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Operating Characteristic Curve

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. OC Curve of an Ideal Sampling Plan.

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Operating Characteristic Curve

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  1. 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

  2. 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

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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%

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