IATF16949:2016 requires control on product or process changes, which are specified in 8.3.6 and 8.5.6. To fulfill these requirements, one may follow the change control procedure as outlined below:
Step 1: Identification of Needs for Changes
The needs for changes may come internally or externally. Internal needs arise from process improvement, capacity expansion, cost reduction, risk management, etc. External needs arise from customer request, customer claims, governmental and legal requirements, etc. It should be noted that the scope of product and process changes is really broad. It’s not limited to the changes in product specification or process parameters which directly impact the product quality. It also includes changes such as new suppliers, new machines, new production line, new control limits of a process, and even new frequency for preventive maintenance. In general, any change in machine, material, measurement, method and environment should be included in the scope of the change control procedure. Regarding to the changes in man, as IATF16949 already have separate requirements in employees qualification, it can be excluded from change control procedure.
Step 2: Change Application
When the need for change is identified, an owner for the change should be assigned and the owner should submit an application of the change proposal to a Change Review Board. The Change Review Board should be a cross-functional team consisting of people from different departments.
When the owner submits the change application, he should identify the content of the change, the purpose of the change, the change level (if a company has a pre-established classification of change levels) and the proposed date of implementation. He should also indicates whether it is a temporary change, and the proposed end date of the change if the answer is “yes”. In automotive industry, customers usually require that suppliers should notify them in advance of product or process changes. In this case, the owner should indicate as well, according to customer requirements, whether the proposed change needs customer notification. Shown below is the suggested information which can be included in a change application.
Step 3: Internal Review on the Change Application
After the Change Review Board receives the application, the members should review the application. If the application is not accepted, the board can terminate the flow. If the application is accepted, it must go to Step 4 if customer notification is needed before further action.
After accepting the application and completing Step 4 if necessary, the board needs to determine whether verification is needed for the changes. If no, then the owner can just implement the change as proposed, and the process stops here. If yes, it goes to Step 5 for change verification.
Step 4: Customer Notification of the Change Proposal
If customer notification is needed according to customer requirements, the customer contact window in the company should send a change notification to the impacted customers, in the format required by the customers. Customer feedback must be received before further action. If customers approve the application, it goes back to Step 3 for internal review on the need of change verification. If customers decline the application, the process stops here.
Step 5: Change Verification
If the change needs verification before implementation, the owner should identify evaluation items and the acceptance criteria, and conduct verification accordingly to determine whether the change can achieve the desired result and cause no negative impact. The owner can consider use the following table to summarize the verification results.
After completing the verification activities, the owner submits the verification reports to the Change Review Board.
Regarding the verification needed for the change, the company or the customers may have a pre-defined list of evaluation items for each type of change. A good example is the Delta Qualification Matrix suggested by ZVEI (German Electrical and Electronic Manufacturers' Association). If such list exists, the owner can also include the evaluation items and acceptance criteria in the change application in Step 2.
Step 6: Internal Review on the Verification Report
After receiving the verification report, the Change Review Board should review the verification activities and results and decide whether the change is acceptable. If not, the change should be rejected and the process stops here. If yes and customer notification is needed, it should go to Step 7 before further action. Otherwise, the change is approved and the owner can start the change implementation (Step 8).
Step 7: Customer Notification of the Verification Report
If customer notification is needed, the verification report should be submitted to the customers after internal approval. If the customers approve the change based on the verification report, it can then be implemented internally as described in Step 8. If the customers reject the change, the process should be terminated here.
Step 8: Implementation of Changes
After the change is approved by the Change Review Board and customers if necessary, the owner can then start the change implementation. The owner should identify what documents should be updated based on the change and notify the document owners to update them accordingly. The owner should also verify the change is implemented according to the planned date. If not, it should be updated with the customers for the proposed new date. Also, the owner should further follow up the product and process after change, and see whether the change achieve the desired objective and whether any negative impact is resulted from the change.
Above, the full process of a change control is described. As some final words of this article, if customer notification is needed, it is suggested that an application should always be submitted before any verification activities. Some companies tend not to notify their customers before they have the verification results. However, if the verification is done and even the results is good, the customers still may reject the change for some other concern. In such case, the verification done is just a waste of resource.
Monday, April 3, 2017
Thursday, March 30, 2017
Difference between Preventive Maintenance and Predictive Maintenance
IATF16949 (and ISO/TS16949) requires preventive maintenance and predictive maintenance for the machines. This article will have a discussion about the difference between these two types of maintenance activities.
First, let’s take a look at their definitions in IATF16949:
Based on their definitions, the most critical difference between preventive maintenance and predictive maintenance is that the former is time-based and it is known when to perform the maintenance, while the latter is machine condition based and it is unknown in advance when to perform the maintenance.
There are some analogies in our daily life for preventive maintenance and predictive maintenance. One analogy for preventive maintenance is the maintenance on your vehicle according to the period suggested by the manufacturer. And one analogy for predictive maintenance is the gas filling in your vehicle tiers: the tire pressure is monitored. Once the tire pressure drops down to a threshold, a light on your vehicle dashboard turns on to notify the driver that it’s time to fill gas into your tires.
For preventive maintenance, one needs to define what should be done to the machines and what is the frequency for such actions. While for predictive maintenance, there’s an extra step: it should be defined first what conditions of the machine should be monitored.
Below is a list of some typical examples of preventive maintenance and predictive maintenance.
First, let’s take a look at their definitions in IATF16949:
- Preventive maintenance: planned activities at regular intervals (time-based, periodic inspection, and overhaul) to eliminate causes of equipment failure and unscheduled interruptions to production, as an output of the manufacturing process design;
- Predictive maintenance: an approach and set of techniques to evaluate the condition of in-service equipment by performing periodic or continuous monitoring of equipment conditions, in order to predict when maintenance should be performed.
Based on their definitions, the most critical difference between preventive maintenance and predictive maintenance is that the former is time-based and it is known when to perform the maintenance, while the latter is machine condition based and it is unknown in advance when to perform the maintenance.
There are some analogies in our daily life for preventive maintenance and predictive maintenance. One analogy for preventive maintenance is the maintenance on your vehicle according to the period suggested by the manufacturer. And one analogy for predictive maintenance is the gas filling in your vehicle tiers: the tire pressure is monitored. Once the tire pressure drops down to a threshold, a light on your vehicle dashboard turns on to notify the driver that it’s time to fill gas into your tires.
For preventive maintenance, one needs to define what should be done to the machines and what is the frequency for such actions. While for predictive maintenance, there’s an extra step: it should be defined first what conditions of the machine should be monitored.
Below is a list of some typical examples of preventive maintenance and predictive maintenance.
Type of Maintenance
|
Typical Examples
|
Preventive maintenance
|
-
Replace a spare part of a
machine periodically, if the life time of the spare part is fixed in days,
months or years;
-
Clean the machine weekly;
-
Apply lubricant to a machine quarterly;
-
Replace the cooling water for
a machine weekly;
-
Fill oil into the machine
bi-weekly;
|
Predictive maintenance
|
-
Count the number of times a
cutter is used and replace the cutter when it reaches the expected life time,
if the life time of the cutter is determined by the times it is used.
-
Monitor the product surface
roughness and sharpen the cutting tool when the surface roughness goes beyond
the control limit;
-
Monitor the vibration of the
machine and tighten the bolts and nuts when the vibration reaches a
threshold;
-
Monitor the gas pressure of a
gas tank and replace the gas tank when the pressure goes below a threshold;
|
How to Calculate GRR%
For GRR analysis on a measurement system, GRR% is used to determine whether the repeatability and reproducibility of the measurement system is acceptable for the purpose of measurement. It is calculated with Equation 1:
In the AIAG’s MSA manual (4th edition), four different approaches are presented to determine TV based on different scenarios:
The above four approaches and the corresponding equations for TV may be confusing to many people who are in charge of MSA in their companies, and they may not be really clear of which equation should be used in actual cases they encounter when doing their GRR analysis. This article is intended to give some additional discussion and clarification about how to decide which equation should be used for TV and in turn GRR% calculation.
To decide which equation to be used, one first needs to consider the purpose of measurement. In general, any measurement conducted on a process has two purposes:
- To judge whether the measured parameter is within or out of the spec limit, for the purpose of OK/NG judgement or product control;
- To decide whether the process is under control (without special cause) and whether the process capability (Cp and Cpk) and performance (Pp and Ppk) meet the requirements, i.e. for the purpose of statistical process control (SPC).
When the measurement is for product control, one cares about the possibility of misjudgment. Misjudgment happens when the true value of a measured parameter is located near the spec limit, indicated with the gray region in the graph below.
The width of the gray region is determined by the variation resulted from the measurement system, i.e. the GRR of the measurement system (The width of gray region is 6 times of GRR. Outside this width, the possibility of misjudgment due to GRR is nearly 0). The wider the gray region is in respective of the tolerance (USL-LSL), the higher the possibility of misjudgment is. Therefore, in order to have a small possibility of misjudgment so that the measurement can really achieve the purpose of product control, the ratio between gray region and the tolerance 6*GRR/(USL-LSL) must be small enough. GRR% should hence be evaluated with the following equation, i.e. the 4th approach presented in the MSA manual:
2. When the measurement is for process control
When the measurement is for process control, one cares whether the obtained data can correctly identify the existence of special causes and whether the measurement can really reveal the true process capability (Cp and Cpk) and performance (Pp and Ppk). Let’s take a look at these two purposes respectively.
2-1. When the measurement is to identify the existence of special causes
In AIAG’s SPC manual, it listed out 8 criteria to identify the existence of special causes, as shown below:
Among all the 8 criteria, the 1st one is mandatory, and the rest are optional. So the discussion here will be just based on the 1st criterion.
To identify the special causes with the 1st criterion, one needs to monitor whether there’s any data point out of the control limits (±3σp). It is similar to judge NG samples from good ones. The difference is that the former uses the control limits, while the latter uses the spec limits. To correctly identify the existence of special causes, one cares about the possibility of misjudgment (i.e. an under-control data point is misjudged as an out-of-control data point, or an out-of-control data point is misjudged as an under-control data point). This is determined by the ratio of the gray region around the control limits with respective to the width of the control limits, i.e. 6*GRR/(UCL-LCL). Therefore, GRR% should be evaluated with the following equation:
2-2. When measurement is to monitor the process capability or process performance
For this purpose, let’s just see how GRR of a measurement system impacts the observed Ppk of a process. It’s similar for other index, including Cpk, Cp and Pp.
Ppk of a process is calculated with the following equation (please refer to P.133 of the 2nd edition of AIAG’s SPC manual)
where σp is the total process variation as observed from the measurement results. This observed process variation includes two sources: one is the actual variation of the process itself σ1, and the other is the variation from the measurement system, which is GRR. According to the property of the normal distribution
So Equation 8 can be rewritten as
It should be noted that Ppk as calculated above is the observed Ppk by the measuring process. It does not reflect the actual performance of the process. The actual Ppk should be calculated as below, without the variation from the measurement system in the denominator:
Comparing Equation 10 with Equation 11, one can see that the larger GRR is, the bigger the difference is between the observed Ppk and the actual Ppk (the former is always smaller). In order to make process control effective, the observed Ppk must be as close as to the actual Ppk, so it causes no misjudgment on the actual process performance. In other words, GRR must be significantly smaller compared with σp, so that Equation 11 can be approximated with Equation 8. Therefore GRR% of the measurement system should be evaluated with the following equation:
This equation is equivalent to Equation 7. So for either purpose 2-1 or 2-2, it comes to the same conclusion, i.e. GRR% should be evaluated as the ratio of GRR with respect to the process variation.
The process variation can be known or unknown when GRR analysis is conducted. Let’s now see how to calculate GRR% based on Equation 7 or 12 in both cases.
When the process variation is unknown, for example, GRR analysis is done when the process is still in design and development stage or the process has just undergone some changes and it has not been studied yet. In such a case, the observed process variation σp can be obtained with following approaches:
- Select a group of samples from the process (It must be noted that the number of parts must be enough to cover the full width of the process variation) and measure the parts variation PV in this group. PV represents the true variation of the process, so the observed process variation σp, according Equation 9, is:
- Use the process variation σp of a similar process, i.e. the 2nd approach:This approach should only be used when it’s not possible to obtain and do measurement on a group of samples representing the full process variation, i.e. the 1st approach is not feasible.
- The process variation is directly known, GRR% can be calculated with the 2nd approach.
- When process variation is not known, but Pp is known, GRR% can be calculated with the 3rd approach.
- When the process variation is not known, but the variation of Xbar, i.e.
or control limits of Xbar, i.e.
is known, GRR% can be calculated with the following equation:
This approach is not mentioned in the MSA manual - If a group of samples is available which represents the full width of the process variation, GRR% can also be calculated with the 1st approach, without using the existing data about the process.
As a summary, the table below lists up the scenarios what equations should be used for GRR% calculation:
Monday, March 27, 2017
做GRR分析时是否可以使用不合格品
在网上看到有个问题:做GRR分析时,是否可以使用不合格品?这个问题的答案是不可以。以下是对于此答案的解释:
进行GRR分析时,GRR%的计算可以根据不同情况采用三种公式(关于三种公式的解释,请参考另一篇文章)。其中,如果测量的目的是为了进行SPC管控,在尚未建立过程的控制限的情况下,GRR%的计算公式如下
此处整个分母代表的是用测量系统观察到的过程的总变化,包括测量系统引起的变化AV&EV和过程本身的变化PV(PV虽然被称为parts variation,但它由过程本身的能力决定,所以是过程本身变化的体现)。因为测量的目的是为了进行SPC管控,所以GRR分析时,需要评价的是测量系统的变化相对于受控状态下过程总变化的大小。如果进行GRR分析的样品中存在不合格样品时,PV将不再代表这个过程在受控状态下的变化(因为存在不合格,代表过程存在特殊因素,所以过程处于非受控状态),而是会大于处于受控状态的过程的变化。根据Equation I,因为PV变大,此时的GRR%将会比没有不合格品时候的GRR%来的小,造成对GRR分析结果的误判。
另外,GRR%计算公式中的AV的计算公式如下
其中Xdiff是进行GRR分析的样品的平均值Xbar的最大值和最小值之间的差值。当存在不合时,这个差值会比没有不合格品的时候要大,从而影响AV的值,并进一步影响GRR%的值。
综上所述,GRR分析时,不应该选择使用不合格品。
进行GRR分析时,GRR%的计算可以根据不同情况采用三种公式(关于三种公式的解释,请参考另一篇文章)。其中,如果测量的目的是为了进行SPC管控,在尚未建立过程的控制限的情况下,GRR%的计算公式如下
此处整个分母代表的是用测量系统观察到的过程的总变化,包括测量系统引起的变化AV&EV和过程本身的变化PV(PV虽然被称为parts variation,但它由过程本身的能力决定,所以是过程本身变化的体现)。因为测量的目的是为了进行SPC管控,所以GRR分析时,需要评价的是测量系统的变化相对于受控状态下过程总变化的大小。如果进行GRR分析的样品中存在不合格样品时,PV将不再代表这个过程在受控状态下的变化(因为存在不合格,代表过程存在特殊因素,所以过程处于非受控状态),而是会大于处于受控状态的过程的变化。根据Equation I,因为PV变大,此时的GRR%将会比没有不合格品时候的GRR%来的小,造成对GRR分析结果的误判。
另外,GRR%计算公式中的AV的计算公式如下
其中Xdiff是进行GRR分析的样品的平均值Xbar的最大值和最小值之间的差值。当存在不合时,这个差值会比没有不合格品的时候要大,从而影响AV的值,并进一步影响GRR%的值。
综上所述,GRR分析时,不应该选择使用不合格品。
Friday, March 24, 2017
How to Use SPC for Process Control and Improvement
SPC is a powerful tool for process control and improvement, but if it’s not properly used, it may cause extra burden to the owners of processes, but bring them with little benefit. To do effective process control and improvement with SPC, one needs to follow the three steps as described below:
1. Process Release
This is done during R&D stage for transferring the process to mass production. A process must be evaluated and can only be released for mass production when it satisfies two conditions:
1) First, collect >= 25 subgroups with a total of >=100 samples of the controlled parameter. The variation within a subgroup should be minimized, so the samples of the same subgroup are suggested to be taken from the same batch or lot, with the least variation in the impacting factors of the process (e.g. materials used, operators, equipment, processing parameters, etc). On the other hand, the variation between subgroups should be maximized. So a subgroup can be taken when the shift is changed, the material lot is changed, or the production line is restarted, etc.
2) Calculate the trial control limits with the data points collected. Plot them in the control charts. Identify any subgroup which signals the existence of a special cause. Exclude these subgroups and repeat this step (more subgroups may be collected to replace the excluded ones if the total number of subgroups falls within 25). Actions should be taken to remove the special cause if it continuously exists in the process.
3) When all the subgroups with special causes are excluded from the control charts, use the reaming subgroups to calculate the control limits and the indicators of the process capability and performance, including Cp, Cpk, Pp and Ppk, and see whether these indicators meet the requirements (e.g. whether Cpk>1.67).
4) If not, take actions on the common cause to improve the process until the indicators meet the requirements.
5) If yes, check the difference between Cp and Cpk. If there exists a big difference, it means the process average is significantly shifted from the process target, and a significant part of the process capability is wasted due to the shift . Actions should be taken to bring the process average close to the target.
6) Also, it’s suggested to check the difference between Cpk and Ppk. If the difference is significant, it indicates the between-subgroup variation is significant, special causes exist and the process is not actually in statistical control. Actions should be taken to remove the special causes.
After all the above steps, special causes originally existed in the process are removed (i.e. the process is now statistically controlled) and all the process capability and performance meet the requirements. The process can now be released for mass production.
After the process is released, the control limits established after the above steps should be continually employed during the mass production. They should not be changed unless there’s intentional change in the process or the reason for the change is clear.
2. Process Monitoring
With the control limits as established during process releasing, the process owner continues the data collection of subgroups, with the defined sampling frequency, sampling scheme and size of subgroups, and monitors:
3. Process Improvement
Even the answers for the three questions in Process Monitoring are all NO, one should never stop there. One needs to study the process and take actions to improve the process, to increase the process capability and performance. The improvement of process requires actions on the common causes, and usually requires the resource support from the management team.
Once the improvement actions have been taken, one needs to go back to Step 1 Process Release, do the evaluation on the process and start over again. As a most significant result from the process improvement, new and tighter control limits are usually established.
1. Process Release
This is done during R&D stage for transferring the process to mass production. A process must be evaluated and can only be released for mass production when it satisfies two conditions:
- The process is under statistical control. In other words, there is no special cause existed and the process is stable and predictable. The distribution of products produced by this process will be the same in the future.
- The indicators of the process capability and performance meet the customer or internal requirements (e.g. many customers require Cpk>1.67).
1) First, collect >= 25 subgroups with a total of >=100 samples of the controlled parameter. The variation within a subgroup should be minimized, so the samples of the same subgroup are suggested to be taken from the same batch or lot, with the least variation in the impacting factors of the process (e.g. materials used, operators, equipment, processing parameters, etc). On the other hand, the variation between subgroups should be maximized. So a subgroup can be taken when the shift is changed, the material lot is changed, or the production line is restarted, etc.
2) Calculate the trial control limits with the data points collected. Plot them in the control charts. Identify any subgroup which signals the existence of a special cause. Exclude these subgroups and repeat this step (more subgroups may be collected to replace the excluded ones if the total number of subgroups falls within 25). Actions should be taken to remove the special cause if it continuously exists in the process.
3) When all the subgroups with special causes are excluded from the control charts, use the reaming subgroups to calculate the control limits and the indicators of the process capability and performance, including Cp, Cpk, Pp and Ppk, and see whether these indicators meet the requirements (e.g. whether Cpk>1.67).
4) If not, take actions on the common cause to improve the process until the indicators meet the requirements.
5) If yes, check the difference between Cp and Cpk. If there exists a big difference, it means the process average is significantly shifted from the process target, and a significant part of the process capability is wasted due to the shift . Actions should be taken to bring the process average close to the target.
6) Also, it’s suggested to check the difference between Cpk and Ppk. If the difference is significant, it indicates the between-subgroup variation is significant, special causes exist and the process is not actually in statistical control. Actions should be taken to remove the special causes.
After all the above steps, special causes originally existed in the process are removed (i.e. the process is now statistically controlled) and all the process capability and performance meet the requirements. The process can now be released for mass production.
After the process is released, the control limits established after the above steps should be continually employed during the mass production. They should not be changed unless there’s intentional change in the process or the reason for the change is clear.
2. Process Monitoring
With the control limits as established during process releasing, the process owner continues the data collection of subgroups, with the defined sampling frequency, sampling scheme and size of subgroups, and monitors:
- Whether the new subgroups indicate the occurrence of any special cause (the rules to identify the special cause can be found in P.75 of AIAG's SPC manual);
- Whether the indicators of process capability and performance fail to meet the requirements;
- Whether the difference between Cp and Cpk or Cpk and Ppk is significant.
3. Process Improvement
Even the answers for the three questions in Process Monitoring are all NO, one should never stop there. One needs to study the process and take actions to improve the process, to increase the process capability and performance. The improvement of process requires actions on the common causes, and usually requires the resource support from the management team.
Once the improvement actions have been taken, one needs to go back to Step 1 Process Release, do the evaluation on the process and start over again. As a most significant result from the process improvement, new and tighter control limits are usually established.
Thursday, March 23, 2017
The Difference Between Cpk and Ppk
What is the difference between Cpk and Ppk? How should they be properly used for process control and improvement? These are probably questions confusing many SPC users. This article will try to answer these questions.
First, let’s compare the difference between Cpk and Ppk. Cpk is an indicator for the capability of the process, the best that the process can achieve, while Ppk is an indicator for the actual performance of the process. A process with, say, Cpk=1.67 may not show its full capability and only shows a Ppk below 1.67, say, 1.50. An analogy to this situation is a student who’s really smart and has the ability to become the top 1 student in the class (his capability), but it’s not necessary that he’ll become the top 1 student (his performance), for reasons such as less devotion than other students.
Second, let’s see why Cpk is an indicator of the process capability, while Ppk is an indicator of the process performance.
To answer this question, we must keep it mind that the first step for SPC control is to adjust the process and ensure it is statistically controlled. Meanwhile, for the sake of easy formulation, let’s assume that the process average coincides with the process target. In such a case
In the above Equation I, (USL-LSL) is the accepted tolerance of the process, and σc the standard deviation of the measured samples (please be noted that it is the standard deviation of all the measured samples, not the average of the subgroups), an indicator of the total process variation. The higher their ratio (i.e. Cpk) is, the lower the chance is to produce a nonconforming product. For a process with a normal distribution and with the process target coinciding with the process average, the correspondence between Cpk and the defective rate (in terms of PPM) is given the following table:
From the table, it can be seen that a higher Cpk results in a lower defective rate, indicating a better ability of the process in producing conforming products.
In Equation I, σc is calculated with the following equation:
where Rbar is the average of the ranges of individual subgroups. Combining Equation I and Equation II, one can see that the capability of a process Cpk is determined by variation within each subgroup.
At this point, one may wonder why the total process variation σc is only determined by the within-subgroup variation. How about the between-subgroup variation? To understand that, we must mention the precondition to evaluate the process capability again: the process is statistically controlled. For such a process, the between-subgroup variation is negligible (according to P.131 in the second revision of AIAG SPC’s manual, the between-subgroup variation is 0 for a statistically controlled process). Therefore, the total process variation, and hence Cpk, is only determined by the within-subgroup variation (please refer to the below image).
In real life, however, a process cannot always be adjusted to statistically controlled state even there is no special cause detected in the control chart. Also, even if the process is in statistical control at the moment of evaluation, a special cause can occur at any future moment and take the process away from statistically controlled state. Therefore, for an actual process, its performance hardly shows its capability as indicated by Cpk. The total variation of the actual process consists of not only the within-subgroup variation, but also the between subgroup variation. The performance of the process, Ppk, is calculated with the following equation
where σp is total variation of the actual process, and it is the combined result of within and between-subgroup variation (please refer to the image below), and is calculated with the following equation:
where Xi is the data point and n is the total number of the sampled data.
As a summary, Cpk is calculated for a process which is under statistical control. The between-subgroup variation is 0, and the process variation comes from within-subgroup variation only. The process in such state is the best performance that a process can achieve, so Cpk represents the process capability. On the other hand, Ppk is calculated for actual process which is not necessarily under statistical control. The process variation consists of both within and between subgroup variations. Therefore, Ppk reflects the actual performance of the process. Ppk can never be larger than Cpk.
Finally, after understanding the difference of Cpk and Ppk, let’s consider how these two indicators should be used for process control and improvement. There’s no question that these two indicators should be monitored to meet customer or internal requriements (e.g. Cpk >1.67). Meanwhile, these two indicators should be monitored together and their difference is evaluated. A big difference between Cpk and Ppk indicates large between-subgroup variation, meaning special cause may exist in the process and actions should be taken to remove the special cause. Cpk and Ppk should never walk alone.
First, let’s compare the difference between Cpk and Ppk. Cpk is an indicator for the capability of the process, the best that the process can achieve, while Ppk is an indicator for the actual performance of the process. A process with, say, Cpk=1.67 may not show its full capability and only shows a Ppk below 1.67, say, 1.50. An analogy to this situation is a student who’s really smart and has the ability to become the top 1 student in the class (his capability), but it’s not necessary that he’ll become the top 1 student (his performance), for reasons such as less devotion than other students.
Second, let’s see why Cpk is an indicator of the process capability, while Ppk is an indicator of the process performance.
To answer this question, we must keep it mind that the first step for SPC control is to adjust the process and ensure it is statistically controlled. Meanwhile, for the sake of easy formulation, let’s assume that the process average coincides with the process target. In such a case
In the above Equation I, (USL-LSL) is the accepted tolerance of the process, and σc the standard deviation of the measured samples (please be noted that it is the standard deviation of all the measured samples, not the average of the subgroups), an indicator of the total process variation. The higher their ratio (i.e. Cpk) is, the lower the chance is to produce a nonconforming product. For a process with a normal distribution and with the process target coinciding with the process average, the correspondence between Cpk and the defective rate (in terms of PPM) is given the following table:
From the table, it can be seen that a higher Cpk results in a lower defective rate, indicating a better ability of the process in producing conforming products.
In Equation I, σc is calculated with the following equation:
where Rbar is the average of the ranges of individual subgroups. Combining Equation I and Equation II, one can see that the capability of a process Cpk is determined by variation within each subgroup.
At this point, one may wonder why the total process variation σc is only determined by the within-subgroup variation. How about the between-subgroup variation? To understand that, we must mention the precondition to evaluate the process capability again: the process is statistically controlled. For such a process, the between-subgroup variation is negligible (according to P.131 in the second revision of AIAG SPC’s manual, the between-subgroup variation is 0 for a statistically controlled process). Therefore, the total process variation, and hence Cpk, is only determined by the within-subgroup variation (please refer to the below image).
In real life, however, a process cannot always be adjusted to statistically controlled state even there is no special cause detected in the control chart. Also, even if the process is in statistical control at the moment of evaluation, a special cause can occur at any future moment and take the process away from statistically controlled state. Therefore, for an actual process, its performance hardly shows its capability as indicated by Cpk. The total variation of the actual process consists of not only the within-subgroup variation, but also the between subgroup variation. The performance of the process, Ppk, is calculated with the following equation
where Xi is the data point and n is the total number of the sampled data.
As a summary, Cpk is calculated for a process which is under statistical control. The between-subgroup variation is 0, and the process variation comes from within-subgroup variation only. The process in such state is the best performance that a process can achieve, so Cpk represents the process capability. On the other hand, Ppk is calculated for actual process which is not necessarily under statistical control. The process variation consists of both within and between subgroup variations. Therefore, Ppk reflects the actual performance of the process. Ppk can never be larger than Cpk.
Finally, after understanding the difference of Cpk and Ppk, let’s consider how these two indicators should be used for process control and improvement. There’s no question that these two indicators should be monitored to meet customer or internal requriements (e.g. Cpk >1.67). Meanwhile, these two indicators should be monitored together and their difference is evaluated. A big difference between Cpk and Ppk indicates large between-subgroup variation, meaning special cause may exist in the process and actions should be taken to remove the special cause. Cpk and Ppk should never walk alone.
Tuesday, March 21, 2017
How to Decide What Analysis can be Exempted from MSA?
The AIAG's MSA manual
requires that five types of analysis shall be done for MSA: bias,
repeatability, reproducibility, linearity and stability. An MSA plan should
cover all these five types for each measurement system appeared in the control plan as discussed in a previous article, unless it can be justified that certain analysis are not
necessary. This article will discuss a couple of examples and explain how one
decides what kind of analysis can be exempted from MSA.
Example I:
Caliper I is
used for thickness check of materials A with a spec of 5+/-0.01mm. Caliper II
is used for thickness check of material B with the spec of B 5+/-1mm. They are
not used for any other measurements. In this case, Caliper I is used over a
range around 4.99~5.01mm. Over such a small range, the impact of linearity to
the measurement result is insignificant. On the other hand, Caliper II is used
over a range around 4~6mm and the linearity of the measurement system could be
a concern. Therefore study of linearity is not needed for measurement system of
Caliper I, but is necessary for measurement system of Caliper II.
Example II:
An electrical platform
scale is used to measure the weight of each product before outgoing. There are
two appraisers assigned for this measurement, but for an electrical platform
scale, the appraisers should have no impact to the measurement result (all the
appraisers do is just to turn on the machine and put the product on the scale.
How they do these things do not change the measurement results), and hence in
this case study of reproducibility is not necessary.
As a general
rule, before deciding what kind of
analysis can be exempted from MSA, one must first understand what variation the
analysis evaluates. The table below is a summary:
Analysis
|
Variation Evaluated
|
Bias
|
Variation
caused by all the factors of the measurement system
|
Repeatability
|
Variation
caused by equipment itself
|
Reproducibility
|
Variation
caused by different appraisers
|
Linearity
|
Variation
caused by measurement range
|
Stability
|
Variation
caused by time difference
|
When
deciding any of the above analysis can be exempted, one must consider whether
the corresponding variation evaluated by this type of analysis has any concern
to the measurement results. If not, then the analysis can be exempted from MSA.
Subscribe to:
Posts (Atom)















