In actual production processes, Six Sigma management teams usually use statistical process control methods (SPC) Evaluate and monitor each stage of the process to establish and maintain the process at an acceptable and stable level to ensure that products and services meet specified requirements.
SPC The main manifestations are various control charts and corresponding process capability analysis, and JMP As a professional statistical analysis software, it provides multi-platform support for both, allowing users to freely choose and use according to their own preferences and specific needs. These platforms mainly include:
- Analysis> quality and process > Control Chart Generator
- Analysis> quality and process > Process Capability
- Analysis> quality and process > Several sub-platform items under the control chart ( Such as mean, single value range )
- Analysis> distributed > Capability analysis
We have received a lot of feedback from users about JMP While receiving good feedback on the unique operating experience, we have also received some common questions from some users: the process capability analysis results of these platforms do not seem to be completely consistent, so what is the truth? Let’s take this opportunity to clear up the confusion.
First, let us review the concept of process capability. Of course, here we refer specifically to the process capability analysis of metrological data. The so-called process capability is to evaluate the ability of the process to meet customer requirements or engineering specifications by comparing the width of the process tolerance limit with the variation width of the process metric value ( picture -1) . When the process producing metrological data is stable and the output follows a normal distribution, if the population standard deviation σ of the process output distribution is known, then in principle, the process capability index Cp and pk and process performance index Pp and Ppk can be defined by the following mathematical expressions. in, Cpk/Ppk relatively Cp/Pp The effect of process output center offset is considered.
figure 1 Schematic diagram of process capability analysis
But in fact, since the overall standard deviation σ of the process is usually unknown, it can only be estimated through sample observations. If the emphasis is on examining the process capability from the perspective of inherent fluctuations in the process, that is, the fluctuations are mainly caused by random factors, then for the process of dividing into subgroups, the width of the change will depend on the size of the subgroup capacity and the type of control chart recommended. The value can be calculated by formula-1( Subgroup capacity <9) ,Mode -2 or formula -3( Subgroup capacity ≥ 9) to estimate; for a single-value observation process that is not divided into subgroups, that is, a process monitored by a single-value moving range control chart, the change width value can be expressed by the formula -4 To estimate, the process capability index is then recorded as Cp and pk , also known as the short-term capability index. If the emphasis is to examine the process capability from the perspective of the total process fluctuation, that is, the fluctuation is caused by both random factors and special factors, the change width value can be expressed by the formula -5 is estimated by the standard deviation of the entire sample s To estimate, the process performance index is then recorded as Pp and Ppk , also known as the long-term capability index . In short, it is Cp and Pp , pk and Ppk The numerators in mathematical expression are exactly the same, the only difference lies in how we estimate and explain process fluctuations or variations. Among them, the recommended choice path for process standard deviation estimation is summarized in the figure -2 shown.
figure 2 Choice path for process standard deviation estimation
Next, we directly use a specific case to explain in detail.
Case description: A certain machine continuously produces steel balls, the diameter of which is an important quality characteristic. In order to control the diameter of the steel ball, every 15 minute sampling 1 times, each time the product is extracted 5 a total of samples 25 times, measure and record data ( surface -1) . It is assumed that the steel ball diameter specification limit is [10.90 , 11.00] , the target value is 10.95 , try to conduct process capability analysis.
Table 1 Steel ball diameter process data monitoring table
Obviously, this is a typical subgroup capacity of 5 quality control process, it is appropriate to adopt
Control chart, below we will pass through JMP Different platforms conduct process capability analysis on them.
- analyze > quality and process > Control Chart Generator Platform
Once you have added the "Specification Limits" column attribute to the process variable column information, in the Control Chart Generator platform ( picture -3) Draw this example interactively When drawing a control chart, the corresponding process capability analysis report will be automatically generated. ( picture -4) .
image 3 Control Chart Generator Platform
Figure 4 Process capability analysis report under the control chart generator platform
in,
- s Sigma (Within Sigma, 0.024764) : Since what is drawn is The control chart, therefore, refers to the formula -1 calculated
, corresponding to the process capability index Cp and pk ;
- total Sigma (Overall Sigma, 0.024787) ：That is to say, formula-5 calculated , corresponding to the process performance index Pp and Ppk .
In the future, we will use the output results of this platform as a reference and compare it with JMP Compare the output results of other platforms.
- analyze > quality and process > Process capability platform
Press Figure-5 Shown sets up the launch process capability platform.
Among them, it is important to point out that in JMP By default, nested subgroups ID After the column, within-subgroup variation statistics ( Red box logo ) The default setting is " unbiased mean of standard deviation " , that is, under this setting, within the group Sigma will be the formula -2 to calculate, and as mentioned before, due to the subgroup capacity of this example <9 , so it is more appropriate to use the "average range" as the variation statistic within the subgroup, so the settings should be changed accordingly.
Figure 5 Launch of the “Process Competencies” platform
Furthermore, usually, due to Control charts are more commonly used, so you can also use JMP software's "files" > first choice > platform > Under the "Process Capability" sub-item, change the default setting of the intra-subgroup variation of the platform to "Range Average" to make it more convenient for daily use. ( picture -6) .
Figure 6 Change default settings for mutations within the "Process Capabilities" platform subgroup
Press Figure-5 After setting, click OK, and then click the red triangle next to the process capability. > The output results obtained by "Individual Detailed Report" will be completely consistent with the control chart generator platform. ( picture -7) .
Figure-7 Individual detailed reports under the process capability platform
- analyze > quality and process > Control Charts > mean platform
Similar to the control chart generator platform, once your process variable column information contains the "Specification Limits" column attribute, in the "Control Chart > In the "Mean" startup dialog box, click the graph -8 Set up and check the capabilities. After clicking OK, you can directly output the "Capacity Analysis" report. ( picture -9) .
Figure-8 Start the "Control Chart" > "mean" platform
Figure-9 "Control Charts > Capability analysis report under the "mean" platform
What needs to be pointed out here is that because in JMP13 Under the default setting conditions, the capability analysis report "Not added Ppk capability label", so in the long run Sigma and control chart Sigma The capability label identification under the group report is consistent, which is also for some JMP One of the reasons for confusion among new users. At the same time, it is also necessary to add that the information in the capability analysis report long Sigma Equivalent to Control Chart Generator and Process Capability Platform total Sigma ,and Control Charts Sigma Equivalent to Control Chart Generator and Process Capability Platform s Sigma .
Secondly, for the ability label identification problem, we can pass "File> first choice > platform > Distribution "check" Add Ppk "Competency Label" ( picture -10) , to avoid the above confusion problem ( picture -11) , and its quantitative output results are consistent with the control chart generator and process capability platform.
Figure-10 Add " Ppk "Competency Label"
Figure-11 By adding " Ppk Capability Labels" to avoid identity confusion
- analyze > distributed > Capability Analysis Platform
Finally, let’s introduce the capability analysis platform under distribution. What is different from the platform introduced previously is that when your procedure lists variables Not included When selecting the "Specification Limits" column attribute, click "Analyze > distributed > Red triangle next to diameter > Capability Analysis" will pop up as shown in the figure -12 dialog box, otherwise, only direct output will be based on the long-term Sigma Capability analysis report.
Figure-12 Start "Analyze > distributed > Capability Analysis” Platform
According to Figure-12 Enter the specification limit information as shown and check "Long-term Sigma ” and “ short-term Sigma , group by fixed subgroup size", after clicking OK, a capability analysis report will be generated ( picture -13) .
Figure-13 "analyze > Capability analysis report under "Distribution"
With "Analysis> quality and process > Control Charts > mean " The platform is the same. This platform also has the problem of setting ability labels. The solution is the same as before and will not be repeated here. In the capability analysis report, long Sigma Equivalent to Control Chart Generator and Process Capability Platform total Sigma ;and short term Sigma It is the press formula -3 Calculated, that is, the process fluctuation is estimated based entirely on sample observations, which is consistent with the equation -1 Not equivalent, that is, under this platform short term Sigma Not equivalent to other platforms s Sigma and Control Charts Sigma , therefore it will inevitably cause subtle Estimation bias and differences with other platforms Cp/Cpk Calculation deviation is also the reason why customers ask more questions.
In addition, it should be pointed out that according to personal understanding, on the one hand, in this case, due to the small size of the sample subgroup (=5) , therefore, using the formula -3 It may not be the most reasonable choice to estimate the inherent fluctuation of the process; on the other hand, the choice of how to estimate the process fluctuation actually depends on the user. There is no absolute right or wrong here, just different perspectives and methods for considering the same problem. . Therefore, as long as you can clarify the characteristics of the quality process you are monitoring, choose the appropriate control chart type, implementation platform and process fluctuation estimation method, and analyze the absolute results, relative relationships and changing trends of each quantitative indicator, I believe you can understand the quality you are concerned about. The process capability of the process is objectively evaluated.
The above is all the content to be introduced in this article. We can see that in addition to "Analysis> distributed > Except for the "Capability Analysis" platform, which is slightly special, the process capability analysis results of other platforms are actually completely consistent. Finally, we will JMP The process capability analysis platform selection path is summarized in the figure below -14 shown, if you happen to be using JMP In the process, if you have relevant questions about the application field of process capability analysis, I hope this article can solve your doubts and help you in your actual work.
Figure-14 JMP Process capability analysis platform selection path
