Table 1 Means, Biases, MSEs and REs of the ML estimates of R based on SRS, RSS and ERSS.

From: Efficiency of ranked set sampling designs in power Lindley system reliability estimation with uncensored and right-censored data

(\(\alpha _1,\theta _1,\alpha _2,\theta _2\))

(\(k_x\),\(k_y\))

(\(n_x\),\(n_y\))

SRS

RSS

ERSS

\(RE_1\)

\(RE_2\)

Mean

Bias

MSE

Mean

Bias

MSE

Mean

Bias

MSE

(0.5,1,0.5,1)

(2,2)

(20,20)

0.4998

-0.0002

0.0087

0.4998

-0.0002

0.0057

0.5008

0.0008

0.0058

1.5228

1.4851

(2,3)

(20,30)

0.4999

-0.0001

0.0071

0.4994

-0.0006

0.0043

0.4996

-0.0004

0.0043

1.6606

1.6398

(3,3)

(30,30)

0.5008

0.0008

0.0057

0.4999

-0.0001

0.0029

0.5003

0.0003

0.0029

1.9742

1.9852

(3,4)

(30,40)

0.4996

-0.0004

0.0048

0.4997

-0.0003

0.0023

0.4999

-0.0001

0.0024

2.1046

2.0470

(4,4)

(40,40)

0.5003

0.0003

0.0042

0.4995

-0.0005

0.0017

0.5001

0.0001

0.0020

2.4355

2.0884

(4,5)

(40,50)

0.5006

0.0006

0.0037

0.5003

0.0003

0.0014

0.5006

0.0006

0.0016

2.5809

2.2890

(0.5,1,1,2)

(2,2)

(20,20)

0.3287

-0.0026

0.0075

0.3285

-0.0029

0.0053

0.3268

-0.0045

0.0052

1.4188

1.4514

(2,3)

(20,30)

0.3291

-0.0022

0.0073

0.3272

-0.0041

0.0048

0.3261

-0.0052

0.0048

1.5261

1.5297

(3,3)

(30,30)

0.3284

-0.0029

0.0050

0.3287

-0.0027

0.0026

0.3292

-0.0021

0.0027

1.8831

1.8700

(3,4)

(30,40)

0.3278

-0.0035

0.0049

0.3284

-0.0029

0.0025

0.3281

-0.0032

0.0025

1.9303

1.9608

(4,4)

(40,40)

0.3291

-0.0022

0.0037

0.3294

-0.0020

0.0016

0.3299

-0.0014

0.0019

2.2872

1.9828

(4,5)

(40,50)

0.3290

-0.0024

0.0036

0.3292

-0.0021

0.0015

0.3303

-0.0010

0.0017

2.4337

2.1179

(1,2,0.5,1)

(2,2)

(20,20)

0.6725

0.0038

0.0076

0.6724

0.0037

0.0052

0.6736

0.0049

0.0052

1.4648

1.4492

(2,3)

(20,30)

0.6736

0.0049

0.0054

0.6714

0.0027

0.0029

0.6719

0.0033

0.0030

1.8616

1.7991

(3,3)

(30,30)

0.6714

0.0027

0.0050

0.6719

0.0032

0.0026

0.6716

0.0029

0.0027

1.8811

1.8749

(3,4)

(30,40)

0.6710

0.0023

0.0040

0.6707

0.0020

0.0017

0.6700

0.0013

0.0020

2.2880

2.0224

(4,4)

(40,40)

0.6719

0.0032

0.0038

0.6707

0.0020

0.0016

0.6696

0.0009

0.0018

2.3689

2.0824

(4,5)

(40,50)

0.6702

0.0015

0.0031

0.6705

0.0018

0.0011

0.6699

0.0012

0.0013

2.7660

2.4404

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