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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%