OIML RECOMMENDATION R87 PRE-PACKAGED PRODUCTS Ben

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OIML RECOMMENDATION R87 PRE-PACKAGED PRODUCTS Ben

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OIML RECOMMENDATION R87 PRE-PACKAGED PRODUCTS Ben Aitken Trading Standards Officer Trading Standards MBIE New Zealand Kevin Gudmundsson Legal Metrology Advisor Trading Standards MBIE New Zealand Sampling Plans Random Sampling Random

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OIML RECOMMENDATION R87 PRE-PACKAGED PRODUCTS Ben Aitken
Trading Standards Officer
Trading Standards
MBIE
New Zealand Kevin Gudmundsson
Legal Metrology Advisor
Trading Standards
MBIE
New Zealand

Sampling Plans Random Sampling

Random Sampling Every combination of pre-packages is equally likely to be chosen

Not always easy to achieve

Removes bias

Random Sampling Gives the best estimate

Makes inferences valid

Random Sampling Methods Determining sample size (n)

First, we need to know the inspection lot size

Consult R87, Table 1 to determine sample size

This allows us to prepare an appropriate random sampling plan

Random Sampling Table 1 Sampling plans for pre-packages

Random Sampling Methods Sampling types

Choosing a random sample not collected from the production line

Choosing a random sample collected from the production line over time

Random Sampling Methods 1. Choosing a random sample not collected from the production line

Random Sampling Sampling – not collected from the production line

Random Sampling

Random Sampling Methods of Random Sampling

‘Mechanical’ method

Begin by allocating a reference number to each prepackage in the inspection lot

Random Sampling Drawing cards from a hat

Record the numbers allocated to the individual prepackages in some physical way
i.e. on cards, slips of paper etc.

After thoroughly mixing, choose as many cards etc. as there are pre-packages needed for the sample.

The corresponding pre-packages of the inspection lot will then make up the sample.

Random Sampling Random number tables

Any position in the table has a probability of 0.1 of being occupied by any particular digit.

Select a starting point by using a random procedure.

Random Sampling Random number tables

Stab a page of the table with a pin

the page number
the row number
the column number

to start taking random digits.

Random Sampling Random number tables

For a lot containing up to 999 pre-packages

001, 002, ….999
ignore any triplet outside the range
similarly for lot sizes between 1000 and 9999 use four digit numbers

Random Sampling Random number generation using a spread sheet

Spread sheets can generate random numbers by using function “=RANDBETWEEN(low,high)”
low being 0, and
high being the number of pre-packages in the inspection lot

Random Sampling Random number generation using a calculator

Many calculators can generate random numbers between 0.000 and 0.999 inclusive

Random Sample Example

Choose a random sample of 50 pre-packages from a lot size of 400.

Allocated each of the 400 packages in the lot their own reference number i.e. 1, 2,….399, 400

A random sequence of individual digits is produced

Random Sampling 50 randomly generated numbers (0-400)

Random Sampling Ordered randomly generated numbers (0-400)

Random Sampling Example

Prepackages numbered 10, 16, 36, 40, 51 and so on are selected and their individual prepackage error is determined

Random Sampling Methods of Random Sampling

Systematic Sampling

Determine the sample size ‘n’
Divide the lot size by the sample size to determine sampling interval ‘k’
Randomly generate a number to determine your start point
Sample every ‘kth‘ package from the lot

Random Sampling Methods 2. Choosing a random sample from the production line using time based sampling

Random Sampling Sampling over time

Reference test of 1 hour’s production.

Random numbers to give random times

To take sample pre-packages after the point of final checks by the packer from the production line

Random Sampling Sampling over time

Divide the hour into 3600 seconds

choose the random times in the range from 0001 to 3600 for the required sample size

Random Sampling The following sequence of numbers would produce the corresponding times throughout the hour.

1287 pack being chosen after 21 min 27 sec
1936 “ “ “ “ 32 min 16 sec
1677 “ “ “ “ 27 min 57 sec
0328 “ “ “ “ 5 min 28 sec

etc

Random Sampling Arrange the times in chronological order and with a stop watch select the pre-packages from the production line

Complete random time exercise now

Random Sampling Random number generation using a spread sheet
Spread sheets can generate random numbers by using function “=RANDBETWEEN(0,3600)”

Random Sampling Random number generation using a spread sheet
Copy and paste numbers into new column, then
Filter random numbers from lowest to highest

Random Sampling Random number generation using a spread sheet
Insert formula “=C2/86400”

Random Sampling Random number generation using a spread sheet
Format cells to display in “mm:ss”

Random Sampling Random number generation using a spread sheet
Expand selection to match required sample size

Random Sampling Thank you for your attention

Any Questions?

OIML RECOMMENDATION R87 PRE-PACKAGED PRODUCTS Ben

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