A new reliability measure in ranked set sampling

Abstract

In this article, a dynamic reliability measure based on ranked set sampling is introduced, and its properties are investigated in theory and simulation. The results support the preference of the suggested index over the analogous one in simple random sampling. A data set from an agricultural experiment is analyzed for illustration.

Appendix

See Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13.

Fig. 1

Estimated REs for $X\sim W(2,1)$ and $Y\sim W(2,2)$ when $m,n = 2,5,10$

Fig. 2

Estimated REs for $X\sim W(2,1)$ and $Y\sim W(2,2)$ when $m,n = 20,50,100$

Fig. 3

Estimated REs for $X\sim W(2,1)$ and $Y\sim W(1,1)$ when $m,n = 2,5,10$

Fig. 4

Estimated REs for $X\sim W(2,1)$ and $Y\sim W(1,1)$ when $m,n = 20,50,100$

Fig. 5

Estimated REs for $X\sim W(1,1)$ and $Y\sim W(0.5,3)$ when $m,n = 2,5,10$

Fig. 6

Estimated REs for $X\sim W(1,1)$ and $Y\sim W(0.5,3)$ when $m,n = 20,50,100$

Fig. 7

Estimated REs for $X\sim N(0,(1.25)^2)$ and $Y\sim N(0,1)$ when $m,n = 2,5,10$

Fig. 8

Estimated REs for $X\sim N(0,(1.25)^2)$ and $Y\sim N(0,1)$ when $m,n = 20,50,100$

Fig. 9

Estimated REs for $X\sim U(0,1.5)$ and $Y\sim U(0,2)$ when $m,n = 2,5,10$

Fig. 10

Estimated REs for $X\sim U(0,1.5)$ and $Y\sim U(0,2)$ when $m,n = 20,50,100$

Fig. 11

Estimated MSEs under SRS when $m = n = 5,10,20$ for (a) $X\sim W(2,1)$ and $Y\sim W(2,2)$, (b) $X\sim N(0,(1.25)^2)$ and $Y\sim N(0,1)$ and (c) $X\sim U(0,1.5)$ and $Y\sim U(0,2)$

Fig. 12

Estimated MSEs under RSS when $m=n=5,10,20$ for (a) $X\sim W(2,1)$ and $Y\sim W(2,2)$, (b) $X\sim N(0,(1.25)^2)$ and $Y\sim N(0,1)$ and (c) $X\sim U(0,1.5)$ and $Y\sim U(0,2)$

Fig. 13

Estimated R(t) as a function of t for the apple trees data