OIML RECOMMENDATION R 87 PREPACKAGED PRODUCTS Ben Aitken

OIML RECOMMENDATION R 87 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 1. Determining sample size (n) • First, we need to know the inspection lot size • Consult R 87, 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 1. Choosing a random sample not collected from the production line 2. 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 – 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 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 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(low, high)” • low being 0, and • high being the number of pre-packages in the inspection lot

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