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Bachelor of Business Administration-BBA Semester II
BBA104/BB 0035–Quantitative techniques for Business
Assignment Set- 2
Q.1. a. What is acceptance sampling? Discuss the concept of OC curve.
b. Discuss the sources of variations in the production process?
ANSWER: Acceptance sampling :
It is the process of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results. Acceptance sampling determines whether a batch of goods should be accepted or rejected.
All three of these statistical quality control categories are helpful in measuring and evaluating the quality of products or services. However, statistical process control (SPC) tools are used most frequently because they identify quality problems during the production process.
An OC curve
The sampling procedure consists of taking a small sample comprising n number of items from a consignment of N number of items and accepting the consignments only if the number of defective items in the sample is less than or equal to a cut-off number c or else rejecting the consignment. The acceptance sampling variables is specified include the size of the lot (N), the size of the sample inspected from the lot (n), the number of defects above which a lot is rejected (c).In using the acceptance sampling plan, there is a probability that lot may be accepted even if the quality is not good; also conversely, the lot may be rejected even if the quality is actually good. The first type of risk is called the “consumers risk” and the second type of risk is called the “producer’s risk”.
The sampling plan, which generates the corresponding OC curve, is an agreement between vendor and the buying company. The producer’s risk corresponding to an acceptable quality level (AQL) is a small percentage of defects that consumers are willing to accept. It is the chance or probability that a lot containing an acceptable quality level will be rejected.
However, sometimes the percentage of defects that passes through is higher than the AQL. Consumers will usually tolerate a few more defects, but at some point the number of defects reaches a threshold level beyond which consumers will not tolerate them. This threshold level is called to the lot tolerance percent defective (LTPD)-is what the buying company is interested in. Therefore, the consumer’s risk is the chance or probability that a lot will be accepted that contains a greater number of defects than the LTPD limit.
In the operating Characteristic curve (OC curve) for 100% sampling these risks were each zero, whereas for any other sampling procedure, there exists finite quantities of both these risks. An appropriate sampling plan satisfies both the conditions.
Q.2. Given below is the data of production of a certain company in lakhs of units. Compute the linear trend by the method of least squares.
| YEAR | 1970 | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 | 1977 | |
| PRODUCTION | 19 | 15 | 19 | 14 | 20 | 26 | 29 | 31 |
ANSWER:
Q.3. From the data given below, compute the index for the year 2009 taking 2008 as the base year by weighted average method of price relatives using (i) arithmetic
mean
(ii) geometric mean;
| COMMODITY | PRICE (RS) | QUANTITY | PRICE (RS) |
| 2008 | 2008 | 2009 | |
| A | 9 | 15 | 14 |
| B | 8 | 6 | 9 |
| C | 6 | 9 | 18 |
| D | 7 | 8 | 9 |
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