Table 1 Run length profile of Bayesian Max-EWMA control chart as a result of a shift in Weibull parameters W(1, 1.5) with \(\gamma\) = 0.10 and considering subgroup size as 3, 5, and 7.

0.25

(µ,σ)

(−1.51,2.04)

(−1.49,0.89)

(−1.45,0.72)

(−1.42,0.61)

(−1.40,0.53)

(−1.38,0.47)

(−1.36,0.42)

(−1.35,0.38)

(−1.33,0.35)

(−1.32,0.32)

(−1.29,0.25)

(−1.28,0.20)

3

3.25 (1.23)

3.47 (0.76)

3.53 (0.65)

3.59 (0.60)

3.63 (0.56)

3.69 (0.53)

3.75 (0.51)

3.79 (0.46)

3.84 (0.43)

3.90 (0.36)

3.96 (0.30)

3.95 (0.22)

5

2.52 (0.81)

2.69 (0.56)

2.77 (0.49)

2.84 (0.42)

2.90 (0.35)

2.93 (0.30)

2.97 (0.22)

2.98 (0.17)

3.00 (0.12)

3.00 (0.09)

2.99 (0.09)

2.96 (0.18)

7

2.18 (0.62)

2.27 (0.45)

2.29 (0.45)

2.32 (0.47)

2.35 (0.47)

2.39 (0.48)

2.45 (0.49)

2.49 (0.49)

2.56 (0.49)

2.60 (0.48)

2.67 (0.46)

2.45 (0.49)

0.50

(µ,σ)

(−0.68,3.16)

(−0.87,1.11)

(−0.84,0.90)

(−0.81,0.76)

(−0.78,0.66)

(−0.76,0.58)

(−0.74,0.53)

(−0,72,0.48)

(−0.71,0.44)

(−0.70,0.40)

(−0.66,0.31)

(−0.64,0.25)

3

2.67 (1.15)

6.38 (2.38)

6.61 (2.12)

6.94 (1.98)

7.22 (1.83)

7.33 (1.64)

7.47 (1.59)

7.49 (1.48)

7.33 (1.40)

7.05 (1.34)

5.97 (1.17)

5.16 (0.90)

5

1.32 (0.46)

4.78 (1.53)

4.89 (1.31)

5.07 (1.19)

5.24 (1.09)

5.30 (0.98)

5.33 (0.91)

5.20 (0.86)

4.96 (0.80)

4.67 (0.78)

3.87 (0.60)

3.38 (0.51)

7

1.63 (0.57)

3.95 (1.13)

4.06 (0.98)

4.20 (0.89)

4.33 (0.81)

4.35 (0.71)

4.35 (0.67)

4.21 (0.64)

4.00 (0.63)

3.71 (0.59)

3.09 (0.40)

2.83 (0.38)

0.75

(µ,σ)

(0.01,4.18)

(−0.42,1.30)

(−0.39,1.05)

(−0.36, 0.88)

(−0.34,0.77)

(−0.32, 0.68)

(−0.29, 0.61)

(−0.28,0.56)

(−0.26,0.51)

(−0.25,0.47)

(−0.21,0.37)

(−0.18,0.30)

3

1.98 (0.88)

13.17 (7.45)

19.84 (12.19)

24.29 (14.79)

25.45 (14.48)

21.41 (10.90)

17.09 (7.96)

13.76 (5.55)

11.31 (4.07)

9.76 (3.08)

7.10

5.87 (1.18)

5

1.49 (0.57)

9.38 (4.40)

13.36 (6.90)

15.53 (7.53)

14.69 (6.15)

11.76 (4.33)

9.18 (2.93)

7.63 (2.16)

6.46 (1.62)

5.73 (1.28)

4.44 (0.79)

3.79 (0.60)

1.24 (0.43)

7.50 (3.16)

10.48 (4.85)

11.79 (5.05)

11.03 (3.91)

8.75 (2.63)

6.81 (1.85)

5.74 (1.37)

4.95 (1.02)

4.45 (0.86)

3.51 (0.57)

3.05 (0.37)

1.0

(µ,σ)

(0.61,5.00)

(−0.05,1.47)

(−0.03,1.18)

(0.00, 1.00)

(0.03,0.87)

(0.05,0.77)

(0.07,0.69)

(0.09,0.63)

(0.11,0.58)

(0.12,0.54)

(0.16,0.41)

(0.19,0.34)

3

1.64 (0.72)

13.49 (8.07)

54.86 (45.68)

370.93 (366.30)

175.64 (164.11)

56.06 (43.89)

25.21 (14.91)

19.93 (10.69)

15.17 (6.67)

12.85 (5.03)

8.04 (2.16)

6.55 (1.44)

5

1.26 (0.47)

8.48 (4.10)

31.98 (24.00)

369.15 (363.70)

80.19 (69.05)

24.05 (14.24)

13.71 (5.98)

10.14 (3.62)

8.16 (2.47)

7.12 (1.95)

4.88 (0.95)

4.13 (0.69)

10

1.10 (0.31)

6.53 (2.80)

23.33 (15.76)

370.78 (366.11)

49.18 (38.50)

16.04 (7.92)

9.72 (3.51)

7.43 (2.19)

6.17 (1.55)

5.39 (1.23)

3.84 (0.65)

3.28 (0.50)

1.25

(µ,σ)

(1.17,5.69)

(0.28,1.65)

(0.29,1.31)

(0.32,1.11)

(0.35,0.96)

(0.37,0.86)

(0.39,0.77)

(0.41,0.70)

(0.43, 0.64)

(0.45,0.60)

(0.49,0.46)

(0.52,0.38)

3

1.46 (0.63)

8.55 (4.46)

17.12 (10.76)

24.91 (17.03)

25.22 (16.24)

23.21 (13.62)

20.39 (10.21)

17.54 (7.84)

14.97 (5.75)

13.28 (4.62)

9.10 (2.49)

7.32 (1.74)

5

1.17 (0.38)

5.69 (2.38)

11.35 (5.94)

16.92 (9.87)

16.24 (8.73)

14.70 (6.86)

12.65 (4.90)

10.64 (3.45)

9.08 (2.58)

8.11 (2.14)

6.03 (1.38)

6.63 (1.65)

10

1.05 (0.23)

4.49 (1.66)

8.81 (4.02)

13.14 (6.87)

12.38 (5.88)

11.23 (4.47)

9.62 (3.14)

8.18 (2.26)

6.98 (1.70)

6.26 (1.43)

4.32 (0.81)

3.59 (0.59)

1.50

(µ, σ)

(1.67, 6.26)

(0.58, 1.86)

(0.58, 1.44)

(0.61, 1.21)

(0.64, 1.05)

(0.66, 0.94)

(0.68, 0.84)

(0.70, 0.77)

(0.72, 0.71)

(0.74, 0.65)

(0.79, 0.51)

(0.82, 0.41)

3

1.35 (0.56)

5.69 (2.63)

8.64 (4.27)

9.82 (4.76)

9.54 (4.21)

9.15 (3.65)

8.82 (3.07)

8.41 ( 2.68)

8.13 (2.39)

7.73 (1.99)

6.89 (1.33)

6.35 (1.00)

5

1.10 ( 0.31)

4.00 ( 1.49)

6.23 ( 2.54)

7.06 ( 2.89)

6.80 ( 2.50)

6.55 ( 2.13)

6.29 ( 1.81)

6.04 ( 1.57)

5.76 ( 1.35)

5.57 ( 1.17)

4.97 ( 0.78)

12.32 ( 5.02)

7

1.02 ( 0.16)

3.31 ( 1.12)

5.09 ( 1.86)

5.80 ( 2.16)

5.58 ( 1.86)

3.02 ( 0.99)

5.11 ( 1.31)

4.96 ( 1.16)

4.77 ( 0.99)

4.40 ( 0.69)

4.08 ( 0.59)

3.67 ( 0.52)

2.00

(µ, σ)

(2.57, 7.16)

(1.16, 2.43)

(1.11, 1.70)

(1.13, 1.41)

(1.15, 1.23)

(1.18, 1.09)

(1.20, 0.98)

(1.23, 0.89)

(1.25, 0.82)

(1.26, 0.76)

(1.32, 0.59)

(1.36, 0.48)

3

1.24 (0.46)

3.53 (1.47)

4.47 (1.81)

4.70 (1.76)

4.64 (1.58)

4.49 (1.37)

4.40 (1.21)

4.26 (1.04)

4.16 (0.94)

4.13 (0.86)

3.87 (0.64)

3.75 (0.54)

5

1.05 ( 0.23)

2.44 ( 0.82)

3.41 ( 1.15)

3.60 ( 1.17)

3.52 ( 1.01)

2.26 ( 0.47)

3.34 ( 0.78)

3.26 ( 0.69)

3.19 ( 0.62)

3.16 ( 0.56)

3.02 ( 0.40)

2.96 ( 0.29)

7

1.01 ( 0.11)

2.07 ( 0.63)

2.89 ( 0.89)

3.02 ( 0.88)

2.97 ( 0.79)

2.89 ( 0.69)

2.83 ( 0.62)

2.77 ( 0.57)

2.71 ( 0.54)

2.68 ( 0.52)

2.57 ( 0.49)

2.46 ( 0.49)

2.50

(µ, σ)

(3.33, 7.82)

(1.74, 3.18)

(1.59, 2.05)

(1.59, 1.61)

(1.62, 1.39)

(1.64, 1.23)

(1.67, 1.11)

(1.69, 1.01)

(1.72, 0.93)

(1.73, 0.86)

(1.80, 0.67)

(1.84, 0.55)

3

1.18 (0.41)

2.26 (0.94)

3.14 (1.18)

3.31 (1.13)

3.25 (1.00)

3.18 (0.89)

3.11 (0.77)

3.06 (0.71)

3.01 (0.64)

2.99 (0.60)

2.88 (0.46)

2.82 (0.46)

5

1.03 ( 0.18)

1.74 ( 0.63)

2.45 ( 0.78)

2.60 ( 0.77)

2.55 ( 0.68)

2.49 ( 0.60)

2.43 ( 0.55)

2.40 ( 0.52)

2.33 ( 0.49)

2.31 ( 0.46)

2.16 ( 0.37)

2.08 ( 0.27)

7

1.00 ( 0.07)

1.49 ( 0.54)

2.10 ( 0.62)

2.25 ( 0.59)

2.22 ( 0.52)

2.16 ( 0.44)

2.13 ( 0.38)

2.09 ( 0.32)

2.05 ( 0.27)

2.04 ( 0.23)

2.00 ( 0.08)

2.00 ( 0.02)

3.00

(µ, σ)

(4.00, 8.33)

(2.35, 4.00)

(2.08, 2.58)

(2.03, 1.86)

(2.04, 1.55)

(2.07, 1.37)

(2.10, 1.24)

(2.12, 1.13)

(2.15, 1.04)

(2.17, 0.96)

(2.24, 0.75)

(2.29, 0.61)

3

1.13 (0.35)

1.75 (0.75)

2.38 (0.92)

2.64 (0.88)

2.63 (0.76)

2.58 (0.69)

2.51 (0.61)

2.49 (0.61)

2.43 (0.54)

2.40 (0.51)

2.28 (0.45)

2.16 (0.36)

5

1.02 (0.14)

1.37 (0.51)

1.88 (0.63)

2.11 (0.62)

2.11 (0.52)

2.08 (0.43)

2.05 (0.37)

2.03 (0.32)

2.01 (0.28)

2.00 (0.23)

1.99 (0.10)

1.99 (0.05)

7

1.00 (0.06)

1.18 (0.39)

1.75 (0.54)

1.84 (0.52)

1.86 (0.46)

1.85 (0.42)

1.85 (0.38)

1.85 (0.36)

1.85 (0.35)

1.85 (0.35)

1.87 (0.33)

1.87 (0.32)

4.00

(µ, σ)

(5.12, 9.07)

(3.61, 5.53)

(3.15, 3.99)

(2.93, 2.81)

(2.86, 2.07)

(2.86, 1.68)

(2.88, 1.48)

(2.91, 1.35)

(2.94, 1.24)

(2.96, 1.15)

(3.04, 0.89)

(3.10, 0.73)

3

1.10 (0.31)

1.33 (0.54)

1.61 (0.67)

1.86 (0.71)

1.97 (0.62)

1.94 (0.71)

1.94 (0.70)

1.95 (0.40)

1.95 (0.35)

1.94 (0.32)

1.96 (0.20)

1.97 (0.17)

5

1.01 (0.11)

1.10 (0.30)

1.26 (0.45)

1.50 (0.55)

1.59 (0.53)

1.59 (0.50)

1.59 (0.49)

1.58 (0.49)

1.56 (0.49)

1.55 (0.49)

1.48 (0.49)

1.42 (0.49)

7

1.00 (0.03)

1.02 (0.15)

1.05 (0.22)

1.29 (0.46)

1.34 (0.48)

1.32 (0.46)

1.29 (0.45)

1.24 (0.43)

1.20 (0.40)

1.17 (0.37)

1.07 (0.26)

1.02 (0.15)