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CMA Intermediate · Operations Management and Strategic Management · Productivity Management and Quality Management

A p-chart is used to monitor the fraction defective in samples of 400 units from a Pune component line. The average fraction defective is 0.04. Using 3-sigma limits, what is the upper control limit (UCL)? (√(0.04×0.96/400) = 0.0098)

The UCL is 0.0694. For a p-chart, UCL equals the average fraction defective plus three times the standard error: 0.04 + 3 × 0.0098 = 0.0694. Sample fractions above this signal an out-of-control process.

  1. A0.0694
  2. B0.0494Correct
  3. C0.0098
  4. D0.0688

Explanation

UCL = p̄ + 3√(p̄(1−p̄)/n) = 0.04 + 3 × 0.0098 = 0.04 + 0.0294 = 0.0694. Option 0.0494 would use only 1 sigma, which is wrong. Option 0.0098 is just one standard error, and 0.0688 wrongly uses 0.0096.

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