Question:
Five samples of size 80 are inspected. A p-chart with ±3σ limits is used. The defective counts are 4, 10, 5, 6, and 5. The upper control limit (fraction defective) is \(\underline{\hspace{2cm}}\) (round off to two decimal places).
Five samples of size 80 are inspected. A p-chart with ±3σ limits is used. The defective counts are 4, 10, 5, 6, and 5. The upper control limit (fraction defective) is \(\underline{\hspace{2cm}}\) (round off to two decimal places).
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For p-charts, use \( \bar{p} \pm 3\sigma_p \), where \( \sigma_p = \sqrt{\bar{p}(1-\bar{p})/n} \).
Updated On: Jan 13, 2026
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Verified By Collegedunia
Correct Answer: 0.15
Solution and Explanation
Total sample size:
\[
5 \times 80 = 400.
\]
Total number of defectives:
\[
4 + 10 + 5 + 6 + 5 = 30.
\]
Fraction defective:
\[
\bar{p} = \frac{30}{400} = 0.075.
\]
Standard deviation:
\[
\sigma_p = \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}
= \sqrt{\frac{0.075 \times 0.925}{80}}
= \sqrt{0.000867} = 0.02947.
\]
Upper control limit:
\[
UCL = \bar{p} + 3\sigma_p
= 0.075 + 3(0.02947)
= 0.075 + 0.08841
= 0.16341.
\]
Rounded to two decimals:
\[
UCL = 0.16.
\]
Final Answer: \(0.16\)
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