Page 182 - DMGT501_OPERATIONS_MANAGEMENT

Operations Management

Notes For R chart
UCL = R + 3 ×
R
= 0.0441 + 3 × ( R /d ) × d
2 3
= 0.0441 + 3 × ( 0.0441/2.326 ) × 0.864
= 0.0441 + 0.0411
= 0.0132

6.10 Acceptance Sampling

Acceptance Sampling can be described as the post-mortem of the quality of the product that has
already been produced. The term Acceptance Sampling ‘relates to the acceptance of a
consignment/batch of items on the basis of its quality.’ It is used for:
1. Acceptance/rejection of the raw-material delivered.

2. Passing/non-passing of the batch of items manufactured.
3. Shipment of items for delivery to customer.

How an Acceptance Sampling Operates?

If for instance from a consignment or a batch of ‘N’ items, a sample of size ‘n’ is taken, in which
‘c’ or less number of items are found defective, then the consignment or batch gets accepted if
more than ‘c’ items are found defective, the entire consignment/batch is rejected.
Thus, the inference or decision regarding a large quantity (or population) of n items is made on
the basis of a sample quantity(n).
Here (N,n,c) as a set, constitute the sampling plan, called Sampling Plan Attributes.

Risk Involved

With any sampling plan, there is always a risk:
1. Very bad lots will be passed.
2. Good lots will be rejected.

These two risks are appropriately called Consumer’s Risk and Procedure’s Risk respectively.

Operating Characteristic Curve (or OC Curve)

We can plot a curve between the % defectives in the lot and the probability of acceptance of the
lot, under any given sampling plan known as the OC curve.
The procedure sends a lot of Acceptable Quality Level (AQL), (given in percent defectives) which
can get rejected, the chance or probability of this being the Procedures Risk (PR), whereas on the
other hand the customer (manufacturing plant) faces the risk of accepting lots as bad as the LTPD
(Low Tolerance Percent Defective), the probability of acceptance of such lots being the Consumer’s
Risk (CR). The probability of acceptance can be determined by making use of the following
expression which is found on Hyper exponential distribution:

b b
P(a) = 1 P(b)
b 0

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