An Incoming Quality Control (IQC) plan is used to decide on the acceptance of a batch on the basis of samples taken from the batch. Several types of sampling are taken into account:

- Control by attributes (single, double and progressive plans)
- Control by measurement (method S, s, progressive).

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## Attribute control

Each part is measured according to an OK/KO scale, and the batch is accepted if the number of KOs measured is below a limit. Attribute testing can be :

- Simple: a certain number of parts are measured once and acceptance of the batch is defined at the end of the measurement of all the parts.
- Double: a first batch of parts is measured, the batch is accepted if the number of defects is less than "Acceptance 1", rejected if the number of defects is greater than "Rejection 1", otherwise a second batch of parts is measured and the batch is accepted if the number of defects is less than "Acceptance 2", rejected otherwise. This type of inspection limits the number of parts measured.
- Progressive: acceptance or rejection of the batch is calculated for each measurement. This type of control is the most effective.

*Advantage of attribute control: easy to set up*

Disadvantage of attribute testing: it is not possible to obtain an AQL of less than 1% without significantly increasing the number of parts measured.

## Measurement control

Each part is measured according to a quantitative scale, and the batch is accepted if the average of the batch is further than k standard deviations from the closest tolerance (k or k factor being defined by the acceptance inspection). Measurement control can be :

- Simple: a certain number of parts are measured once and acceptance of the batch is defined at the end of the measurement of all the parts,
- Progressive: acceptance or rejection of the batch is calculated for each measurement. This type of control is the most effective.

*Advantage of attribute testing: significantly reduces the number of parts measured compared to attribute testing.*

*Disadvantage of attribute testing: Each part has to be measured quantitatively.*

## Efficiency curve

When setting up a statistical incoming inspection, it is important to be aware that it is not possible to stop 100% of incoming defects. The supplier and customer must therefore agree on an acceptable level of quality, i.e. the average percentage of defects that the incoming inspection must allow to pass.

The purpose of the control efficiency curve is to predict control results as a function of the quality rate of the batch measured.

**Let's take the following example:**

We receive a batch of 1000 parts containing 50 defects. The incoming inspection is as follows. 80 parts in the batch are inspected, and the batch is accepted if 1 defect or less is measured. Otherwise, the batch is rejected. Using the laws of descriptive statistics, we can show that (open descriptive/discontinuous statistics) :

The probability of measuring 1 defect or less is 7.7%. As a result, this batch has a 7.7% chance of being accepted and a 92.7% chance of being rejected.

We can therefore predict that with an inspection of 80 parts and an acceptance level of 1 defect, a batch of 1000 parts containing 5% of defects has a 7.7% chance of being accepted.

The efficiency curve is therefore used to give the probability of acceptance for all possible batches. The x axis of the efficiency curve is the percentage of defect contained in the batch. The Y axis is the acceptance percentage.

The following figure shows the efficiency curve for an inspection of 80 parts and an acceptance level of 1 defect:

We can see that if there are 50 defects, the acceptance level is 7.7%.

## P95 and P10

To characterise this curve, we generally use two characteristic points of the curve:

*P95*The P95 corresponds to the defect rate of a batch resulting in an acceptance level of 95% with the control in place. In the previous example, the P95 is 4, i.e. a batch containing 4 defects has a 95% chance of being accepted.

*P10*The P10 corresponds to the defect rate of a batch resulting in an acceptance level of 10% with the control in place. In the previous example, the P10 is 47, i.e. a batch containing 47 defects has a 10% chance of being accepted.