Preprint version
MODIFIED TABLES FOFl TilE SELECTION OF DOUBLE SAMPLING ATrRIBUTE PLAN INDEXED BY AOL AND LQL
V.ly
Preprint version
1\cl
2:
F(n,JAc 1, d 1) + d1
-
(3)
Ac, .. 1
and (4) 1\c
L
where F{n/Ac, d) =
t(nld)
d-0
,·:~~ ~ '1
f(nld) = exp (-11p) (np)d /d!
For the sake of convenience, the value of n2 is assumed as k times of n 1• F:er ,: 'Jl •• various combinations of Ac 1, Re 1, Ac 2 , and Re 2 and for fixed k, the unity values n 1p 1 and n 1p 2 (and hence p2/p 1) were obtained by solving the equation {3) fixed
and
combinations.
Similarly, the unity values p 1ASN(P 1) and were ob tained by solving equation (4). The values of Ac 1, Re 1, Ac2 , are selected meeting the conditions (1) and (2) suggested by Hamaker Strike (1955) for eliminating plans that are intuitively bad. It is well known that p 2/p 1 is an inverse measure of may, therefore, find a number of double sampling plans having a p2/p 1 or just less than the desired p~p 1 • Among sucl1 double sampling plans, having minimum sum of ASN at AQL and LQL may be prefered.
For the
discussed earlier, one may find the following double sampling plans. Calculated p2/p,
3.89 3.88 3.87 3.86 3.79 3 .71 3.68 3.67 and so on
p 1 ASN(p 1) +
AC 1
p 2 ASN(p 2)
n,p, for u = .05
7.964 9.628 8.482 9.292 10.157 10.019 8.711 9.502
1.171 1.427 1.295 1.747 1.969 1.966 1.322 1.859
0
2
4 6
0 3
4 5
6
3 3
5
11
5 5
10 5 7
1 3
5
5
5 6
Among the above, the plan involving smaller sum of ASN must be corresponding to minimum p 1ASN(p 1)+p 2ASN(p2 )
since p 1 and p2 are Thus, in the above example, the plan satisfying requirements is fixed as Re 1=4, Ac 2 =5, and Re 2=6 and n 1 =1.171/0.01
117. Tables II through
Preprint version
Vlo S 1ASN(pl)
"aPI for
p2ASN(p2)
0(111'.0$
" ' .OS
0 . 16i o. 266 0.327 O.JSO 0.513 0.679 0.754 0 . 795 0 .a11 0.676 1.262 1.316 1. 146 0.065 1.036 1.346 I. 526 I . 871 2. 054 2 . 219 2.612 2. 782 2.931 3.367 3.524 ).660 4. Ill 4.278 ~ .402 4 . 907 5.041 5.154 5.688 5. 813 5. 917 6.476 6.592 6.685 7.170 7.378 7.468 6.410 8.070
0.207 o . J7( 0. 4a2 o. 52l 0. 679 o. ala o. 956 1.022 1. 049 1. 3]3 1. 501 1. 5a5 I. 63 t I. 845 2 . 329 2 .)62 2. 842 2. 90( 3 .)66 J . aoo 3. 914 (. J42 4.7]3 4 . 902 5.297 5. 649 5. 872 6. 236 6.554 6. 828 7 . 163 7. 4SJ 7 . 774 8 . 083 a . J
lc IV.
(CON II I-il ii ll)
--··· ··---------· Ac
1 Rt 1 A< 7
Rc (
"2 1 P1 lor ~·.01 ~-.
·-0 0
2 2
0
2
0
2 2
0
I
l l 3 J
1
l
I 0
l 4 4 4 4 4 4 4 4 6 5
0
1 I
2 l 2 2 l 0 0
0 I
s
1 2 l 4 5 6 4
I 6 7 8 4
a 9 10 11 12 s 6 6 12
I
5 5 5 5 5 6 6 6
1l 14 15 16 8 9 16 17 18
1
s
9
s
7 7 6 6 6 6 7 7 7 7
20 23 19 11 12
l l I I
I 1 I I
I I
2
l 2 }
l }
I
J:
Uu
IJ 14
IS 16 17
J 4 5 6 1
1
10.90 9.67 9.17 9.06
I 6 7
a 9 5 9 10
I
6. 73
6.57 6. 52
II
the plan
---- - - -----------------
1ASN( 1>l) Pz'Pt
lor p ASH(pl) t. •. Ol 1 •· .OS
.
r 1•s•cr 1 > " 2'" •
p 1ASNCpl l
!or
PzASN(f'l) « • . 01
' •· z.s•c,.2>
"1"1 lor cc• .0 1
p AS11Cp ) 1 1 lor o•.O,
8 • . 01
·------·-·-- -·-----·- - - -
40 . (4 21.09 16.90 16.67
2
12 13 6 7 7 13 14 15 16 IT 9 10 17 10 19 10 21 24 20 12 13 14 15 16 17 16
10
fl
I
5. 86 5. OS 4.84
4. 