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%