Average Sample Number (ASN) in SQC

Definition of Average Sample Number (ASN)

Average sample number (ASN) is a metric used in statistical quality control to quantify the average number of samples required to detect a specific level of non-conformance within a given population or process. It provides a measure of the sampling efficiency by indicating how many units need to be inspected before a defective unit is likely to be found.

Formulas for Average Sample Number

There are various formulas to calculate average sample number depending on the sampling method used. However, the general formula for ASN is:

ASN = \frac{1}{P(d)}

Where:

• ( P(d) ) is the probability of detecting non-conformance (defects) in a single sample.

Methods for Calculating ASN

1. Binomial Distribution Method: This method is commonly used when dealing with attribute data. It involves calculating the probability of detecting defects in a single sample using the binomial distribution formula and then taking the reciprocal to obtain the ASN.
2. Hypergeometric Distribution Method: When dealing with finite populations, the hypergeometric distribution is employed to calculate the probability of detecting defects. The reciprocal of this probability gives the ASN.

Examples of ASN Calculation

1. Binomial Distribution Example: Suppose a manufacturing company inspects batches of 100 units for defects, and the probability of detecting a defect in a single unit is found to be 0.05. The ASN would be:

ASN = \frac{1}{0.05} = 20

This implies that on average, 20 batches need to be inspected to detect one defective unit.

2. Hypergeometric Distribution Example: In a quality control process where a sample of 20 items is drawn from a population of 500, with 10 defective items in the population, the probability of detecting at least one defective item in the sample can be calculated using the hypergeometric distribution. The reciprocal of this probability gives the ASN.

Remarks on ASN

• ASN serves as a crucial metric in determining the effectiveness of sampling plans in detecting defects.
• It helps in optimizing resources by ensuring that an adequate number of samples are inspected to maintain quality standards without excessive testing.
• The calculation of ASN requires a clear understanding of the sampling method and the underlying distribution of defects within the population.

Conclusion

Average sample number (ASN) plays a pivotal role in statistical quality control by providing a quantitative measure of sampling efficiency. By understanding ASN and its calculation methods, businesses can design effective sampling plans that strike a balance between maintaining quality standards and optimizing resources. As organizations continue to emphasize quality management, the importance of ASN in ensuring product reliability and customer satisfaction cannot be overstated.