Why did you use this formula versus another formula? Answer: (R÷d2) was used instead of the formula for the sample standard deviation because (R÷d2) considers only short term variation, while the…

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Options

• A(R÷d2) was used instead of the formula for the sample standard deviation because (R÷d2) considers only short term variation, while the formula for the sample standard considers long term variation. (R÷d2) assumes that the process is stable. If the process is not stable, the out of control points will jump out of the control limits based on (R÷d2). The (R÷d2) limits are tighter than limits based on the sample standard deviation.

• A
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Explanation

Option A is correct because it accurately describes the fundamental distinction between two estimates of process variation in Statistical Process Control (SPC): R̄/d2 captures only within-subgroup (short-term) variation, while the sample standard deviation captures total variation - both within and between subgroups (long-term).

The logic behind using R̄/d2 is deliberate: control charts are designed to detect process shifts between subgroups. By basing control limits on short-term variation only, any special cause that causes a subgroup mean to shift will appear outside those tighter limits - which is exactly what you want. If you used the sample standard deviation (which already absorbs between-subgroup variation), the limits would be wider and less sensitive to detecting instability.

Since this question presents only one answer choice, there are no distractors to evaluate - it's testing recognition and understanding of the concept rather than elimination.

Memory tip: Think of R̄/d2 as the "within-the-box" estimate - it only sees variation inside each subgroup sample. The sample standard deviation sees the "whole picture," including drift over time. Control charts use the "within-the-box" estimate precisely so that between-box drift becomes visible as out-of-control signals.

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