Question

5 samples of pasteurized milk from a single lot were analyzed and their total plate counts were (cfu/ml): 25,000; 37,000; 15,000; 45,000 and 20,000; Which of the following statements are true with respect to n, c and quality of the lot on the basis of the given data:

• A. n=5; c=2; acceptable
• B. n=5; c=3; satisfactory
• C. n=5; c=2; satisfactory
• D. n=5; c=3; unsatisfactory

Hint:

To evaluate a three-class sampling plan lot:
1. Check if any sample exceeds \(M\). If yes, reject the lot immediately.
2. Count the number of samples between \(m\) and \(M\).
3. If this count \(\le c\), accept the lot. If it exceeds \(c\), reject the lot.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Microbiological standards use a three-class sampling plan to evaluate food lots.
- \(n\) is the number of sample units selected from the lot.
- \(m\) is the threshold value for satisfactory microbiological quality; any count \(\le m\) is fully acceptable.
- \(M\) is the absolute limit of contamination; any count exceeding \(M\) is completely unacceptable.
- \(c\) is the maximum allowable number of sample units that can yield values between \(m\) and \(M\) (marginally acceptable quality).

Step 2: Detailed Explanation:
Let us apply the FSSAI three-class sampling plan criteria for the Standard Plate Count (SPC) of pasteurized milk:
- The FSSAI standards define:
\[ n = 5, \quad c = 2, \quad m = 30,000\ \text{CFU/mL}, \quad M = 50,000\ \text{CFU/mL} \]
Now, let us evaluate the five analytical test results against these criteria:
1. \(15,000\ \text{CFU/mL} \le 30,000 \implies \text{Satisfactory} \)
2. \(20,000\ \text{CFU/mL} \le 30,000 \implies \text{Satisfactory} \)
3. \(25,000\ \text{CFU/mL} \le 30,000 \implies \text{Satisfactory} \)
4. \(37,000\ \text{CFU/mL}\) resides between 30,000 and 50,000 \(\implies \text{Marginally Acceptable}\)
5. \(45,000\ \text{CFU/mL}\) resides between 30,000 and 50,000 \(\implies \text{Marginally Acceptable}\)
- Analysis of the results:
- Three samples are fully satisfactory (\(\le m\)).
- Exactly two samples are marginally acceptable (between \(m\) and \(M\)).
- No samples exceed the absolute limit \(M\) (\(50,000\ \text{CFU/mL}\)).
- Since the number of marginally acceptable samples is exactly equal to \(c = 2\), the lot meets the standard and is classified as acceptable.

Step 3: Final Answer:
Based on the FSSAI three-class sampling plan, the lot has \(n = 5, c = 2\) and is classified as acceptable.