Single Sampling Plan

Single Sampling Plan

A single sampling plan is a plan, in which, one sample of specific size is taken to decide on the acceptability of the lot. The following are the parameters on which it operates : N = Lot size ; n = sample size and c = Acceptance number.

OPERATING CHARACTERISTIC CURVE (O.C. CURVE)

Operating Characteristic Curve is a plot of submitted lot quality versus the Probability of acceptance. It is an excellent evaluation technique of a sampling plan. In judging a particular sampling plan it is desirable to know the probability that the lot submitted with a certain percentage defective will be accepted or rejected. The following figure shows an OC curve.

The figure indicates a 100% probability of acceptance of submitted lot when the quality of lot is zero percent defective and a near 0% probability of acceptance for those lots having 12% defective. Point A and B on the OC curve refer respectively to the acceptable quality level (AQL) and the lot tolerance percent defective (LTPD). Point A is situated on the OC curve at an intersection of a horizontal drawn through the 97.5% probability point. While point B, is at the intersection of 10% horizontal line and the curve. Their probability percentages agree with AQL and LTPD acceptance probabilities that are common.

The corresponding quality of lots submitted for inspection in the figure shown is AQL 1% and LTPD is 9.1%. The OC curve permits the determination of the probability of acceptance for lots of varying quality. The OC Curve depicts the graphical relationship between arrangement of lot quality levels and the corresponding probability of acceptance and is based on the poisson’s distribution.

The following two parameters are needed to calculate and plot an OC Curve : n = Sample size and c = Acceptance number.

Assume a range of values of percent defectives for the lot submitted for inspection and calculate the expected number of defectives by multiplying by it with the sample size ‘n’.