## 4 Major Terms Which Are Generally Used In Acceptance Sampling

iii. Rejectable Quality Level (R.Q.L.) or Lot Tolerance Percent Defective (L.T.P.D.)

iv. Operation Characteristics Curve (O.C.)

#### (i) Average Outgoing Quality (A.O.Q.):

When the initial quality of the goods inspected is high, then the outgoing quality will also be high and in the same way, when the initial quality will be high as the sampling inspection will easily sort out the defective items from the lot. A.O.Q. is the expected fraction defectives in the outgoing lots after sampling inspection. (Fig. 20.3).

A.O.Q. = Actual number of defectives in the lots after inspection /Total number of items in the lot

Alternately if N is the size of each lot, n is the size of the sample inspected from each lot, p is the proportion of defectives per specifications and Pa is the probability that a lot of proportion defective p will be acceptable to the consumer, then

A.O.Q. = P PA (N – n) /N

A.O.Q. curve is shown in Fig.20.3. The peak of the curve corresponds to the poorest quality of the batches and is known as Accepted outgoing quality level of the sampling scheme.

#### (ii) Accepted Quality Level (A.Q.L.):

It represents maximum proportion of defectives which the consumer finds acceptable. It is the maximum percent defectives that for the purpose of sampling inspection can be considered satisfactory. It is the fraction defective that can be tolerated without any serious effect upon further processing or on customer relations. In fact, this level has a high probability of acceptance and is rather producer’s safe point.

#### (iii) Rejectable Quality Level (RQL) or Lot Tolerance Percent Defective (LTPD):

This prescribes the dividing line between good and bad lots. Lots at this level of quality are considered to be poor and have low probability of acceptance. The probability of accepting a lot at RQL represents consumer’s risk.

#### (iv) OC Curve:

Operation Characteristics curve for a sampling plan is a graph of fraction defective in a lot against the probability of acceptance. In practice, the performance of acceptance sampling for discriminating good and bad lots mainly depends on the size of the sample (n) and the number of defectives (c) that can be permitted in sample. For any fraction defective ‘F the OC curve shows that such a lot will be accepted by the sampling plan. For different sampling plans, OC curve will differ (Fig. 20.4).

Characteristics of OC Curve:

Features & Characteristics of OC curve are:

(i) Sampling acceptance plans with same percent samples give different quality protection.

(ii) Fixed sample size tends towards constant quality protection.

(iii) The OC curve of plans with acceptance number greater than zero are superior to those comparable plans with acceptance number as zero.

(iv) The larger the sample size and acceptance number, steeper is the slope of the OC curve.

(v) A sampling scheme that discriminates perfectly between good and bad lots has a vertical OC curve.