Quality Textiles International Scenario

Quality Textiles International Scenario

Since Quality Textiles quality assurance department checks their product regularly, they know that their process for fabric weight has a mean of 2.73 oz/in² and a standard deviation of 0.31. Goetsch and Davis (2010), wrote " UCL and LCL represent the ±3σ limits of the process averages and are drawn as dashed lines on the control charts" (p.450). They further wrote that "99.73% of all sample values will be found between + 3σ and -3σ" ( p. 366). Based on this information the following limits can be derived:

Lower Control Limit (LCL) = 2.73 - 3(.31) = 1.80 ( LCL = μ - 3σ)

Upper Control Limit (UCL) = 2.73 + 3(.31) = 3.66 ( UCL = μ + 3σ)

The table presented below provides the data retrieved from the University of Phoenix student website. The mean, standard deviation, and histogram of the provided data follow.

# of Samples x values C.1xC2 d d² Col 1 x Col5

1 1.92 1.92 -1.06 1.12 1.12

1 2 2 -0.98 0.96 0.96

1 2.06 2.06 -0.92 0.85 0.85

1 2.32 2.32 -0.66 0.44 0.44

1 2.36 2.36 -0.62 0.38 0.38

1 2.41 2.41 -0.57 0.32 0.32

2 2.43 4.86 -0.55 0.3 0.6

1 2.44 2.44 -0.54 0.29 0.29

1 2.46 2.46 -0.52 0.27 0.27

1 2.57 2.57 -0.41 0.17 0.17

1 2.61 2.61 -0.37 0.14 0.14

1 2.62 2.62 -0.36 0.13 0.13

1 2.63 2.63 -0.35 0.12 0.12

1 2.69 2.69 -0.29 0.08 0.08

1 2.71 2.71 -0.27 0.07 0.07

1 2.74 2.74 -0.24 0.06 0.06

1 2.75 2.75 -0.23 0.05 0.05

1 2.78 2.78 -0.2 0.04 0.04

1 2.79 2.79 -0.19 0.04 0.04

1 2.8 2.8 -0.18 0.03 0.03

2 2.81 5.62 -0.17 0.03 0.06

1 2.86 2.86 -0.12 0.01 0.01

1 2.9 2.9 -0.08 0.01 0.01

1 2.94 2.94 -0.04 0 0

1 3 3 0.02 0 0

1 3.02 3.02 0.04 0 0

1 3.06 3.06 0.08 0.01 0.01

1 3.09 3.09 0.11 0.01 0.01

1 3.12 3.12 0.14 0.02 0.02

1 3.18 3.18 0.2 0.04 0.04

1 3.26 3.26 0.28 0.08 0.08

1 3.29 3.29 0.31 0.1 0.1

2 3.3 6.6 0.32 0.1 0.2

1 3.31 3.31 0.33 0.11 0.11

1 3.33 3.33 0.35 0.12 0.12

1 3.34 3.34 0.36 0.13 0.13

2 3.35 6.7 0.37 0.14 0.28

1 3.44 3.44 0.46 0.21 0.21

1 3.5 3.5 0.52 0.27 0.27

1 3.55 3.55 0.57 0.32 0.32

1 3.65 3.65 0.67 0.45 0.45

1 3.78 3.78 0.8 0.64 0.64

1 3.99 3.99 1.01 1.02 1.02

2 4 8 1.02 1.04 2.08

1 4.01 4.01 1.03 1.06 1.06

n= 50 ∑ X=149.06 ∑ d² =13.39

Mean (μ) Standard