

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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.