QUALITY CONTROL

Ronan ALLIBERT

Bsc in Electronic & Electrical Engineering

Iain King

25/10/99

As Quality policies become more and more used, products final inspection meets the same emphasis. Acceptance sampling is one of the method to realise this inspection process. There are two others techniques also known that consist to realise random checking for the first one and 100% product control for the second. We will discuss later about those two versus acceptance sampling, and start by introducing acceptance sampling and its principles.

This method of inspection consist to take a random sample (in a lot) and to decide if the lot is acceptable or not ( accept/reject) according to acceptance criteria. Stated simply, sampling plans are used to make product disposition decisions for each lot of product.  With attribute sampling plans, these accept/reject decisions are based on a count of the number of defects and defectives, while variables sampling plans require measurements and calculations, with decisions based on the sample average and standard deviation. Plans requiring only a single sample set are known as single sampling plans; double and multiple sampling plans may require additional samples sets.  For example, an attribute single sampling plan with a sample size n=50 and an accept number a=1 requires that a sample of  50 units be inspected.  If the number of defectives in that sample is one or zero, the lot is accepted. Otherwise it is  rejected.

Ideally, when a sampling plan is used, all bad lots will be rejected and all good lots accepted.  However, because accept/reject decisions are based on a sample of the lot, there is always a chance of making an incorrect decision. So the behaviour of a sampling plan can be described by its operating characteristic (OC) curve, which plots percent defectives versus the corresponding probabilities of acceptance. 

An OC curve is generally summarised by two pints on the curve: the acceptable quality level (AQL) and the lot tolerance percent defective (LTPD).  The AQL describes what the sampling plan generally accepts; formally, it is that percent defective with a 95% percent chance of acceptance. The LTPD, which describes what the sampling plan generally rejects, is that percent defective with a 10% chance of acceptance. 

For the sampling plan to be valid, one must obtain representative samples of the lot. Failure to select representative samples can seriously compromise the sampling plan’s protection. One way to obtain a representative sample is to select a random sample. This involves randomly selecting the first sample and then randomly selecting each additional sample from the units remaining in the lot. Other alternatives are stratified sampling (uses of sub-groups) and periodic sampling.

Acceptance sampling detects poor quality but doesn’t prevent it. Detractors like Deming would also say that a random process of defecting can’t statistically be distinguished, and by then defecting products can’t be found by this process.

We could say then that a 100% checking would be more reliable, but 100 % inspection is not appropriate for destructive tests, it takes a lot of time (when lots are large), it costs a lot, and the boringness of its application doesn’t ensure high level reliability.

Spot-checking by its lack of being statistically based doesn’t give the assessment of the risks of making a wrong decision.

Preventing defects is certainly more desirable than detecting them through inspection, that is way will we will now look at process control (Statistical Process Control: SPC). SPC does not eliminate the need for acceptance sampling. As indicated in Table II, there are fundamental differences between the two techniques. In SPC, control charts are used to make process control and process improvement decisions, and actions are taken on the process to ensure that future products are good. In contrast, sampling plans are used to make product disposition decisions, and actions are taken on previously produced lots to ensure the quality of released product.   Ideally, with SPC in place no defectives will ever be made and acceptance sampling will become unnecessary: in practice, however, all processes have some risk of failure, and thus some procedure for accepting and rejecting product is generally required.

This technique requires also routine product inspections. Variables sampling is recorded on an acceptance control chart. Figure 2 provides an example of such a chart containing fill-volume data. 

The inside pair of limits, UCL and LCL, are the control limits. A point falling outside these limits signals that the process is off target and that corrective action is required. The outside pair of limits, UAL and LAL, are the acceptance limits. A lot whose sample falls outside these limits is rejected.

In the figure, lot 13 is outside the control limits but inside the acceptance limits, which indicates that the process has shifted. Corrective action on the process is required to maximise the chance that future products will be good; however, no action is required on the product lot. Rejecting whenever a point exceeds the control limits can result in the rejection of perfectly good lots. Similarly, it is wasteful to wait until the acceptance limits are exceeded before taking corrective action on the process. Therefore, separate limits for process and product actions are required. Such limits are also frequently called action limits, warning limits, and alert limits. No matter what the name, however, if the result of exceeding a limit is to act on the process, the limit is serving the purpose of a control limit; if action is instead taken on the product, the limit is serving as an acceptance limit.

Neither SPC or acceptance testing can detect a problem before defectives are produced. However, by accumulating data over time, attribute control charts can indicate small changes in the process average that acceptance sampling will not reveal. Used in combination, sampling plans provide immediately protection against major failures while control charts protect against minor sustained problems.