SOP: Random Sampling of Product Lots Using Random Number Tables

GIFSQ — Global Institute for Food Safety & Quality

Principle

The sample selected for examination must be representative of the lot; every piece must have an equal chance of being selected. In random sampling each item of the lot is serially numbered and the items to be examined are chosen from a table of random numbers (or at fixed intervals of N/n), so that no bias enters the selection. For lots packed in layers of boxes, the sampling is stratified over the layers.

Materials

• The lot, with its N items serially numbered
• The book’s table of random numbers
• The sampling plan giving the number n of samples to draw

Procedure

Serially number every item (can, case) in the lot from 1 to N

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Open the random number table at any point — any block, line and column — and choose a starting number smaller than N

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Read subsequent numbers downwards or sidewards, discarding any number higher than N and any number already chosen, until n sample numbers are obtained

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Alternatively, select the first sample at random and draw the remaining samples at intervals of N/n

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For stratified lots (boxes stacked in layers), choose the required number of cases at random or at intervals of N/n from the whole stack, and take one item from each chosen case for analysis

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Estimate the lot’s average quality characteristic and the proportion of defectives from the sample using the expressions below

Calculation

Sample average:

x̄ = (x₁ + x₂ + … + xₙ) / n

Proportion of defectives:

p = d / n

Where,

• x̄ = sample average, an estimate of the average quality characteristic of the lot
• n = number of samples
• p = proportion of defectives in the sample, an estimate of the proportion of defectives in the lot
• d = number of defectives observed among the samples

Worked example 1 — simple random sampling

A lot of 300 cans of baby food is serially numbered; 8 cans are to be selected at random. A three-digit number is selected at random (220 in block 2, line 2, column 3 of the book’s random number table). Going down the column, the numbers below 300 are 084, 025, 104, 081, 256, 011, 141 and 225; hence the cans numbered 11, 25, 81, 84, 104, 141, 225 and 256 are drawn as samples.

The same selection may be made starting elsewhere in the table: starting at 022 (first line, column 3 of the same block) and reading downwards and across as described in the book gives the cans numbered 22, 112, 141, 199, 204, 211, 228 and 262.

Worked example 2 — systematic interval sampling

Instead of random numerals, a single sample is selected from the lot and the rest are drawn at intervals of N/n. In the example above, N/n = 300/8 = 37.5, taken as 38. If the first sample drawn is the 23rd can, the cans numbered 61, 99, 137, 175, 213, 251 and 289 are drawn as the remaining samples.

Worked example 3 — stratified sampling

Canned products are packed in boxes stacked in layers: 24 cans per box, 100 boxes per layer, 5 layers — 12,000 cans in the stack. According to the sampling plan, 13 cans are to be drawn as samples at random. Thirteen cases are chosen at random using the table (or at intervals of N/n), and one can is taken from each case for analysis.

Precautions

• In the selection of samples, adequate care must be taken so that there is no bias.
• Begin at any block, line and column of the random number table, and read downwards or sidewards consistently.
• Discard numbers higher than the lot size N and repeat numbers.

References

Ranganna, S., Handbook of Analysis and Quality Control for Fruit and Vegetable Products, 2nd edition.