1 operating characteristic curve outline operating characteristic curve –oc curve of an ideal...
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Operating Characteristic Curve
Outline• Operating Characteristic Curve
– OC curve of an ideal sampling plan– Effect of changing the sampling plan– Type A and Type B OC curve– Three special points on the OC curve
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OC Curve of an Ideal Sampling Plan
• Suppose that 2% is the maximum tolerable proportion defective in a lot
• So, an ideal sampling scheme would reject all lots that were worse than 2% defective and accepted all lots 2% defective better
• The OC Curve of such an ideal scheme would be vertical at p=0.02
• However, no sampling plan can give such an ideal OC curve
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Effect of Changing the Sampling Plan
• The larger the sample size, the steeper the slope of the OC Curve– Note that this statement is true if both n and c are
increased proportionately.
• If only n increases, every Pa decreases and the curve shifts downward - so, producer’s risk increases and consumer’s risk decreases
• If only c increases, every Pa increases and the curve shifts upward - so, producer’s risk decreases and consumer’s risk increases
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Type A and Type B OC Curve
• Type A OC Curve– Assumes a finite lot. So, – Hypergeometric distribution is the correct one.– Binomial or Poisson distribution often provides a
good approximation.– Such curves are discontinuous e.g., there cannot
be 1% defective in a lot of 750.
N
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Type A and Type B OC Curve
• Type B curve– Assumes an infinite lot.– Binomial distribution is the correct one.– Poisson distribution often provides a good
approximation.
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Type A and Type B OC Curve
• Type A curve is always lower than the Type B curve. Type A curve always has less probability of acceptance than Type B curve.
• As the lot size increases, type A curve approaches Type B curve.
• If , then both the curves are almost identical.
• So far, we have constructed Type B curves.
100./ Nn
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Three Special Points on the OC Curve
• Three points on the OC curve have been given particular importance in the design of systems of sampling plans:
1. p0.95 the proportion of defectives for which Pa = 0.95
Note: at this point producer’s risk, = 0.05 or 5%
2. p0.50 the proportion of defectives for which Pa = 0.50
3. p0.10 the proportion of defectives for which Pa = 0.10
Note: at this point consumer’s risk, = 0.10 or 10%