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B. Panahbehagh and R. Bruggemann
Table 2 Selecting a RSS of size d × m in the case of d cycles of a RSS of size m. X (h)ij for
h, i = 1, 2, . . . , m and j = 1, 2, . . . , d is h-th order statistics in i-th set for j -th cycle. The
highlighted units will be selected as the final sample for full measurement and the other units will
be used just for ranking
Ranks
Cycle
Set
1
2
· · ·
m
1
1
X (1)11
X (2)11
· · ·
X (m)11
2
X (1)21
X (2)21
· · ·
X (m)21
. . .
. . .
. . .
. . .
. . .
m
X (1)m1
X (2)m1
· · ·
X (m)m1
2
1
X (1)12
X (2)12
· · ·
X (m)12
2
X (1)22
X (2)22
· · ·
X (m)22
. . .
. . .
. . .
. . .
. . .
m
X (1)m2
X (2)m2
· · ·
X (m)m2
. . .
. . .
. . .
. . .
. . .
d
1
X (1)1d
X (2)1d
· · ·
X (m)1d
2
X (1)2d
X (2)2d
· · ·
X (m)2d
. . .
. . .
. . .
. . .
. . .
m
X (1)md
X (2)md
· · ·
X (m)md
Table 3 Selecting a VSR of size n • =
m
m=1 d h . X (h)i for h, i = 1, 2, . . . , m is h-th order
statistics in i-th set. The highlighted units will be selected as the final sample (assuming) for full
measurement and the other units will be used just for ranking
Ranks
Set
1 (1-th Stratum)
2 (2-th Stratum)
· · ·
m (m-th Stratum)
Sets
1
X (1)1
X (2)1
· · ·
X (m)1
2
X (1)2
X (2)2
· · ·
X (m)2
3
X (1)3
X (2)3
· · ·
X (m)3
. . .
. . .
. . .
. . .
. . .
K
X (1)K
X (2)K
· · ·
X (m)K
with
V ( μ VSR ) =
σ 2
Km
+
1
m 2
m
h=1
1 −
d h
K
d h
σ
2
h
(1)
where μ h = E(X (h) ) and σ (h) = V (X (h) ) are the mean and variance of the hth order statistics based on f μ . As we can see in equation (1), if
d h
K −→ 0, then