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 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

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

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.

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.

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.

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%