Table 2 Run length profile of Bayesian Max-EWMA control chart as a result of a shift in Weibull parameters W(1, 1.5) with \(\gamma\)=0.25 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

2.46 (1.17)

2.74 (0.79)

2.79 (0.71)

2.84 (0.65)

2.87 (0.58)

2.93 (0.54)

2.98 (0.53)

2.99 (0.43)

3.03 (0.39)

3.05 (0.37)

3.05 (0.31)

3.01 (0.27)

5

1.87 (0.77)

2.10 (0.46)

2.12 (0.39)

2.12 (0.34)

2.12 (0.33)

2.11 (0.32)

2.12 (0.33)

2.11 (0.32)

2.12 (0.33)

2.12 (0.32)

2.09 (0.29)

2.03 (0.19)

7

1.60 (0.62)

1.84 (0.42)

1.90 (0.33)

1.95 (0.25)

1.97 (0.17)

1.99 (0.10)

1.99 (0.07)

1.99 (0.04)

1.99 (0.03)

1.99 (0.02)

1.99 (0.05)

1.98 (0.10)

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

1.96 (1.00)

5.74 (2.99)

6.22 (2.92)

6.78 (3.04)

7.28 (3.18)

7.58 (3.02)

7.89 (3.09)

7.92 (3.01)

7.67 (2.80)

7.19 (2.54)

5.61 (1.82)

4.52 (1.22)

5

1.48 (0.63)

3.97 (1.66)

4.15 (1.55)

4.38 (1.69)

4.52 (1.39)

4.57 (1.28)

4.54 (1.19)

4.44 (1.10)

4.18 (1.00)

3.85 (0.91)

3.09 (0.65)

2.65 (0.53)

7

1.25 (0.46)

3.18 (1.19)

3.29 (1.07)

3.42 (0.99)

3.54 (0.93)

3.52 (0.82)

3.49 (0.75)

3.37 (0.71)

3.16 (0.66)

2.93 (0.60)

2.36 (0.49)

2.06 (0.26)

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

1.51 (0.71)

13.13 (9.90)

26.32 (22.10)

45.30 (39.60)

59.18 (53.36)

50.09 (43.58)

32.10 (26.23)

22.55 (17.06)

15.92 (10.83)

12.31 (7.34)

7.35 (3.11)

5.45 (1.79)

5

1.17 (0.40)

8.49 (5.55)

15.71 (11.85)

22.41 (17.22)

23.19 (17.42)

16.22 (10.93)

10.61 (5.99)

7.91 (3.78)

6.18 (2.50)

5.22 (1.83)

3.67 (0.91)

3.01 (0.62)

1.07 (0.26)

6.49 (3.69)

11.26 (7.79)

14.61 (9.95)

13.90 (8.94)

9.54 (5.13)

6.59 (2.87)

4.23 (1.32)

4.25 (1.31)

3.69 (0.99)

2.75 (0.60)

2.29 (0.46)

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

1.31 (0.55)

12.51 (9.61)

61.46 (57.13)

370.87 (367.43)

348.36 (344.16)

142.09 (138.02)

73.03 (66.94)

39.54 (33.40)

25.911 (20.49)

19.30 (13.62)

8.89 (4.45)

6.42 (2.41)

5

1.09 (0.29)

7.58 (4.94)

39.57 (35.42)

370.89 (365.34)

173.67 (170.29)

47.57 (42.11)

20.20 (14.96)

12.35 (7.48)

8.89 (4.60)

7.14 (3.19)

4.17 (1.20)

3.36 (0.77)

10

1.02 (0.15)

5.56 (3.14)

28.26 (24.46)

370.87 (364.22)

105.35 (100.46)

25.09 (19.74)

11.31 (6.90)

7.48 (3.61)

5.68 (2.26)

1.94 (0.22)

3.06 (0.71)

2.57 (0.55)

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

1.21 (0.45)

7.12 (4.76)

17.29 (13.83)

31.77 (27.64)

40.80 (35.39)

43.02 (37.31)

22.66 (16.88)

36.07 (30.02)

28.31 (22.21)

23.14 (16.89)

11.16 (6.11)

7.56 (3.23)

5

1.05 (0.21)

4.61 (2.54)

10.81 (7.48)

20.05 (16.16)

21.90 (17.12)

21.10 (15.69)

17.50 (12.17)

13.62 (8.24)

10.41 (5.50)

8.67 (4.10)

4.97 (1.61)

3.09 (0.65)

10

1.01 (0.10)

3.56 (1.70)

8.01 (5.09)

14.35 (10.79)

15.09 (10.87)

13.52 (8.89)

10.94 (6.17)

8.55 (4.07)

6.74 (2.70)

5.71 (2.06)

3.56 (0.92)

2.82 (0.62)

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

1.16 (0.39)

4.40 (2.52)

7.48 (4.96)

9.34 (6.31)

9.79 (6.21)

9.76 (5.90)

9.46 (5.33)

9.04 (4.81)

8.52 (4.23)

8.07 (3.67)

6.87 (2.38)

5.98 (1.69)

5

1.03 ( 0.18)

3.10 (1.47)

5.16 (2.85)

6.29 (3.53)

6.20 (3.27)

6.10 (2.96)

5.75 (2.48)

5.46 (2.16)

5.22 (1.86)

4.88 (1.57)

3.62 (0.78)

3.64 (0.73)

7

1.00 (0.07)

2.51 (1.05)

4.10 (1.96)

4.97 (2.47)

4.82 (2.17)

4.60 (1.92)

4.41 (1.62)

4.17 (1.35)

3.95 (1.18)

3.75 (1.00)

3.24 (0.64)

2.85 (0.51)

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

1.10 (0.32)

2.42 (1.22)

3.49 (1.76)

3.82 (1.88)

2.99 (1.14)

3.70 (1.51)

3.60 (1.32)

3.47 (1.16)

3.40 (1.06)

3.33 (0.97)

3.11 (0.70)

2.98 (0.54)

5

1.01 (0.13)

1.80 (0.77)

2.59 (1.09)

2.84 (1.16)

2.81 (1.03)

2.71 (0.90)

2.64 (0.80)

2.55 (0.70)

2.49 (0.63)

2.58 (0.64)

2.27 (0.46)

2.15 (0.36)

7

1.00 (0.04)

1.52 (0.60)

2.19 (0.83)

2.36 (0.84)

2.33 (0.76)

2.27 (0.66)

2.21 (0.58)

2.14 (0.49)

2.11 (0.44)

2.09 (0.39)

2.01 (0.21)

1.99 (0.11)

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

1.07 (0.26)

1.70 ( 0.81)

2.34 (1.09)

2.59 (1.10)

2.56 (0.99)

2.51 (0.87)

2.46 (0.77)

2.41 (0.69)

2.34 (0.61)

2.32 (0.56)

2.18 (0.41)

2.10 ( 0.31)

5

1.00 (0.08)

1.30 (0.50)

1.82 (0.73)

1.97 (0.73)

1.96 (0.60)

1.95 (0.59)

1.91 (0.53)

1.89 (0.48)

1.87 (0.43)

1.86 (0.41)

1.85 (0.35)

1.86 (0.34)

7

1.00 (0.02)

1.14 (0.36)

1.54 (0.59)

1.68 (0.61)

1.90 (0.69)

1.65 (0.53)

1.62 ( 0.51)

1.60 (0.50)

1.57 (0.49)

1.57 (0.49)

1.47 (0.49)

1.40 (0.49)

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

1.05 (0.23)

1.36 (0.60)

1.77 (0.81)

2.01 (0.83)

2.02 (0.75)

2.00 (0.68)

1.95 (0.60)

1.93 (0.54)

1.90 (0.50)

1.90 (0.46)

1.88 (0.36)

1.89 (0.31)

5

1.00 (0.07)

1.18 (0.40)

1.39 (0.55)

1.57 (0.61)

1.57 (0.57)

1.55 (0.54)

1.52 (0.53)

1.51 (0.51)

1.47 (0.50)

1.45 (0.49)

1.35 (0.47)

1.25 (0.43)

7

1.00 (0.01)

1.04 (0.19)

1.21 (0.42)

1.34 (0.49)

1.33 (0.48)

1.29 ( 0.45)

1.24 (0.43)

1.22 (0.41)

1.17 (0.38)

1.14 (0.35)

1.04 (0.21)

1.01 (0.12)

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

1.03 (0.19)

1.16 (0.39)

1.26 (0.49)

1.42 (0.59)

1.48 (0.59)

1.47 (0.55)

1.43 (0.51)

1.41 (0.50)

1.38 (0.49)

1.36 (0.48)

1.27 (0.44)

1.19 (0.39)

5

1.00 (0.04)

1.02 (0.16)

1.08 (0.27)

1.16 (0.38)

1.19 (0.40)

1.15 ( 0.36)

1.12 (0.33)

1.09 (0.29)

1.06 (0.25)

1.05 (0.21)

1.00 (0.09)

1.00 (0.03)

7

1.00 (0.01)

1.00 (0.06)

1.02 (0.14)

1.05 (0.23)

1.06 (0.25)

1.04 (0.20)

1.02 (0.16)

1.01 (0.11)

1.00 (0.08)

1.00 (0.05)

1.27 (0.47)

1.00 (0.00)