. 2024 Jan 2;14:226. doi: 10.1038/s41598-023-50137-w

Table 11.

Comparison of ARLs when $r_{o} = 370 and n = 20$ .

	Proposed HEPD when scale parameter is shifted using $λ =$ 4	Proposed chart based on HND	Exponential distribution based CC using RSS	Existing chart proposed by Naveed et al.⁸ based on HEPD	Existing chart proposed by Naveed et al.⁸ based on HND	Existing chart proposed by Aslam and Jun¹
Control coefficient $\to$	$W_{1} =$ 1.0607 $W_{2} = 1.0064$	$W_{1} =$ 1.2538 $W_{2} =$ 0.974	$W_{1} = 1.466$ $W_{2} = 1.469$	$k =$ 3.123	$k =$ 3.184	$k = 3.214$
Truncated constant $\to$	$q_{1} = 0.8561$	$q = 0.8602$	$h = 0.73433$	$h = 0.3728$	$h =$ 0.3192	$h = 0.2244$

Proposed HEPD when scale parameter is shifted using

λ =

Proposed chart based on HND

Exponential distribution based CC using RSS

Existing chart proposed by Naveed et al.⁸ based on HEPD

Existing chart proposed by Naveed et al.⁸ based on HND

Existing chart proposed by Aslam and Jun¹

Control coefficient

\to

$W_{1} =$ 1.0607

$W_{2} = 1.0064$

W_{1} =

1.2538

W_{2} =

0.974

$W_{1} = 1.466$

$W_{2} = 1.469$

k =

3.123

k =

3.184

k = 3.214

Truncated constant

\to

q_{1} = 0.8561

q = 0.8602

h = 0.73433

h = 0.3728

h =

0.3192

h = 0.2244

Shifts	$ARL$	$ARL$	$ARL$	$ARL$	$ARL$	$ARL$
1	373.27	373.85	371.05	370.26	370.16	370.571
0.97	38.11	42.83	90.12	292.24	293.62	300.077
0.95	21.27	23.98	52.22	248.94	250.99	260.157
0.93	13.82	15.60	33.93	211.59	214.12	225.166
0.90	8.35	9.43	20.02	165.13	168.09	180.721
0.85	4.41	5.00	9.95	108.03	111.15	124.189
0.80	2.71	3.08	5.64	69.69	72.57	84.412
0.70	1.86	2.11	3.51	27.85	29.84	37.758
0.60	1.42	1.58	2.37	10.65	11.81	16.256
0.50	1.06	1.13	1.38	4.05	4.65	6.854
0.10	1.00	1.01	1.07	1.00	1.00	1