For most of the past hundred years it has been the usual practice within manufacturing to employ sampling methods to determine the acceptability of products. The purpose of this sampling is to allow an assessment of specified features of a product without the expense - in time or money - of checking every item in a consignment or batch.



Correctly applied, sampling is a particularly useful tool where the assessment process actually damages or even destroys the item(s) being examined. In the defence industries samples of military ordnance are tested as part of the manufacturing process, with further samples being taken during the customer acceptance routines. Clearly a round of ammunition fired to assess its quality is no longer available to ship to the customer. Sampling is therefore the only system for checking customer acceptable performance in that instance. Sampling also has value when the total volume available precludes the assessment of each individual part. Take for example opinion surveys of the population.

Sampling is a statistical tool, with a discipline of its own within the mathematics environment. Properly designed a sampling scheme can provide, in conjunction with other controls, an assurance not otherwise readily available. There is however no way known to be absolutely certain that an inspected batch of product is 100% defect free. With sampling there is the risk that a sample will not adequately reflect the condition of the batch from which it was drawn, and by definition a product accepted by any sampling scheme will repeatedly accept material that is to some extent deficient. This is in the nature of sampling.

Sampling is effected through the use of a 'Sampling Plan'. Every plan requires that a number of items (the sample) are withdrawn from the product batch (always larger in number than the sample size). The sample is then checked/tested/assessed to a pre-specified standard and the number of items failing this minimum quality standard is recorded.

The sampling plan will have a pre-defined permitted number of defects, which if not exceeded allows the sampled batch to pass to the next stage of operation - maybe delivery to the customer. This sample size can be any number, and the 'acceptable failures' quantity any number from Zero upwards.

From the above it should be clear that sampling is a useful tool but with significant risks where the process is not understood. Key to understanding the risks is the Operating Characteristic of the chosen scheme. Known as the OC curve, this defines the risk of accepting or rejecting given levels of defective product sampled by the plan. Sampling tables are readily available as national standards, and always include the OC curves for the defined plans.

There is a usual belief that taking a fixed percentage of a batch is an effective sampling scheme, 10% of batches of 100 and 1000 are therefore seen as giving similar levels of assurance that the final decisions are correct. For a given 'permitted defects' number in a sample (even if that is zero) the larger sample size will always provide a greater certainty for the conclusion. Repetitive sampling must be implemented in a way that maintains a consistent risk level. Where the 'fixed percentage' system is utilised it is obviously in the suppliers interest to send smaller batches of product, since those have a greater probability of being accepted than would be the case for larger batches.

In conclusion, the characteristics of a sample reflect the characteristics original batch from which it was drawn. From this variables data it is possible to draw conclusions regarding the condition of the items in the larger batch that were not examined

Conclusions can also be gleaned from this data regarding the condition of the process itself. Unfortunately the vast majority of sampling endeavours are limited to making an accept/reject decision, and do not go on to assess the batch variability from the samples taken from it, as long as an acceptable end result is achieved from the sampling. In respect of the management process this is a lost opportunity that serves only to increase expense.