How to calculate Cmk value (equipment capability index)?

This is a process of SMT (Electronic Industry Installation Operation):

At present, the general trend of products is miniaturization, and at the same time, it is necessary to improve performance and reduce costs, which will inevitably lead to greater technological development in various fields of SMT. For example, users of high-performance mounting systems want new development of suppliers, which can greatly increase mounting output and improve mounting accuracy. As for the most important aspect of mounting: mounting accuracy, users hope that the specified equipment parameter values can remain unchanged for several years. These specified values are usually used as part of the Machine Capability Test (MCT), which is checked at the supplier for the customer who installed the machine.

MCT process

The standard deviation of installation system and the average deviation of nominal value are two core variables of installation accuracy, which are measured as part of MCT. MCT is carried out according to the following steps: firstly, a certain minimum number of glass elements are attached to the adhesive film on the glass plate. Then use a high-precision measuring machine to measure the installation deviation of all installed glass components in X, Y and θ directions. Then, the measuring machine calculates the installation deviation (the average deviation of the nominal value) on the axes X, Y and θ of the relevant position.

The MCT results illustrated in figure 1 give the following values of core installation accuracy:

Standard deviation = 8? m

Installation offset = 6? m

Figure 1. Graphical representation of MCT results

In general, we can expect the installation deviation to conform to the normal Gaussian distribution, allowing conversion to a larger statistical base, such as 3 or 4σ. For commonly used statistical cardinality, the installation system specified above has 32? The accuracy of m.

By comparing the obtained accuracy with the required tolerance limit, the applicability of the machine to special requirements can be evaluated. Machine Capability Index (CMK) has been proved to be the most suitable for this. It is usually used to evaluate the process capability of a machine.

Once the upper specification limit (USL) and the lower specification limit (LSL) are defined, cmk can be used to calculate the installation accuracy.

Because the limit value is generally symmetrical, we can use the simplified standard limit SL=USL=-LSL to calculate, as shown in figure 1.

Cmk= specification limit-installation deviation 3x standard deviation = 3SL-? 3σ

The following cmk results are for the conditions proposed in figure 1 and the customer-defined 50? M specification limit.

cmk= SL-? 3σ = (50-6)? m 24? m = 1.83

Therefore, cmk evaluates the deviation and average deviation (installation deviation) of the installation position from three times the standard deviation value.

In practice, how do we deal with statistical variables σ, cmk DPM and number of defects per million (DPM)? In today's electronic manufacturing, it is hoped that cmk will be greater than 1.33 or even greater. The cmk of 1.33 also shows that the process capacity has reached 4σ. 6σ process capability is a common requirement today, which means that cmk must be at least 2.66. In electronic production, DPM is used for practical reasons, because each defect will generate cost. The relationship between statistical cardinality 3, 4, 5 and 6σ and the corresponding defect rate per million (DPM) is as follows:

3σ= 2700 DPM 4σ= 60 DPM 5σ= 0.6 DPM 6σ= 0.002 DPM

The following is a practical example of its use: In applications requiring maximum packaging density (such as mobile phones), the mounting accuracy of 020 1 components may be 75? m .

The first case: we rely on 75? Installation accuracy of m/4σ. In this case, we hope that no more than 60 out of 1 million devices will exceed 75? M's window.

In the second case, MCT generates a cmk of 1.45 according to specific specifications. Because the cmk of 1.33 accurately defines a 4σ process, we can expect that the defect rate caused by installation deviation is less than 60 DPM.

Optimization of installation deviation

In the process of SMT production, if it is suspected that the whole mounting characteristics on the printed circuit board have moved too much in a specific direction due to the influence of external machinery, the mounting equipment must be recalibrated. Therefore, the installation deviation must be reduced as much as possible. Electronic manufacturers of surface mount components (SMD) with a large number of mounting systems optimize the mounting offset in a way similar to MCT, and use other measuring machines. The installation offset results obtained on the relevant position axes X, Y and θ are manually input into the installation system for compensation.

What is described below is the mounting offset optimization method combined in the mounter.

The idea here is to allow similar measurement programs to run on the installation system, which is usually part of MCT. The purpose is for the machine to find the installation offset of x, y and θ, and then use it in a way that will not cause offset.

The whole process is as follows: stick the maximum number of glass elements (such as 48) on the glass plate with double-sided tape. The outer edge of each glass element has a reference mark. There is also a reference mark on the board, next to the reference mark of the component (Figure 2).

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Figure 2. Find out the principle of installation deviation.

Immediately after installation, the PCB camera continuously takes four photos of the corresponding reference marks on the circuit board and components. Then, the X, Y and θ installation offsets calculated by the evaluation program and accepted by the user are transmitted to the relevant machine data storage area. Traditional manual displacement input is no longer needed. Because the integration method uses relative measurement instead of absolute measurement, the position accuracy and dynamic response of the installation system will not adversely affect the quality of the results. Only the image resolution and quality of PCB camera are important. Therefore, the described patented method has the characteristics of a measuring machine.

The following example shows how to improve the cmk of 1.33 to 1.92 using integrated layout offset optimization.

Assume the following initial conditions:

SL = 50? m

Standard deviation = 8? m

Installation offset = 18? m

Original cmk:

cmk= SL-? m 3σ = (50- 18)? m 24? m = 1.33

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Reduce the installation misalignment to, say, 4? M is shown in Figure 3, then the value of cmk will be greatly improved.

Cmk with optimized installation offset:

cmk= SL-? m 3σ = (50-4)? m 24? m = 1.92

The mounter installed on the production line can be upgraded to the highest mounting accuracy possible without complicated, expensive and usually difficult to purchase measuring machines. More or less, just press the button of the optimization process, and the installation system will become a high-precision measuring machine.