Based on the LA port container cycle times shown above, which of the following statements fits best?

Question

BlackTom AI · Accepted Answer

X̄-chart upper control limit is computed as Ẍ + A2·R̄. For an X̄–R chart with subgroup size n = 4 the standard constants are A2 = 0.729, D3 = 0 and D4 = 2.282.

From the chart the centerlines read Ẍ (the grand average of subgroup means) ≈ 6.68 and R̄ (the average range) ≈ 2.66. Using the formulas:

1) Compute the X̄-chart UCL:
A2·R̄ = 0.729 × 2.66 = 1.93914
UCL_X̄ = Ẍ + A2·R̄ = 6.68 + 1.93914 = 8.61914 ≈ 8.62

2) For completeness compute the other limits:
LCL_X̄ = Ẍ − A2·R̄ = 6.68 − 1.93914 = 4.74086 ≈ 4.74 (so not 0)
UCL_R = D4·R̄ = 2.282 × 2.66 = 6.06612 ≈ 6.07 (so not 3.28)
LCL_R = D3·R̄ = 0 × 2.66 = 0 (so not 1.91)

Why the correct answer is correct: applying the standard X̄-chart formula with the chart’s reported grand mean (≈6.68), the average range (≈2.66), and the A2 constant for n = 4 yields UCL_X̄ ≈ 8.62, matching the statement.

Why the other choices are incorrect:
- “The upper control limit of the Range chart is 3.28”: using D4 for n = 4 gives UCL_R ≈ 6.07, not 3.28.
- “The lower control limit of the Xbar chart is 0”: the computed LCL_X̄ ≈ 4.74, so it is well above 0.
- “The lower control limit of the Range chart is 1.91”: for n = 4, D3 = 0 so LCL_R = 0, not 1.91.
- “None of the responses”: one response is correct, so this is false.

Conclusion: the statement “The upper control limit of the Xbar chart is 8.62” is correct, consistent with the chart values and control‑chart formulas.

Based on the LA port container cycle times shown above, which of the following statements fits best?Single choice

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