Table 9 The run length characteristic (ARL, SDRL (in 2nd row) and MDRL (in 3rd row)) of the proposed EWMA-SR and HWMA-SR for different distributions when \(n=15\) and \(ARL_0=500\).

From: Efficient signed-rank based EWMA and HWMA repetitive control charts for monitoring process mean with and without auxiliary information

EWMA-SR Repetitive

HWMA-SR Repetitive

\(\delta\)

\(\omega =0.03\)

\(\omega =0.05\)

\(\omega =0.2\)

\(\omega =0.03\)

\(\omega =0.05\)

\(\omega =0.2\)

Normal (0,1)

0.0

500.4

499.8

500.5

500.8

501.5

500.9

498.3

471.6

505.8

515.9

454.9

412.1

359

369

333

403

421

450

0.1

23.5

36.8

53.6

17.2

21.2

23.1

15.9

25.2

49.1

24.5

16.3

22.7

20

30

39

8.5

18.5

19.5

0.5

3.4

4.4

5.2

1.4

1.7

1.8

0.9

1.1

0.8

0.8

0.8

1.1

3

4

5

1

1.5

1

1

2

2

2

1

1

1

0.3

0.5

0.8

0

0

0

2

2

2

1

1

!

3

2

2

2

1

1

1

0

0

0

0

0

0

2

2

2

1

1

1

Laplace (0,\(1/\sqrt{2}\))

0.0

503.6

504.0

504.2

501.7

499.1

501.9

490.3

512.5

501.1

556.8

537.9

542.2

343.5

340

333.5

395

386

260.5

0.1

14.9

15.7

29.0

8.7

13.4

15.9

9.2

11.1

25.6

7.1

11.3

16.6

13

13

21

7

10

7

0.5

3.1

2.5

2.7

1.2

1.2

1.4

0.8

0.7

0.7

0.6

0.6

0.7

3

2

2

1

1

1

1

2

2

2

1

1

1

0.3

0.1

0.4

0

0

0

2

2

2

1

1

1

3

2

2

2

1

1

1

0

0

0

0

0

0

2

2

2

1

1

1

LG (0,\(\sqrt{3}/\pi\))

0.0

501.2

502.3

502.9

505.3

499.3

499.0

510.9

509.9

496.3

461.1

413.1

362.7

423.2

340

355

413

380.5

497

0.1

20.4

21.7

45.4

10.1

14.6

22.5

13.8

16.7

41.6

9.7

16.1

15.4

17

17

33

5.5

9

20

0.5

3.3

2.6

2

1.2

1.4

1.5

0.9

0.8

0.7

0.6

0.9

0.8

3

2

2

1

1

1

1

2

2

2

1

1

1

0.2

0.2

0

0

0

0

2

2

2

1

1

1

3

2

2

2

1

1

1

0

0

0

0

0

0

2

2

2

1

1

1

Student’s t-Distribution (4)

0.0

499.0

502.8

500.3

502.2

500.4

500.7

487.5

504.8

498.7

421.3

488.6

386.5

357.5

353.5

348

465.5

254.5

362.5

0.1

23.1

34.2

51.2

11.5

15.7

20.3

17.3

24.6

49.5

13.6

18.5

17.6

20

28

36

5.5

11.5

17.5

0.5

3.4

2.1

2

1.5

1.6

1.3

0.9

1.1

0.8

0.8

0.9

0.9

3

2

2

1

1

1

1

2.1

2.5

2

1

1

1

0.3

0.5

0

0

0

0

2

2

2

1

1

!

3

2

2

2

1

1

1

0

0

0

0

0

0

2

2

2

1

1

1

Student’s t-Distribution (8)

0.0

499.4

499.0

501.4

499.2

499.9

507.6

493.6

511.3

498.3

497.7

476.9

462.8

348

340

342.5

415

389.5

377.5

0.1

23.6

34.9

53.2

14.4

19.8

21

18.3

24.9

51.9

14.9

20.9

21.2

18

27

36.5

11

11.5

11

0.5

3.4

4.1

2.1

1.4

1.4

1.5

0.9

1.1

0.9

0.8

0.8

0.8

3

4

2

1

1

1

1

2.1

2.4

2

1

1

1

0.3

0.5

0

0

0

0

2

2

2

1

1

1

3

2

2

2

1

1

1

0

0

0

0

0

0

2

2

2

1

1

1

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