1. Process capabilities Cp and Cpk

 

 

 

Both Cp and Cpk are the English abbreviations of Process Capability Index. The difference between the two is described later. Now it is usually called process capability index, also known as process capability index or process capability index. It is an application of statistical process control. (Statistic Process Control, SPC) is an important indicator for quality control. In the IPC9850 standard, Cpk is required to be the process capability index of the placement machine, and the calculation method of Cpk is specified.

 

 

 

1. Basics of process capability analysis - histogram and normal distribution curve

 

 

 

In statistical analysis, we face a large amount of data. For example, if we use a placement machine to mount 400 1608 chip components, we will get 400 pieces of data in each of the X and Y directions by testing the deviation between the actual placement position and the standard position. . If more components are mounted, more data will be obtained.

 

 

 

Obtaining data is only the beginning of statistical analysis. First, the data must be processed and sorted to find out its statistical rules, that is, the shape of the data distribution is analyzed in order to make statistical inferences about its overall distribution characteristics. The intuitive histogram is the most commonly used method in process capability analysis.

 

 

 

(1) Histogram

 

A histogram divides the collected measured value characteristic values or result values into several equal intervals as the horizontal axis, and uses the number of measured values falling into each interval as the vertical axis, and arranges them in order by the area enclosed by the horizontal and vertical axes. A histogram is also called a histogram because it resembles a graph lined up with "pillars". The histogram can visually represent the frequency of data appearing in each interval, and is also called a frequency chart in statistical process control technology.

 

 

 

We illustrate the formation and meaning of histograms through an example. For simplicity, we assume that the distance between the X direction of 100 components and the reference point is measured on the mounted test board, and 100 measured values are obtained. We arranged these 100 numbers from small to large and found that the minimum value was 24.620mm, the maximum value was 24.728mm, and the other numbers were in the middle. For the convenience of analysis, we group the measured values according to statistical requirements. The number of groups is shown in the table below.

 

 

 

 

 

For example, we divide 100 numbers into 9 groups and calculate the group distance

 

(24.728−24.620)/9=0. 108/9=0.012

 

 

 

Based on this, determine the boundaries of each group, calculate the group median of each group, and then classify the data into each group according to the group boundary. The number of data falling into each group is regarded as the frequency, forming a table as shown in the following table. The clustering and dispersion trends of the measured values can be seen in the table below. However, the visualization of tables is not as good as graphics. According to Table 2.1, a more intuitive histogram as shown in the figure below can be drawn according to the method of forming a histogram. Based on the histogram, you can understand the distribution shape of the data, analyze the trend of data deviation, and formulate the limits of deviation control, thereby achieving effective control of the process.

 

 

 

Group boundary data and frequencies

 

 

 

 

 

 

 

(2) Normal distribution graph and normal distribution curve

 

The histogram shown in the above figure is high in the middle and low on both sides, and is basically symmetrical on the left and right, indicating that the data is concentrated in a central position. This distribution pattern is called normal distribution, which is the data distribution under normal conditions. A histogram that conforms to a normal distribution is called a normal distribution plot.

 

 

 

For histograms, if we increase the measured data and the number of groups, then the envelope of this histogram will tend to be a continuous curve (as shown in the figure below). This curve is called a normal distribution curve.

 

 

 

 

 

Two basic parameters are needed to describe a normal distribution: the characteristic number μ that represents the center position of the distribution and the characteristic number σ that represents the degree of dispersion of the data distribution. We will discuss μ and σ later. Here we first understand the impact of μ and σ on the distribution of data. The normal distribution has this rule: if the measured values of the output quality characteristics of a process obey the normal distribution, then about 68.26% of all measured values fall within the range of μ−σ and μ+σ; approximately 95.46% of the measured values fall within the range of μ−2σ and μ+2σ, and approximately 99.73% of the measured values fall within the range of μ−3σ and μ+3σ. The possibility of falling outside the range of μ±3σ is very small, and the probability of occurrence is only 0.27%; and the possibility of falling outside the range of μ−4σ and μ+4σ is even smaller, and the probability of occurrence is only 0.0006%, as shown below shown.

 

 

 

 

 

2. Key indicators of process capability analysis—μ and σ

 

 

 

(1) The meaning of μ and σ

 

μ and σ are the basic parameters for quality control using statistical process control technology. When using mathematical statistical methods in specific quality control, we are faced with a large amount of statistical data. These data are not messy, but have rules to follow. Specifically, there are two basic elements. The first is whether the data are There is a tendency to concentrate on one position; the second is whether this position is our desired goal, or how far it is from our desired goal. Expressed in mathematical language, the first parameter that reflects the discrete trend of the data is σ, and the second parameter that represents the distance between the target in the data trend concentration and our expected position is μ.

 

 

 

For example, we want to examine the accuracy of the placement machine, use the placement machine to mount a batch of chip components, and use measurement statistics methods to obtain a large amount of measurement data. The data used to measure the mounting position of chip components include X and Y deviations and rotation angle θ deviations. To simplify, we only look at the deviation in the X direction. Our goal is that the X-direction center of the component coincides with the X-direction center of the pad, but in fact there will always be a deviation. Let this number be Δx. In order to express the placement accuracy of the placement machine, we must hope that: the first Δx It may be small; the second Δx cannot exceed a certain limit, for example, it cannot exceed 1/2 of the width of the component, as shown in the figure below, so there are upper and lower limits. We set the upper and lower limits as Tu and Tl respectively, then Δx must be within the upper and lower limits to be qualified.

 

 

 

 

 

If the placement machine is working in a normal state, then the measurement data should conform to the normal distribution. We can draw a histogram based on the obtained data and approximate the normal distribution curve. Using the normal distribution curve and the concepts of upper and lower limits, we can intuitively understand the actual meaning of μ and σ, as shown in the figure below.

 

 

 

 

 

From the above we can see:

 

• The μ value is the distance between the measured data and the target value. The smaller the μ value, the closer the normal distribution curve is to the target value, and the higher the placement accuracy of the placement machine;

• The σ value is an index that represents the degree of convergence of measurement data. The smaller the σ, the “slimer” the normal distribution curve, the better the data aggregation, and the higher the placement precision of the placement machine.

 

 

(2) Calculation of μ and σ Before calculating μ and σ, we need to first understand the basic concepts of statistics involved in applying mathematical statistics methods for quality control.

 

① The concepts of population and sample:

 

• Overall - also called parent, refers to the entire object under study, such as all the components on the test board as shown in the figure below.

 

 

 

 

• Individual - The basic unit that makes up the whole is called an individual, such as an element shown in the figure above.

• Sample – A portion of individuals randomly selected from a population for measurement and analysis, as shown in the figure above.

• Sample size – also known as sample size, is the number of individuals included in a sample.

② Application of the concepts of population and sample—replacing population parameters with sample parameters:

In practical applications, the statistical population often contains a very large number of individuals. For example, a production line mounts hundreds of thousands of components every day, and the workload of statistical measurement is very large. Therefore, sampling inspection and measurement methods are adopted in actual work. Theoretically, sample parameters are not equal to population parameters, but when the sample selection method and sample size comply with statistical laws, and the error between sample parameters and population parameters reaches an acceptable level, we can use sample parameters instead of population parameters.

③ Calculation of μ and σ:

The calculations of μ and σ are as follows.

• μ and σ are calculated based on statistical data, but because the statistical population data is very large, in fact, μ and σ are calculated based on samples, not an exact number, and should be called estimates.

 

• Depending on the sampling method and sample size, the estimation methods of μ and σ are also different. Of course, the final results will also be different, so please pay attention when using them.

 

• μ and σ are parameters representing the population. In practical applications, they are replaced by parameters x and s representing the sample.

 

 

Calculate the average estimate of μ commonly used sample measurements

 

 

 

In the formula,

X is the sample measurement value, and "-" is added to X to indicate the average; n is the number of samples.

 

When calculating σ, the sample standard deviation S is commonly used instead of σ. The traditional standard deviation estimation formula is:

 

 

 

In the formula, S is the sample standard deviation; Xi is the sample measurement value, and "-" is added to X to indicate the average; n is the sample number.

Note: This formula is only correct if the data is normally distributed. For randomly sampled data from the population, this is the only way to estimate the standard deviation. In addition, there are many methods for estimating σ, which can be chosen according to actual needs.

 

In the IPC9850 standard, the use of

 

3. Basic concepts of process capabilities

 

Process capability is also called process capability, which generally refers to the size of the process fluctuation range under steady state, or the size of the inherent fluctuation range of the process.

 

(1) Prerequisites for process capability Factors affecting the production process - 5M1E are explained below.

① 5M：

• Man - operator; manager, etc.;

 

• Machine - machines, equipment, instruments and tools, etc.;

 

• Material - production raw materials, raw materials and components;

 

• Method - process specifications, operating methods, working methods and management systems, etc.;

 

• Measure - measurement, testing methods and rules, etc.

 

 

② 1E：

• Environment - working environment and security conditions, etc.

 

 

The above 6 factors cover all possible factors that affect the production process in production.

 

The premise for discussing process capability is that 5M1E is operating under stable conditions. Statistically speaking, the process is under statistical control. In other words, it means that the process is only affected by random factors. In this state, the process fluctuations obey statistical laws. As we introduced earlier, the process output quality characteristics obey a normal distribution at this time.

 

(2) Quantification of process capabilities

Capability is a non-quantitative concept, and in actual production only things that can be quantified can be compared and controlled. Therefore, it is necessary to give quantifiable indicators for process capabilities.

 

According to the theory of mathematical statistics, it can be known that if the process output quality characteristics obey the normal distribution, then the possibility of its measured value falling outside the μ±3σ range is very small, and the probability of its occurrence is only 0.27%. Therefore, we can use the range from μ−3σ to μ+3σ to draw the fluctuation range of the process output quality characteristics. In other words, we can use 6 times the size of σ to characterize the fluctuation range of the process output quality characteristics in the steady state. For a stable process, the fluctuations at this time are inherent to the process and are minimal. Therefore, we define the size of this inherent fluctuation range as process capability. In mathematical language, “6σ” represents process capability. Through this definition, process capability becomes a quantitative process capability index.

 

For each process, due to the different 5M1E of the process capability, that is, the different technical levels of people, machines, materials, methods, environment, and measurements that affect the process, the σ value of the inherent fluctuation will be different, and the process capability will also be different. The smaller the 6σ, the smaller the fluctuation of the process output quality characteristics, the thinner and taller its distribution pattern, and the stronger the process capability. On the contrary, the larger the 6σ, the fatter and shorter the distribution graph is, which means the greater the fluctuation of the process output quality characteristics, and the weaker the process capability. The figure below shows the process normal distribution curves of three different σ values. Process 1 has the strongest ability and process 3 has the weakest ability.

 

(3) Understanding of process capabilities

We illustrate this by adding two Tu and Tl representing the upper and lower limits of the process tolerance on the normal distribution curve representing high-level capabilities, as shown in the figure below. Assume that the upper and lower limits of the specification tolerance required by a certain product are Tu and Tl, then When it is less than Tl and greater than Tu, the area enclosed by the curve, the X-axis and the upper and lower limit straight lines is the out-of-tolerance product, that is, the unqualified product. According to the definition of the normal distribution curve, it can be confirmed from Figure 2.61 that for the set tolerance, the number of unqualified products in process 1 is almost zero, the number of unqualified products in process 2 is the shaded area in the figure, and in process 3 Shown in the diagonal part of the drawing, it is obvious that process 3 has the most defective products, so for the given specification tolerance, process 1 is more than capable and process 3 is the weakest.

 

 

 

Process capability reflects the inherent technical level of the process. If the selected process method is not good, for example, the process parameters are unreasonably designed or the performance of the machine equipment is too poor, the quality of the process product will fluctuate greatly and the requirements will not be met. If we use process capability to describe it, it means that the σ output by the process is too large at this time. Even when people, machines, materials, methods, environments, and measurements are all in a stable and normal state, the process cannot meet the requirements. This inherent fluctuation cannot be reduced by controlling the process operation. Only by improving the process method and improving the technical level of the process, such as improving the process or improving product design, can the inherent fluctuation of the process be reduced. Using σ to quantitatively measure the inherent capabilities of the process makes it possible for us to analyze the inherent level of the process to meet customer or process requirements.

 

4. Process capability index Cp and Cpk

 

(1) Calculation of Cp and Cpk

 

σ only reflects the inherent technical level of the process and has nothing to do with our requirements for process control (for example, customer requirements and corporate internal control requirements). In actual production, process capability is relative, and measuring process capability must be meaningful under certain process control requirements. A certain production line may not be able to produce high-precision products, but it may have no problem producing ordinary products. Therefore, it is necessary to compare the process capability σ with the process control requirements to determine whether the process capability is sufficient. In order to measure whether this capability is sufficient, we introduce the concepts of process capability index Cp and Cpk.

 

We have introduced the upper and lower limits of the tolerance Tu and Tl before. Obviously, the difference between Tu and Tl is the specified tolerance range, which we use T to represent. We define the ratio of the tolerance range to the process capability as the process capability index, generally symbolized by Cp. means that its calculation formula is

 

 

 

In the formula, T is the tolerance range, T=Tu−Tl; Tu is the upper limit of the tolerance; Tl is the lower limit of the tolerance; σ is the overall process capability. In actual work, the sample standard deviation S is used instead of σ.

 

The process capability index Cp reflects the precision of the process, and there is a one-to-one correspondence between its size and the number of potentially defective products produced by the process.

 

Based on the size of Cp, the potential output failure of the process can be calculated. Usually we use the table lookup method to obtain the corresponding relationship between Cp and defective product rate. The relationship between commonly used Cp and defective product rate is shown in the table below.

 

 

 

We have pointed out earlier that describing a normal distribution requires two basic parameters: representing the distributionThe feature number μ at the center position and the feature number σ indicating the degree of dispersion of the data distribution. When we discuss the process capability index Cp, μ is not involved, that is, it is assumed that the distribution center of the measurement data is consistent with the target value, that is, μ = 0. But in fact, this situation is just an ideal special case, and there cannot be any deviation between the process distribution center and the target value. As shown in the figure below, although the output fluctuations of process 1, process 2 and process 3 are all the same, and their fluctuations are not large in terms of relative tolerance ranges, due to the existence of deviations, the actual values of process 1 and process 3 are The output fluctuations exceeded the tolerance range, and more defective products appeared. It can be seen that the deviation between the process distribution center and the target value directly affects the output result of the process.

 

 

 

 

Therefore, when there is a deviation between the process distribution center and the target value, the comparison between the size of the process capability and the tolerance range is no longer a simple ratio relationship, but the degree of deviation between the distribution center and the target value must be taken into consideration. In this case, we use the process capability index Cp to characterize the ability of the process to meet requirements.

 

 

 

The calculation formula of Cp is:

 

 

 

1) Basic calculation formula

 

Cpk=（1−k）Cp

 

In the formula, k represents the offset between the process distribution center and the target value in the case of offset. The calculation formula is

 

 

 

In the formula, M = (T1 + Tu) / 2, which is the tolerance center, or the target value of the process; T and μ are defined as before. In actual calculation, the average value X of the sample is used instead of μ.

 

 

 

k is actually the accuracy of the process. When analyzing the accuracy of the process, it is represented by Ca, that is, k=|Ca|. The absolute value of Ca is because the tolerance, whether positive or negative, will result in the final deviation from the target value, which will weaken the process capability. role. Knowing Cp and k, Cpk can be calculated and the percentage of defective products can be found, as shown in the table below.

 

 

 

 

 

Using Ca instead of k, the calculation formula of Cpk can also be written as

 

 

 

2) Practical calculation formulas

 

Cpk=(1−|Ca|)×Cp

 

In actual statistical calculations, when the process control requirement is a two-sided tolerance, the following formula is generally used (as shown in the figure below).

 

 

 

 

 

Each parameter in the above formula has been defined previously and is derived using the calculation formula of Cp and k.

 

 

 

 

 

3) Special calculation formula

 

Some process controls only require upper or lower tolerance limits. For example, when a placement machine mounts components, the coverage area of component leads and pads is required to be greater than 50% or 75%. When the process is one-sided tolerance, the calculation formula of Cpk can be simplified to

 

 

 

Only the lower limit is required

 

 

 

Just ask for the upper limit

 

 

 

 

 

In the formula, Cpu and Cpl are another expression of the process capability index for one-sided tolerance.

 

The graphical representation of the calculation formulas for the above two situations is shown in the figure below.

 

 

 

 

 

(2) Analysis of Cp and Cpk

 

① From the formula Cpk=(1−k)Cp, we know that when k tends to 0, Cpk =Cp. Therefore, the Cp value represents the potential of Cpk, and Cp is also called the potential process capability index.

 

Cp cannot tell us the position of the system distribution in the quality range. As shown in the figure below, Cp is the same in the two processes, but because the position of the system distribution center in the quality range is different, the final defective product rate is also different.

 

 

 

 

 

Only when the measured value has a two-sided tolerance and the process distribution center coincides with the target value, Cp=Cpk (k=0 at this time), Cp is always greater than or equal to Cpk.

 

 

 

② Analyzed by the formula Cpk=Cp × (1−|Ca|), Cpk reflects the relationship between Cpk, Ca and Cp, involving both the parameter Ca representing the accuracy of the measured value and the parameter Cp representing the precision of the measured value. , so Cpk is a capability index that is more representative of the actual process, so Cpk is also called the on-site process capability index.

 

 

 

As shown in Figure (a) below, although the process has good Cp (the Cp value is large, it has potential process capabilities), due to the large Ca, a large number of defective products appear (the Cpk value is small, and the potential process capabilities are not used). , the process needs to be improved.

 

 

 

 

 

When we perform process modulation, the accuracy is improved, that is, the Ca value is reduced, the system distribution center is closer to the target value, and within the same quality range, defective products are eliminated (increasing the Cpk value), giving full play to process capability, as shown in (b) above.

 

 

 

(3) Cpk level

 

1) Usually divided into 4 levels according to Cpk value

 

 

 

 

 

2) Subdivide the levels and applications of Cpk

 

As shown in the table below.

 

 

 

 

 

(4) Qualification rate of products corresponding to Cp and Cpk

 

The qualification rate of typical Cp and Cpk corresponding products is shown in the table below.

 

 

 

 

 

(5) Cpk and 6σ method

 

6σ management is the most influential contemporary quality management method. It is a scientific and systematic quality control system based on digitalization. The 6σ management method is beyond the scope of this book, but the meaning of σ and the relationship between σ and Cpk are closely related to what has been discussed.

 

 

 

When discussing Cp and Cpk, we have given the definition and calculation formula of σ, which are also applicable to the meaning and calculation of σ in 6σ management. When using σ as the confidence level, we need to make it clear:

 

① The process discussed is the normal distribution curve.

 

② If the distribution center of the process data group (actual quality mean) is consistent with the ideal quality control target value (theoretical quality mean), in this ideal state, the 6σ level means Cp=Cpk=2, and the product at this time is not The pass rate or failure rate is only 0.002PPM (0.001 PPM on one side), as shown in the solid curve in the figure below.

 

 

 

 

 

③ But in fact, due to various reasons, the distribution center μ of the data group often deviates from the quality control target value. The actual normal distribution curve that reflects the product quality distribution characteristics will always have its center value offset by mass in the x direction. Control the target value to a certain distance. In the 6σ management method, this offset is set to +1.5σ, or −1.5σ, in which case it will only offset in one direction. When the offset is the largest, the distance between the center of the normal distribution curve, that is, the process mean μ value, and the nearest specification limit is 4.5σ (6σ−1.5σ), as shown by the dotted line in Figure 2.67. At this time, the corresponding curve is The area enclosed between the abscissa axis and Tu is 3.4 PPM; the distance between the center of the normal distribution curve and the other specification limit line Tl is 7.5σ, and the area enclosed between the corresponding curve and the abscissa axis and the Tl line trend 0ppm.

 

 

 

Since the actual process is a non-ideal and biased system, the quality level when using 6σ as the confidence level is 3.4PPM, which means that there are only 3.4 defective products per million products produced, or only 3.4 defective products per million operations. 3.4 turnovers. 6σ represents a product quality qualification rate of 99.9997% or above, which is a high standard that is very close to "zero defects".

 

 

 

The σ and Cpk of the unbiased ideal system, the corresponding percentage of qualified products and the PPM of non-conforming products are shown in the table below.

 

 

 

 

 

The σ, Cp and Cpk of the system with a deviation of ±1.5σ and the corresponding percentage of qualified products and PPM of non-conforming products are shown in the table below.

 

 

 

 

 

(6) Process capability analysis and improvement methods

 

Measuring and calculating Cpk is to improve production efficiency and ensure product quality, so scientific analysis must be conducted on the calculated Cpk.

 

① When Cpk≥1.33, it indicates that the process capability is sufficient. At this time, the stability of the process must be controlled to prevent significant changes in process capability. If the process capacity is considered to be too large, the standard requirements and process conditions should be analyzed. On the one hand, the product quality level can be improved, and on the other hand, the equipment accuracy can be reduced.

 

② When 1.33≥Cpk≥1, the process capability is acceptable but not sufficient. However, when Cp is close to 1, there is a risk of out-of-tolerance. The reasons should be analyzed and measures should be taken to strengthen process control.

 

③ When Cpk < 1, it indicates that the process capability is insufficient. Improvement measures should be taken, process conditions should be changed, standards and technical requirements should be checked, confirmed and revised, equipment should be checked, adjusted and calibrated. If necessary, people, machines, materials and methods should be inspected. Conduct comprehensive inspections on various factors such as , environment and measurement to improve process capabilities.

 

 

 

5. Application of Cp and Cpk

 

 

 

① The size of Cp and Cpk depends on various factors such as people, machines, materials, methods, environment and measurement in the production process. However, in some cases, based on different methods of collecting and analyzing data, the results of Cp or Cpk may be very different. difference. Therefore, when analyzing Cpk, you must first confirm the method of collecting and analyzing data in the process, determine your own indicators according to the specific situation, and conduct scientific analysis and comparison.

 

② When an enterprise evaluates its own and suppliers' process capability index, it is not enough to have the Cpk value. From the above introduction, we can know that at least the Cp value should be used as a reference, so that we can have a more comprehensive understanding of the process. .

 

③ The testing, calculation and analysis of Cp and Cpk are only methods for quality improvement, not the purpose. The important thing is to make an overall plan and grasp the main contradiction. The cost of collecting, calculating, and reporting data can be high. Process capability standards themselves do not directly add any value. These standards are estimates of the expected results of the process, so efforts to improve the process are paramount.

 

④ If the variation of the final result exceeds the prediction by a large amount, you can consider whether there is any influence from the measurement system. In actual production, some companies have experienced situations where the uncertainty of their measurement system accounts for half of the total variation in product output, and they also use this system to analyze improvement plans for the production process.

 

⑤ Cp and Cpk, as an index to measure process capabilities, cannot be perfect. The "Cpk only theory" and the "Cpk useless theory" are not advisable. A large international company's explanation of the evaluation index is of guiding significance: "All indexes have Inadequate and potentially misleading. Any inferences drawn from calculated indices can be appropriately explained from the data used to calculate them."

 

 

 

6. Other relevant indices

 

 

 

In placement machine applications, in addition to the two commonly used indices to measure process capabilities, Cp and Cpk, some other capability indicators are sometimes used, as described below.

 

 

 

(1) Process performance index Pp and Ppk

 

① Pp (Performance Indies of Process): Process performance index without considering process deviation. It is defined as the tolerance range divided by process performance without considering whether the process has deviation.

 

② Ppk: Process performance index when considering process offset, defined as the tolerance range divided by process performance when considering whether the process has offset or not.

 

The relationship between Pp and Ppk is the same as that of Cp and Cpk. The meanings of parameters such as tolerance and process performance are also the same. The calculation methods and formulas are also the same. However, Cp and Cpk must be sampled in the steady state of the system, while Pp and Ppk There is no such requirement. The advantage of the latter is that it can reflect the current actual state of the system and does not require the calculation to be performed in a steady state.

 

Usually, Ppk is used to represent the short-term capability index, or when the output currently meets the specification requirements without considering long-term stability. For example, in the case of small batch production, it is simpler and more convenient to use Ppk.

 

Pp and Ppk reflect the current actual status of the system, and generally require Ppk ≥ 1.67. For detailed discussion and calculation of Pp and Ppk, please refer to relevant information.

 

 

 

(2) Machine capability index Cm and Cmk

 

Cm (Capability index of machine) and Cmk are also equipment capability indicators similar to Cp and Cpk. The difference is that Cp and Cpk reflect the process capability index. The "process" here is the five basic elements of man, machine, material, method and environment. The process of comprehensive action of quality factors, while Cm and Cmk only target the "machine" in it, and do not involve people, materials, methods, and the environment (that is, people, materials, methods, and the environment are considered to be ideal stable factors), so they are simply Reflects the "machine" capability index.

 

 

 

The relationship between Cm and Cmk is the same as Cp and Cpk, the meanings of parameters such as tolerance and process performance are also the same, and the calculation methods and formulas are also similar. Since only the influence of the equipment itself is considered, other factors must be strictly controlled during sampling to avoid interference from other factors.

 

 

 

The different requirements of Cpk and Cmk are described below.

 

• Cpk: at least 1.33;

• Cmk: at least 1.67;

• Cpk: Take 25 groups of at least 100 samples at an appropriate frequency when the process is stable and controlled;

• Cmk: Generally, 10 groups of 50 samples are taken within about one hour after the machine production stabilizes;

CMK is mainly used to confirm the capability of the machine itself and perform Cmk measurement when newly purchased equipment, or equipment has been overhauled or re-debugged, or when product quality problems occur. For detailed discussion and calculation of Cm and Cmk, please refer to relevant information.

 

 

 

2. Other parameters of the placement machine

 

 

 

In addition to the parameters and indicators described above, other parameters are also very important, which often determine what kind of products the existing equipment can produce and what kind of equipment should be used for production of specific products.

 

 

 

1. Component mounting range

 

 

 

The component mounting range mainly refers to the range of the largest and smallest components that can be mounted and the smallest features of the components that can be identified. Due to limited hardware conditions, each machine also has a certain component placement range due to its characteristics. For component placement performance, please refer to relevant information. The main factors that affect the range of components mounted by the placement machine are as follows.

 

 

 

(1) SMD head structure

 

The distance between the nozzles of the turret-type patch head is small, and the stress during the placement process is complicated. Therefore, it is only suitable for mounting smaller and lighter components, rather than the turret-type (translational) patch head. Due to the characteristics of the structure and movement mode, the adaptability range is much wider in terms of component size and weight. For example, the general turret-type placement head is adapted to component sizes not exceeding 35mm × 35mm and thickness not exceeding 6mm, while the range of the translational placement head can reach more than 100mm × 100mm and the thickness can reach more than 20mm.

 

 

 

(2) The size of the camera field of view and the distribution of the suction nozzles

 

The distribution of the placement head nozzles and the size of the camera field of view are the main factors that affect the component placement range. For turret-type and rotary-type placement machines, since components can only be photographed and identified once, the size of the largest component that can be mounted is related to the field of view of the component identification camera. For platform-type placement machines, the suction nozzles are distributed in an in-line manner, and the identification of components can be corrected through multiple video combinations.

 

 

 

The features of the component can be identified in several different ways, but different features require different pixels. For example, chip components require 5 to 10 pixels; one pin pitch of pin components requires 4 pixels; one ball pitch of spherical components requires 8 pixels, etc. The resolution of the camera is also fixed, so the smallest features of the component it can recognize can also be calculated. For example, if the resolution is 2.3 mpp, the length and width of the smallest chip component that can be recognized are 0.292mm;The distance between the small feet is 0.234mm; the minimum ball distance for spherical components is 0.468mm.

 

 

 

(3) Influence of placement speed

 

Mounting speed mainly affects the weight of components that can be mounted. In the high-speed placement process, the faster the component moves, the greater the acceleration value, and the greater the Newtonian force the component receives, so it is easier to produce defects such as material throwing and placement position deviation. For example, general high-speed machines can only place components weighing 6 g, while multi-function placement machines can weigh more than 35 g.

 

 

 

2. Substrate support range

 

 

 

The substrate support range refers to the size range of circuit boards that the placement machine can carry. It depends on the frame size and mechanical structure of the placement machine and cannot be changed for a specific placement machine.

 

 

 

The size of the circuit boards of electronic products ranges from small module circuit boards with a length and width of only a dozen millimeters to special equipment backplanes with a side length of nearly one meter. The thickness ranges from flexible circuit boards with a thickness of only 0.2mm to server motherboards with a thickness of more than 5mm. .

 

 

 

Generally, the minimum size of the substrate supported by the placement machine is 50mm×50mm (length×width), the maximum size of the substrate is 350mm×350mm, and the thickness of the substrate is 0.5~5.0mm. Some placement machines have larger substrate support, such as Genesis from Universal Instruments Corporation (UIC). The size of the circuit board ranges from 50.8mm × 50.8mm to 813mm × 610mm, and the thickness ranges from 0.508 to 6.35mm (the length and width of the circuit board exceeds 508mm) ×508mm, if the thickness exceeds 5.08mm, a large plate clamp needs to be installed).

 

 

 

If the size of the circuit board is small, you can consider paneling into multiple products (as shown in the figure below). In the SMT assembly stage, multi-product panelization can reduce the transmission time of various equipment on the patch production line, reduce the time for calibration of circuit board reference points, and improve equipment utilization.

 

 

 

 

 

3. Maximum loading capacity

 

 

 

The maximum loading capacity of the placement machine is related to its feeder slots. The distance between each station of a placement machine is fixed, so the number of feeder stations of a placement machine is also fixed. However, due to the different packaging widths of different components, the number of machine stations occupied by the corresponding feeders is different, so the quantities that can accommodate different materials are also different.

 

 

 

Generally, in equipment comparison, the maximum number of 8mm feeders that can be loaded by each placement machine is used as a reference. Currently, the number of 8mm feeders that can be loaded by a single placement machine ranges from 64 to 256. For example, the number of stations of Universal Instruments' Genesis placement machine is 72, and a dual-track feeder can be used to load two 8mm materials at one station. The maximum number of 8mm materials it can load is 144. The 12mm feeder occupies 1 station, 16mm, 24mm and 32mm each occupy 2 stations, 44mm occupies 3 stations, 56mm occupies 4 stations, 72mm and 88mm occupies 5 stations.

 

 

 

It can be seen that for materials of different widths, a machine can accommodate different quantities. The multi-function placement machine can also be equipped with a pallet feeder platform as needed. A pallet feeder platform can accommodate multiple pallets of different materials. The Genesis placement machine's tray feeder can accommodate 58 different tray components, and the component trays can be stacked.

 

 

 

The greater the maximum loading capacity of the placement machine, the stronger the adaptability to different products; however, the larger the overall size and weight of the placement machine, the higher the corresponding price.

 

 

 

4. Electrical and gas parameters and environmental requirements of the machine

 

 

 

Electricity and gas are necessary conditions for equipment operation. Before installing the patch production line, you must consider preparing appropriate electricity and gas to ensure normal production.

 

 

 

(1) Electrical parameters of the placement machine

 

• Voltage: Generally, there are two types: AC 200~240 V and 360~400 V. There are differences in different countries and regions;

• Number of phases: generally 3 phases and 5 wires;

• Frequency: There are two types: 50 Hz and 60 Hz, which vary in different countries and regions;

• Current: Generally, the current is 20~50 A;

• Power: Generally 3~10 kW.

 

 

(2) Gas parameters of the placement machine

 

• Air pressure: Air source requirements are generally 5 to 7 kg/cm2 (70 to 95 psi);

 

• Air flow: 100~300 l/min.

 

 

 

(3) Environmental requirements

 

• Temperature: The generally required temperature is 10~30℃, and the recommended temperature is 15~30℃;

• Humidity: 10% to 90%, 50% to 70% recommended;

• Noise: no more than 75 dB, recommended no more than 60 dB;

• Altitude: below 1000 m.

 

 

5. Appearance size, weight and physical load-bearing requirements of the machine

 

 

 

The appearance size, weight and physical load-bearing requirements of the machine play a key role in the storage, transportation, site selection, installation and operation of the machine. How much space is required for an SMT production line, whether the equipment can be installed in the existing factory building, and the carrying capacity of the existing floors will affect a company's equipment selection and investment.

 

 

 

3. Some index terms related to placement machines

 

 

 

In process management and control, equipment maintenance and management, and production line evaluation and improvement in the electronics assembly industry, companies and suppliers currently use many indicators that describe equipment capabilities and processes, such as "placement rate", "placement rate" "Efficiency" and "utilization rate", etc., because there is no unified definition and recognized standard, it causes a lot of troubles for communication and application.

 

 

 

As a common language for technical communication, it is okay for some companies to use their own specific names, but within the entire electronics manufacturing industry, the technical terms that most people are accustomed to should still be used. This book collects, organizes and analyzes various materials, and proposes terminology that conforms to Chinese standards and the habits of most people. It also includes terms from various company backgrounds and sources for readers' reference.

 

 

 

1. Mounting cost

 

 

 

(1) Profit rate of placement machine

 

In the cost of SMT equipment, the placement machine plays an important role. For chip placement machine application manufacturers, whether they are OEM (original equipment manufacturer) or EMS (electronic manufacturing service provider), return on investment is a factor that must be seriously considered. Equipment investment return involves many factors, the most important of which is the profitability of the placement machine. SMT suppliers usually give data such as the placement speed and floor space of the equipment, but for manufacturers, in addition to the parameters provided by the supplier, the best way to calculate the profitability of the SMT machine (over time) is Calculate the placement cost of each component. By comparing placement costs, you can find affordable equipment for your manufacturing company's applications.

 

 

 

Currently, the actual cost of placing each component is not indicated in the technical specifications and flamboyant sales literature. However, if there was a way to break down factors such as operator requirements, floor space, actual speed, changeover time, and spare parts costs, the placement cost issue becomes clear and can be used as a way to compare various machines in the same application. a common approach that will ultimately benefit the entire industry.

 

 

 

(2) Component mounting cost

 

Although reducing the mounting cost of components is a very complex issue, it is not very difficult to evaluate the mounting cost before purchasing the equipment. Currently, the following two methods are commonly used.

 

① Simple estimation: Based on the placement speed provided by the supplier or the actual number of placement components per hour, the placement cost of each component can be simply estimated. The calculation formula is

 

CMC=C/N

 

In the formula, CMC is the placement cost; C is the price of the placement machine; N is the number of placements per hour.

 

 

 

For example, for a placement machine priced at 1.245 million yuan, the number of placements per hour provided by the supplier is 12,250, and the placement cost is

 

1245000÷12250=101.6 (yuan)

 

 

 

This is just a comparison number and can be estimated for all machines under consideration. Obviously, the lower the number, the better. This calculation, N per hour, can be used as a rough comparison to the rates in machine specifications. If we can get the number of patches per hour in actual production, it will of course be closer to reality.

 

 

 

However, to determine the actual placement speed in production, actual placement tests need to be conducted under certain conditions. Each type of machine will have a different placement discount factor for each type of board. Some machines can only achieve 50% of the machine specifications, and some machines may achieve 70%. Prerequisites for the test shall ensure that the rate includes all transfer and reference point identification times, specifying the reel, tube or pallet used for component supply, etc. The best way to conduct this experiment is to prototype the PCB and send it as CAD data to all suppliers under consideration, making sure the supplier has his placement rate in writing and guarantees it.

 

 

 

② Through computer software evaluation:

 

Further estimates can be made with the help of computer software. Companies have developed universal software tools for calculating and analyzing the cost of each mounted component, regardless of the individual equipment supplier. By inputting the manufacturing data of SMT manufacturers, you can easily find the biggest factors wasting time and where the most substantial costs are. It quantifies the placement cost issue that people often only discuss qualitatively, and provides a way to show off when facing different suppliers. The data of the placement machine can be used as a basis for more accurate evaluation.

 

 

 

(3) Factors affecting placement costs

 

In an SMT factory, there is nothing more regrettable than an advanced production line that cost a lot of money to purchase and sit idle. However, in many businesses this is what happens all the time. Why is this? One reason is that, while many of today's placement machines are very good machines, they are not designed to handle small batches (requiring multiple changeovers per day); another reason may be that changeover times are too long. However, the answer is usually not unique, and there may be as many explanations as there are machines. Therefore, reducing the placement cost of each component is not an easy task.

 

 

 

Through actual statistics and analysis of the placement efficiency of the placement machine when processing small batches (requiring multiple conversions per day), it is found that the conversion time used when converting products has a great impact on component placement costs. For example, every day (with two Shift calculation) If 10 changeovers are required, a small improvement in changeover time (such as a 20% reduction) means a 17% reduction in cost per placed component. In contrast, a 20% increase in machine output results in only a 2% reduction in cost per placed component. Reducing the conversion time from 60 minutes to 10 minutes means that the CMC can be reduced by approximately 70%.

 

 

 

Compared with increasing production, this reduction is very significant; assuming a 50% increase in production, from 10,000CPH to 15,000CPH, it can only reduce CMC by 5%.

 

 

 

Operator requirements are the second most important factor in reducing CMC. If the machine is difficult to use and the software is complex, multiple operators will need to be used to achieve shorter changeover times, which increases labor costs. For example, when a third operator is added to use the machine, the cost increases by 25%.

 

 

 

Therefore, when investing in an SMT machine for high-variety and high-volume applications, it is cost-effective to carefully examine placement machine changeover times and operator requirements while considering factors such as the machine's nominal speed and floor space requirements. It is also a method that has been proven to be effective in practice.

 

 

 

In short, SMT placement equipment capabilities are increasing, so placement costs are decreasing. With the continuous introduction of new placement machines, the design complexity of SMT production lines continues to increase. Whether it is EMS or OEM, it is necessary to choose the right machine to meet the changing needs and minimize placement costs in order to maintain its presence in the world. competitiveness in the market.

 

 

 

2. Placement rate

 

 

 

When purchasing a placement machine, the main considerations are its placement accuracy, placement speed and component adaptability. In actual use, in order to effectively improve product quality, reduce production costs and improve production efficiency, how to improve and maintain placement The machine placement rate is the primary issue facing users.

 

 

 

The placement rate is not a performance indicator of the placement machine itself, but an indicator set in order to measure the integrity of the equipment and the normal process in actual production.

 

 

 

(1) The meaning of placement rate

 

The so-called placement rate refers to the ratio of the actual number of components mounted to the number of picked components within a certain period of time. It is calculated by the following formula

 

EP=（N−N1）/N × 100%

 

In the formula, EP is the placement rate; N is the number of picked components; N1 is the total number of discarded parts.

 

Among them, the total number of discarded pieces refers to the sum of the number of errors such as the number of adsorption errors, the number of identification errors, the number of pieces set up, and the number of lost pieces. The identification errors are divided into two types: device specification and size errors and device optical identification defects.

 

 

 

(2) Factors affecting placement rate

 

① Components:

 

• Component size error;

• Surface roughness exceeds standard;

• Defective component taping;

• Component surface contamination.

② Printed board:

 

• Poor surface flatness.

 

③ Feeder:

 

• Wear of the drive part;

• Deformation of feeder structural parts;

• Feeder is poorly lubricated.

④ Nozzle:

 

• Nozzle wear;

• The suction nozzle is blocked by debris (such as scraps from paper tape packaging);

• The air source circuit failure causes insufficient vacuum negative pressure;

• Filter is clogged due to contamination.

⑤ Detection system:

 

• The attenuation of the light intensity of the light source causes recognition errors;

• Recognition errors caused by contamination on the surface of the component thickness detection sensor.

⑥ Process management:

 

• The quality of staff;

• Equipment maintenance system.

 

 

(3) Application of placement rate in production

 

The placement rate is a barometer of the integrity of the placement machine and the normal production process. In actual production, the production status of each machine is monitored by statistical placement rate. Once it is found that the placement rate of a certain placement machine is lower than Specify a standard (such as 99.95%) and treat it immediately as an equipment abnormality. The cause of the abnormality should be found and the problem should be solved before continuing work. In addition, you can also specify the number of shifts per week or month that meet the standard, as well as the minimum placement rate standard (for example, 99.90%).

 

 

 

3. Output rate

 

 

 

Yield refers to the ratio of the number of qualified products obtained when the manufacturing process of a product is completed to the number of product components submitted for production. The calculation method is as follows

 

Y=Np/Nc×100%

 

Number of qualified products / number of product components submitted for production

 

 

 

In the formula, Y is the output rate; Np is the number of qualified products, including products that pass once and products that pass repairs; Nc is the number of product components submitted for production. Generally, the number is based on the number of sets in the component table. According to the vulnerability level of different components, each The number of components can be different.

 

 

 

The output rate can be calculated by product, or by components and parts. When counting by product, the remaining components in Nc are generally not subtracted; when counting by components and parts, Nc can subtract the remaining reusable parts, or it can not be subtracted. It is up to the enterprise according to the product and system. Regulation.

 

 

 

The output rate is not directly related to the grade and speed of the production line equipment. If the assembly of electronic products works properly, it can produce high-quality components at high speed; but if problems arise, the same production line can also produce scraps at high speed.

 

 

 

When there is a problem with throughput, the overwhelming majority of people tend to blame production, which is incomplete and prevents errors from being corrected in manufacturing. In fact, the output rate is controlled by:• Design for Manufacturability (DFM);

• Quality of incoming materials;

• Production processes and equipment;

• Employee quality and process management.

 

 

4. Utilization rate

 

 

 

"Activation rate" is the Japanese name for Activation or Utilization in English. It is more common to use "Activation" within Japanese-funded enterprises or in technical exchanges. In Chinese, it is generally expressed as "efficiency", "effectiveness", "operation" and "starting", which refers to the ratio of the effective amount to the total amount (for example, product quantity and startup time, etc.).

 

 

 

• “Time utilization rate”: utilization rate or activation rate;

• “Performance utilization rate”: performance efficiency;

• “Quality utilization rate”: quality indicator or pass rate;

• "Speed utilization": speed efficiency, etc.

 

 

The meanings and calculation methods of the above indicators such as "usage rate" and "qualification rate" can be found in other chapters of this book. In addition, in Japanese-funded enterprises or in Sino-Japanese technical exchanges, the concepts of "utilization" include "real utilization rate", "value utilization rate", "operation utilization rate", "machine utilization rate" and "Personnel utilization rate" etc.

 

 

 

In these names, "activation" still means "efficiency" and "effectiveness".