Standard deviation and deviation of the average value from the nominal value of a placement system, two core variables for placement accuracy, are measured as part of an MCT. The MCT is performed in the following sequence: First, a certain minimum number of glass components are placed on a glass board into adhesive foil. Then the placement deviation of all placed glass components is determined in X, Y and q using a high-precision measurement machine. The measurement machine then calculates the placement offsets (deviation of average value from nominal value) in the relevant positioning axes X, Y and q.

The MCT result represented graphically in Figure 1 yields the following core placement accuracy values:
Standard deviation σ = 8 µm.
Placement offset µ = 6 µm.

Figure1. Graphic representation of an MCT result.

Generally, we can expect the placement deviations to correspond to normal Gaussian distribution, allowing conversion to a wider statistical basis of, for example, 3 or 4. With reference to the statistical basis 4 σ so often used, the placement system specified above would have an accuracy of 32 µm.

Placing the derived precision in relation to a required tolerance limit then assesses machine suitability for a specific requirement. The machine capability index (cmk) has proven most suitable for this. It typically is used to assess the process capability of machines.

The cmk can be used to calculate the placement accuracy once an upper and lower specification limit (USL and LSL) has been defined.

As limit values usually are symmetrical, we can perform the calculation with a simplified specification limit SL = USL = - LSL, as shown in Figure 1.

The following cmk results for the conditions presented in Figure 1 and a specification limit of 50 µm defined by the customer:

The cmk therefore evaluates the spread and average deviation (placement offset µ of the placement position in relation to three times the value of the standard deviation σ

How do we deal with the statistical variables sigma, cmk and defects per million (DPM) rate in practice? In electronics manufacturing today, it is expected that the cmk will be greater, even significantly greater, than 1.33. A cmk of 1.33 also indicates that a 4 σ process capability has been achieved. A process capability of 6 s, which so often is a requirement today means that the cmk must then be at least 2.66.

In electronics production, the DPM number usually is used for practical reasons because every defect produces costs. The relationship between statistical bases 3, 4, 5 and 6 σ and the correspondingDPM rates are established on the left:

If, in the SMT production process, it is suspected that the entire placement pattern on the printed circuit board (PCB) has moved significantly in a particular direction because of external mechanical effects, the placement equipment must be recalibrated. This placement offset therefore must be reduced as far as possible. Surface mount device (SMD) electronics manufacturers with a large number of placement systems perform placement offset optimization in a similar way to MCT and use an additional measuring machine. The resulting placement offsets in the relevant positioning axes X, Y and q are entered manually in the placement system for the purposes of compensation.

Directly after placement, four sequential images of the corresponding reference marks on the board and component are taken with a PCB camera. Then the placement offsets in X, Y and q determined by the evaluation program and accepted by the user are transferred into the relevant machine data memory areas.
Conventional manual entry of the offsets is no longer necessary. As this integrated method uses relative measurement rather than absolute measurement, the positioning precision and dynamic response of the placement system do not adversely affect the quality of the results. Only the image resolution and quality of the PCB camera are significant.
This described and patented method therefore has measurement machine properties.

The following example shows how the cmk of 1.33 can be increased to 1.92 with integrated placement offset optimization.
The following initial conditions are assumed:

SL = 50 µm
Standard deviation σ = 8 µm
Placement offset µ = 18 µm

Reducing the placement offset to, say, 4 µm as shown in Figure 3 results in a significant improvement of the cmk value.

Figure3. Graphic representation of placement offset optimization.

A placement machine installed in the production line can be upgraded to the highest possible placement accuracy without the need for complicated, expensive and often unavailable measuring machines. More or less by simply pressing a button for the duration of the optimization process, the placement system is converted into a high-precision measuring machine.

Surface Mount Technology June, 2001