In a control chart, the consecutive measurements are 11, 13, 09, 07, 08, 09, 09, 09, 08, and 12. For the entire process, the goal is 10 and the standard deviation is 1. For this data set, it is…

Question

Options

• Ais under control.
• Bis out of control.
• Chas an increasing trend.
• Dhas a decreasing trend.

• A
  14% (4)
• B
  71% (20)
• C
  7% (2)
• D
  7% (2)

Explanation

Option B is correct because two data points hit the control limits: the value 13 reaches the Upper Control Limit (UCL = goal + 3σ = 10 + 3 = 13) and the value 7 reaches the Lower Control Limit (LCL = 10 − 3 = 7) - any point at or beyond ±3σ from the mean signals an out-of-control process. Option A is wrong because touching a control limit is, by definition, an out-of-control event. Options C and D are wrong because the data shows no consistent directional trend - it starts high (11, 13), drops to a cluster of below-center values, then climbs back to 12, which is a non-systematic, erratic pattern rather than a sustained rise or fall.

Memory tip: Think "3-sigma = alarm" - calculate UCL and LCL first (goal ± 3σ), then scan the data; if any single point lands on or outside those lines, the answer is always "out of control," no matter what the surrounding points look like.

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