Operating Characteristic Curve Outline Operating Characteristic Curve OC
- Slides: 7
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 1
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 2
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 3
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. 4
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. 5
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. 6
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. p 0. 95 the proportion of defectives for which Pa = 0. 95 Note: at this point producer’s risk, = 0. 05 or 5% 2. p 0. 50 the proportion of defectives for which Pa = 0. 50 3. p 0. 10 the proportion of defectives for which Pa = 0. 10 Note: at this point consumer’s risk, = 0. 10 or 10% 7
