Table 3: Approximated performance of the Phase I EWMA chart with λI = 0.6 obtained from randomly generated sets of k = 50 normal samples of size n for both the formulations of the ESEM and a nominal 1% FAR level.

Approach

n

TAP

FAP

d

d

0.4

1.0

1.6

2.0

0.0

0.4

1.0

1.6

2.0

Localized shifting pattern

Shen’s formulation

5

3.3

26.1

72.5

91.3

1.0

1.1

1.2

1.6

2.1

10

6.5

58.1

97.0

99.9

1.0

1.1

1.4

2.8

4.1

Zwetsloot’s

formulation

5

3.2

25.8

69.0

89.3

1.0

1.1

1.2

1.3

1.4

10

6.1

57.3

96.7

99.9

1.0

1.1

1.2

1.3

1.4

Diffuse shifting pattern

Shen’s formulation

5

1.3

1.4

2.1

3.0

0.9

1.0

1.0

1.0

1.1

10

1.0

1.3

1.5

2.1

1.0

1.0

1.0

1.1

1.1

Zwetsloot’s

formulation

5

1.2

1.2

1.5

2.3

1.0

0.9

1.0

0.9

0.9

10

1.0

1.2

1.3

1.5

1.1

1.0

1.1

1.0

1.0

Single step shifting pattern

Shen’s formulation

5

7.0

56.5

91.9

97.9

0.9

1.0

1.1

1.2

1.2

10

15.9

87.3

99.3

100.0

1.0

1.0

1.2

1.2

1.2

Zwetsloot’s

formulation

5

6.8

57.1

91.8

97.5

1.0

1.0

1.2

1.3

1.3

10

16.3

87.2

99.3

99.9

1.0

1.1

1.2

1.3

1.3

Multiple step shifting pattern

Shen’s formulation

5

5.8

47.9

86.8

95.9

1.0

1.2

1.6

2.0

2.3

10

12.7

80.9

98.2

99.8

1.0

1.3

1.7

3.2

3.6

Zwetsloot’s

 formulation

5

5.7

44.3

78.7

93.7

1.0

1.5

3.7

4.9

5.3

10

11.6

79.7

96.1

99.6

1.0

1.6

4.9

5.4

5.9