There are many mature methods about SPC in product yield control. For example, based on the P/NP diagram of product defect rate analysis, the U/C diagram of product defect points, or the distribution form of product defect rate conforms to the normal distribution, directly follow the method of continuous data processing, as shown in Figure 1 .
U of #defects
P of #defective
figure 1)
So, what kind of control chart should be used for some data that do not conform to a specific distribution? Today we will introduce another control method --- the quantile method.
What is the quantile method?
Returning to the basic principle of SPC, we need a standard that can identify outliers. The control charts routinely used by SPC are to distinguish abnormalities by setting a control limit (Control Limit) (Rule 1, others will not be discussed for the time being). As we all know, in the case of standard distribution, the probability of the area outside the control limit is less than 0.5%, and the low probability event is the object we need to study. Borrowing the same idea, when the sample size is sufficient but the data distribution is not clear, we use the method of analyzing the percentage quantile of the data to select a fixed value as the threshold (control limit) to identify small probability product batches. Then drill down and assess the risks.
So, how to use the quantile method to select control limits? This will depend on your own risk setting. For example, when we do hypothesis testing, we like to set α = 0.05 and β = 0.1. Based on the same management standards as traditional SPC, the provisional 0.5% here means based on historical large data, we hope to identify 0.5% batches for further evaluation and analysis, as shown in Figure 2.
figure 2)
How to calculate quantiles?
Calculation of quantiles is actually very simple. In addition to the bar graph shown in Figure 2, JMP’s “Tabulate” platform can batch calculate each product, each scrap type, and each layer of management. restrictions, as shown in Figure 3. According to the data structure of your own database, you can simply drag and drop, so that you can quickly get the desired result. One thing to note here is that the product yield rate and scrap rate are selected according to individual needs, so the choice of quantiles needs attention. The figure below is the quantile for calculating the scrap rate, so the quantile of 99.5% is used as the control limit in the calculation.
image 3)
Why use the quantile method?
So, why use the quantile method? When is it appropriate to use it? Does this method also have certain limitations?
- First of all, the quantile method can analyze the situation that the sample structure does not conform to a certain distribution
When the collected sample data does not conform to a specific distribution, the results obtained by enforcing the calculation of control limits will be biased. When using traditional control charts, the first step is to perform distribution fitting on the sample data, and judge whether the data are normal distribution, binomial distribution or Boisson distribution. If the distribution fit is very different, you need to convert the data or increase the sample size to continue the analysis, and the quantile method can directly specify the standard you need according to the level of large data, thus making up for the shortcomings of the traditional method.
- The method of calculating the control limit is simple and diverse
Using the quantile method can get a unique value as the control standard, which is very simple to calculate and there are many ways to calculate it. It can be realized with professional statistical analysis software, such as the "Distribution" (Distribution) and "Tabulate" (Tabulate) functions in JMP, or it can be calculated using Excel (arrange a set of data from large to small, and use the total amount of data to Calculate the serial number of the desired quantile and select it directly).
- Unique control standard, easy to implement
Due to the quantile method calculation, the control limit is unique for each project. On-site QC can easily query the control standard according to the control table, and then confirm whether the product needs to be suspended and notify the engineer for the next step of analysis . (If the company has a production management system, you can try to digitize the control table and link it with the production management system to realize the functions of automatic product control and notification). After a period of time, when the control limit is updated, the engineer can issue a new table and recycle the old table for management (the DB can be refreshed if there is an automatic management system).
For traditional proportional control charts, control specifications need to be calculated for each batch, and whether the results of each batch meet the specifications is recorded. Such an operation process has high requirements for the QC of on-site production. Therefore, it brings higher requirements for personnel management, such as the recruitment and training work faced after the turnover of personnel, which is not conducive to on-site management and product control.
Although there are many bright spots in the quantile method, there are certain limitations in its use, such as:
- There are requirements for sample size
Since the quantile method is a fitting method based on large data, there are requirements for the sample size according to the selected standard. For example, a quantile of 10% requires at least 10 batches to achieve the minimum resolution. A 0.5% quantile requires at least 200 batches to distinguish.
- Not suitable for new project management
The yield control of new products and new projects should follow the design yield requirements, predict the basic yield indicators based on standard manufacturing capabilities and tolerance management, then analyze and improve the entry point, adjust and improve the quality of product batches, and wait until the project is officially released. Start data collection and calculate control limits. However, the quantile method needs a large sample as the basis, which is not suitable for the trial production stage, and during the trial production stage, NPI (or similar departments) often adjust the design or parameters, so the results will change greatly. Stratification (such as bimodal or multimodal data) will be found when observing all trial production data, which is not suitable for management with any kind of control chart. It is recommended to directly set up staged target management, and do SPC management after the mass production of new products is released.
Do regulatory limits need to be updated?
Through the above description, we understand the idea of the quantile method to control SPC. Then, is the control limit fixed after it is set? The answer is obviously no. Regulatory limits should be regularly updated based on actual levels. For example, the production line accumulates more and more production experience for a product, and the product yield rate will naturally develop in a good direction, so the control limit should be recalculated with samples of a certain period.
After reviewing and calculating the regulatory limits of existing products, how to judge whether the regulatory limits need to be updated ( Because the samples are different, the new control limit will be more or less different from the original control limit )? This varies from person to person, and you can set a threshold according to your own situation. Personal experience is based on long-term fluctuating levels of production thresholds. As shown in Figure 4, the author automatically judges whether the control limit needs to be updated after obtaining the threshold by editing the formula.
The + after the column name in Figure (4) means that there is an editing formula in this column.
JSL ——Automated analysis, twice the result with half the effort
Due to the large number of products and more corresponding obsolete codes, the final analysis workload is quite large, and there are many operation steps involving JMP. To this end, we have adopted JMP's unique JSL (JMP Script Language) code, by recording the specific work steps, and then saving and installing, so that the next time you use it, you can analyze it with one click, without having to start from scratch every time Do it again, as shown in the figure below.
Through JSL, we can conduct batch-type automatic analysis of the data that needs to be analyzed, which is convenient for QE to review the control of all products within a limited period, which greatly saves the workload and time cost of QE, so that more energy can be devoted to solving problems problem rather than identification.
