Consider a double-sampling plan with $n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6$ Which of the following equalities are not correct if the lot will be accepted?
A) $x _ { 1 } = 5 \text { and } x _ { 2 } = 0,1 , \text { or } 2$
B) $x _ { 1 } = 4 \text { and } x _ { 2 } = 0,1 , \text { or } 2$
C) $x _ { 1 } = 3 \text { and } x _ { 2 } = 0,1 , \text { or } 2$
D) $x _ { 1 } = 0,1 , \text { or } 2$
E) None of the above are correct

Question

Quizplus · Accepted Answer

In a double-sampling plan, the lot is accepted in the first stage if $x_1 \leq c_1$, which means if the number of defects in the first sample ($x_1$) is less than or equal to the acceptance number for the first sample ($c_1$). Given $c_1 = 2$, any $x_1 > 2$ would not lead to acceptance in the first stage. For option A, $x_1 = 5$, which is greater than $c_1$, so the lot would not be accepted based on the first sample alone, making the conditions for acceptance in option A incorrect.

Consider a Double-Sampling Plan With n1=80,n2=80,c1=2,r1=5, and c2=6n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6n1​=80,n2​=80,c1​=2,r1​=5, and c2​=6

Consider a Double-Sampling Plan With $n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6$