GATE 2023 MN – Question 36
Fixed-carbon control limits are 40%±15% at 3σ. Rule 1: four of five successive readings on the same side of the mean, more than 1σ away, indicate loss of control. Rule 2: any point beyond a 3σ limit indicates loss of control. For readings 49, 51, 56, 20, 46, 48, 47, 49, 45, 41, 42, 40%, classify the process.
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Correct answer: (A) Out of control under both rules
Explanation
Here σ = 15/3 = 5 percentage points. Readings above 45% are more than 1σ above the mean. The five-reading window 46, 48, 47, 49, 45 contains four such readings, so rule 1 is met. Also 56>55 and 20<25 violate the 3σ limits, so rule 2 is met. Thus A.