C-chart - Application of Control Charts

Attribute Charts in General, c Charts in Particular

Attribute control charts arise when items are compared with some standard and then are classified as to whether they meet the standard or not. The control chart is used to determine if the rate of nonconforming product is stable and detect when a deviation from stability has occurred. The argument can be made that a LCL should not exist, since rates of nonconforming product outside the LCL is in fact a good thing; we WANT low rates of nonconforming product. However, if we treat these LCL violations as simply another search for an assignable cause, we may learn for the drop in nonconformities rate and be able to permanently improve the process.

The c Chart measures the number of nonconformities per "unit" and is denoted by c. This "unit" is commonly referred to as an inspection unit and may be "per day" or "per square foot" of some other predetermined sensible rate.

Steps in Constructing a c Chart

1. Determine cbar.

There are k inspection units and c(i) is the number of nonconformities in the ith sample.

1. Since the mean and variance of the underlying Poisson distribution are equal,

   

   Thus,

   

   and the UCL and LCL are:

   

2. Plot the centerline cbar, the LCL and UCL, and the process measurements c(i).
3. Interpret the control chart.

Example:

Farnum Example:    
data is from Farnum (1994):     
Modern Statistical Quality Control and Improvement, p. 248    

 Non-conforming   
Day Errors/1000 lines   
1 6   
2 7   
3 7   
4 6   
5 8   
6 6   
7 5   
8 8   
9 1   
10 6   
11 2   
12 5   
13 5   
14 4   
15 3   
16 3   
17 2   
18 0   
19 0   
20 1   
21 2   
22 5   
23 1   
24 7   
25 7   
26 1   
27 5   
28 5   
29 8   
30 8   
    
    
Calculations:    
    
CBAR = 4.4667   
    
UCL = cbar + 3*sqrt(cbar) = 10.80701366 
LCL = cbar - 3*sqrt(cbar) = -1.873680327 = 0
 (when LCL < 0, set LCL = 0) 
  
Day CL UCL  LCL NonConforming
1 4.4667 10.80701366 0 6
2 4.4667 10.80701366 0 7
3 4.4667 10.80701366 0 7
4 4.4667 10.80701366 0 6
5 4.4667 10.80701366 0 8
6 4.4667 10.80701366 0 6
7 4.4667 10.80701366 0 5
8 4.4667 10.80701366 0 8
9 4.4667 10.80701366 0 1
10 4.4667 10.80701366 0 6
11 4.4667 10.80701366 0 2
12 4.4667 10.80701366 0 5
13 4.4667 10.80701366 0 5
14 4.4667 10.80701366 0 4
15 4.4667 10.80701366 0 3
16 4.4667 10.80701366 0 3
17 4.4667 10.80701366 0 2
18 4.4667 10.80701366 0 0
19 4.4667 10.80701366 0 0
20 4.4667 10.80701366 0 1
21 4.4667 10.80701366 0 2
22 4.4667 10.80701366 0 5
23 4.4667 10.80701366 0 1
24 4.4667 10.80701366 0 7
25 4.4667 10.80701366 0 7
26 4.4667 10.80701366 0 1
27 4.4667 10.80701366 0 5
28 4.4667 10.80701366 0 5
29 4.4667 10.80701366 0 8
30 4.4667 10.80701366 0 8

c - Chart:

Six Sigma Answer to Material Shortages

One of Six Sigma¡¯s strengths is its facility for revealing causes and solutions that run contrary to our initial assumptions. When a persistent condition resists all attempts at improvement, or when an obvious fix to a newly discovered problem turns out to be lacking, a methodical approach like Six Sigma¡¯s can uncover even the most unlikely of causes and deliver results.

In the following case study the continuous improvement team was in for just such a surprise. Conventional wisdom was wrong, and the path the team started down hid unexpected complexities.

Definition

The XYZ Pump Garage program overall performance was poor. Future customer orders would not have been forthcoming without substantial improvements in quality and delivery.

• On-time delivery was 80% vs. >99% goal.
• Direct labor overtime was running 15% vs. a goal of zero.
• Field reported defects were found in 50% of system shipments vs. 0.5% goal.
• Project margin was approximately 22% vs. a 33% goal.

A process improvement team was formed with members from Customer Service, Manufacturing, Production Control, Engineering, Operations, and Purchasing.

Measurement

' Initial ' majority team consensus was that the program¡¯s poor on-time delivery was the result of material shortages due to understaffing in Purchasing. More buyers seemed to be the probable solution. The team suspected that the field defects were principally a result of poorly trained assembly staff.

The team began daily monitoring of data for number of daily kit shortages, overdue suppliers, and daily purchasing workload based on Material Requirements Planning (MRP) demands. Field personnel were interviewed for detailed descriptions of field defect rework.

Briefly summarized, the data showed:

• Typical labor overtime occurred near the end of the manufacturing process.
• 100% of all kits were issued with shortages.
• The key suppliers were >3 days late 50% of the time.
• The MRP system was posting material demands inside the material lead times!
• The requested delivery dates for material in the MRP system did not match well with project ship dates!
• A majority of customer-reported defects appeared to be the result of incomplete or incorrect manufacturing documentation.

1. Overtime was being worked to make up lost time due to late material deliveries.
   
2. Understaffing in Purchasing was not the problem! An army of buyers would not result in on-time material when the MRP ¡®buy¡¯ signal came too late or not at all. The team¡¯s true analysis problem was to understand why the MRP System was giving wrong signals. The team decided to focus on one specific sales order line item that exemplified the problem set for a typical system.
   
   What they found:

1. The sales order was coded incorrectly in a fashion that would generate several MRP problems.
2. Item master attributes were not properly populated for many of the material items that had MRP problems.
3. Customer engineering change orders (ECO) had been accepted without renegotiating product delivery dates with the customer to allow time for ECO implementation, including new material delivery.
4. A check of other customer order line items showed similar problems.
   

1. Customer ECO information was not being properly transmitted and propagated throughout the organization, resulting in out-of-date manufacturing instructions and field defects.
   
2. Problems would not have occurred if program participants had properly followed the procedures and work instructions documented in the Quality Management System.

Improvement

The improvements we implemented can be summed up in one word: training. The company had grown significantly during the past year and while all employees had received training, it had sometimes been rushed or had not been completely absorbed by the new personnel. Mandatory training was scheduled immediately for all Customer Service, Engineering, and Operations personnel on the documented procedures for sales order entry, customer engineering change orders, creating item masters, and creating engineering masters. Retraining took 7 working days with approximately 30 personnel participating.

ERP data for all active purchase orders was audited for the most common errors the team had recently discovered. This process required 5 working days.

New delivery dates were negotiated with the customer¡¯s buyer based on the new solid data foundation. This was difficult, but fortunately the customer¡¯s buyer is a mature personality with a long-term partnership attitude.

Results:

• Within 4 weeks material shortages had improved considerably.
• On-time delivery reached 100%.
• Overtime labor became negligible.
• After 8 weeks there had been no field defects found in the 6 systems shipped in the prior 5 weeks.
• Margin has improved to 28%, but this needs further investigation.
• Teamwork between organizations improved as a result of greater appreciation for the needs and complexities of their respective jobs.

Control

On-time delivery, customer field defects, and margin remain the bottom-line metrics for process control on the XYZ program. However, most importantly, as a result of the XYZ team findings, a new continuous improvement team was formed: the Enterprise Resource Planning Data Integrity Team (EDIT). EDIT is tasked with developing a set of strategies and process control tools to insure there are no repeats of the XYZ difficulties on other programs.

Implications

This single Six Sigma project thus had far-reaching implications for the XYZ Pump Garage program. First, in fulfilling the immediate purpose of improving our performance, we achieved customer retention for the near future. On a broader level, we also seized an opportunity to enhance our overall long-term approach to improvement. The value of reaching beyond obvious solutions having been so dramatically reinforced, we created a new continuous improvement team charged with making the pursuit of quality a more proactive endeavor.

Six Sigma Case Study: Defect Reduction in the Service Sector

by Chris Bott

This case study discusses the effective use of Six Sigma tools to improve our plastic issuance processes. It will take you through a project American Express completed, “Eliminate Non-received Renewal Credit Cards.?This analysis demonstrates how we applied Six Sigma techniques to reduce the defect rate with ongoing dollar savings.

Define and Measure the Problem
(Data has been masked to protect confidentiality.)

• On average (in 1999), American Express received 1,000 returned renewal cards each month.
• 65% (650) were due to the fact that the card members changed their addresses and did not tell us.
• The U.S. Post Office calls these forwardable addresses. Please note: Amex does not currently notify a card member when we receive a returned plastic card.

Analyze the Data

We applied various Six Sigma tools to identify Vital Xs, or the root causes of the defect. The use of Chi Square indicated the following:

• By type of card/plastic: We isolated significant differences in the causes of returned plastics among product types. Optima, our revolving card product, had the highest incident of defects but was not significantly different in the percentage of defects from the other card types.
• Issuance reason: Renewals had far and away the highest defect rate in the three areas in which we issue plastic—replacement, renewal, and new accounts.
• Validated reason for returned: Because we suffered scope creep early in the project, it was important to confirm what our initial data was telling us. After testing the five reasons for returns, returns with “forwardable?addresses were overwhelmingly the largest percentage and quantity of returns.

Improve the Process

An experimental pilot was run on all renewal files issued. This “bumping?against the “National Change of Address?service was implemented on all renewal cards in mid August. Due to the strict file matching criteria, this solution will impact 33% of the remaining population (or 333 cards monthly).

As a result of a successful pilot, we were able to reduce the defect rate by 44.5%, from 13,500 to 6,036 defects per million, reflecting annual savings of $1,228. Figure 1 outlines the combined test results.

Fig. 1 Combined Test Results

Non-Received Renewal Credit Cards	Baseline	Test Results
Defect rate	1.35%	.6%
DPMO	13552	6036
COPQ		$3,360
Total annual savings		$1,228
Sigma level	3.71	4.01

Control the Process

To ensure that we perform within the acceptable limits on an ongoing basis, it is important to monitor the new process. To achieve “control?status, we will be using the p chart, a tool that tracks proportions of returns over time.

In addition, our vendor has constructed reporting, which gives us the ability to monitor the defect rate on a monthly basis. The report will tell us if any credit cards that were “bumped?against the "National Change of Address" database were returned back to our warehouse.

Impact on Customer Satisfaction

Using the "National Change of Address" will enable over 1,200 card members to get their credit cards. Prior to this implementation, these card members would have never received their cards automatically. Revenue and customer satisfaction will undoubtedly increase.

(Illustration) Control Plan

Control Plan

Linda : This is the last Step in Control, and therefore, the last step in Six Sigma. Now is the time to make the final decisions on how to control the process in its full implementation and complete the Rockledge Case!

Linda : You were introduced to the components of a Process Control System back in Step 1, but we weren't ready to decide on the control strategies for Rockledge yet, because we hadn't validated the measurement system or confirmed the improvement in the pilot site. Now that we can be sure that the improvements are sound in a pilot environment, we're ready to set up the control system for the full implementation.
Linda : In this lesson you'll learn to describe the options for controlling the process, starting with Risk Management.
Linda : The second strategy to be considered is Mistake Proofing.
Linda : And finally, there are statistical process control charts.
Linda : The latter is perhaps the most complex of the three mechanisms, so you'll be guided through the different types of charts available
Linda : And the creation and evaluation of one commonly used chart. We've got a lot of ground to cover before we're done with this case.

Linda : Before you get into the various control options, here is a reminder of the X's that we need to control at Rockledge. Keep them in mind as you are learning about the strategies, and we'll come back to the case towards the end of this lesson.

Linda : Here are the three mechanisms you can choose from to maintain your process improvement. They are not exactly sequential, meaning that you don't try risk management first, then mistake proofing, and then SPC. However, there is somewhat of a hierarchy.
Linda : Risk Management and Mistake Proofing should be considered before resorting to SPC because they are strategies for avoiding potential problems altogether, whereas SPC can only monitor for potential problems. This become more apparent as we look at each one in more detail.

Linda : The risk management process is similar to the failure modes and effects analysis covered in the measure phase; however, now the focus is on identifying risks to the "X's" -- the sub-processes or product characteristics that were improved.
Linda : Both tools ask you to attach a score to the risk. With the F-M-E-A, the risk priority number is calculated by multiplying Severity times Frequency of Occurrence times Detectability; while the Risk Management score is Impact times Probability. The two formulas use different terms, but really Serverity and Impact are synonymous, and so are Frequency of occurrence and Probability. The key difference is that Dectabality is also included in the FMEA score.
Linda : Risk Management provides a systematic method for identifying risk elements that might interfere with improvement and control, quantifying those elements, establishing a risk abatement plan, and continuously monitoring the progress of the plan. It is a clear method of communicating risks to management and drives clear decisions on risks.
Linda : This is a sample Risk Management document. Select each numbered area to hear how it relates to the steps in the process.
Linda : In this area, potential risks to your improved processes or product characteristics are identified through a description and a type classification
Linda : In this area, the risks are rated according to probability of occurrence and impact on the process. Charts are available in the Resources section of this course to determine those ratings. Those two factors are multiplied to give the issue an overall score.
Linda : Once the risk is identified and rated, a plan is established for abatement, responsibility is assigned, and a measure of success is established.
Linda : Finally the abatement plan is monitored for completion. When the plan is complete, the probability and occurrence should be revised, the risk score recalculated, and that number entered as residual risk.

Linda : The second, and really the most ideal, approach to process control is mistake proofing. As I mentioned before, Mistake Proofing is a method for avoiding errors in a process, so it should be considered prior to utilizing Statistical Process Control.
Linda : The simplest definition I can give is "Mistake Proofing is a technique for eliminating errors by making it impossible to make mistakes in the process.

Linda : The traditional approach to controlling a process was inspection.
Linda : The problem with inspection is it allowed errors to continue,
Linda : caused wasted time and money, as well as customer dissatisfaction due to defects,
Linda : and relied on the abilities of the inspector to catch the defects.
Linda : The mistake-proofing process instead takes action on the original cause of errors,
Linda : By brainstorming sources of errors using tools such as the fishbone chart,
Linda : taking action on the errors
Linda : And thus preventing defects from occurring. It is this attention to process improvement that will take us to Six Sigma performance.

Linda : How you mistake proof a process is different with every situation. As a greenbelt it will be your responsibility to brainstorm mistake-proofing solutions for processes in your work, so I want to give you an opportunity to practice thinking in this manner. Here are a few processes to consider. How could they be mistake-proofed? Type some ideas in each field.

Linda : Unfortunately, mistake proofing is not always possible or economically practical. When that is the case, you must use statistical process control, or SPC, to keep your improvements in control.
Linda : An SPC chart is essentially a feedback system. It's a time-ordered plot of the data that provides a statistical signal when variation is present in a process so that you can take actions to eliminate it. Generating such charts requires ongoing data collection on a process, so you can see why it would be a second choice to mistake proofing.
Linda : Think of a process mapped on an SPC chart like a car driving along a highway, the yellow lines defining a lane represent the expected variation for the process.
Linda : The car might wiggle back and forth a little in its lane - that is inherent to the driving process.
Linda : But when the car heads outside of the lane, there is some special cause interfering, like the driver talking on his cell phone! When the police see that driver getting out of control, they can intervene.
Linda : However, for most processes it is not so easy to see when they begin to move out of control. That is why you collect measurements and create SPC charts and data, because they give you the ability to detect and act upon special causes that are impacting the process performance. That is the basic idea behind statistical process control, but it is not quite that simple. There are several different types of charts and many data patterns you should be aware of. Linda : There are three categories of control charts: Variable control charts; Attribute control charts; and Process focused charts.
Linda : A variable control chart tracks continuous data such as cycle time, length, or diameter, so it provides the most thorough information of all the charting options. And while collecting one piece of continuous data is more costly, fewer pieces are required to get sufficient information on a process.
Linda : An attribute chart tracks discrete data such as pass/fail, good/bad or yes/no. There can be many characteristics tracked in one chart and it is less expensive to maintain, but provides far less information about the process than variable control charts.
Linda : A Process focused chart monitors several characteristics of the same process. It measures only deviation from an established target.

Linda : When selecting a control chart, you choose between an Attribute or Variable charts, based on the data you have. I'll give you a brief overview of the selection process.
Linda : Let's start with Variable control charts, which are used for continuous data. You must first determine the volume of the data.
Linda : Low volume typically occurs because of expense of data collection or when you have a fairly homogenous process output, such as a batch of chemicals. In this case you use Individuals and Moving Range Charts.
Linda : High volume refers to data that is conducive to subgroup sampling. This is the data type we have been primarily focusing on in this training. The X-bar and Range, charts are the most common option for this data type.
Linda : Attribute charts are used for discrete data, such as yes or no.
Linda : The first question to ask is if your lot, or sample, size is constant.
Linda : If the answer is No, you can monitor for the number of defects per lot with the u chart or the percentage of nonconforming units with the p chart
Linda : If the answer is Yes, you can monitor the number of defects per inspection lot with the c chart or the number of non-conforming units with the np chart.

Linda : In this training we will focus on variable control charts because they provide the most valuable information for control, and specifically on a very commonly used chart set, the Xbar and R charts. Some common types of variable control charts are
Linda : the X-bar chart which is a plot of sample means collected over time
Linda : The R chart, which is a plot of a sample range over time
Linda : The S chart, which is a plot of sample standard deviation over time
Linda : And, the individuals chart which is a plot of the individual measurements overtime.

Linda : Like any other statistical process in this training, the SPC chart's usefulness begins with deciding on rational data subgroups that will provide the most information about the process. An example from the production of plastic resin will help to illustrate proper use of the Xbar and R charts.
Linda : In resin production, raw materials go into a device called an extruder that mixes the materials
Linda : and it generates resin pellets.
Linda : Our chart will focus on how to control one of the variables in this process, which is the temperature in the extruder.
Linda : Data subgroups should consider size, frequency and number of samples.
Linda : The sample size for each subgroup should be anywhere from 3 to 5 data points collected in quick successsion. That number will represent normal piece-to-piece variability in a short time period, so that unusual variation between subgroups would signal a process shift that should be investigated.
Linda : In terms of frequency, subgroups should be collected often enough to reflect potential opportunities for change. That might be hourly, daily, monthly, at every shift change, etcetera.
Linda : And, the number of samples should be enough to assure that sources of variation have had time to appear.
Linda : For the extruder case, each sample includes five data points taken in quick succession. The samples are collected every 30 minutes during an eight-hour shift.
Linda : In Minitab, the control charts are generated by choosing Control Charts from the Stat menu. As I mentioned before, we'll look at the X-bar R charts,
Linda : but Minitab will also create several others.
Linda : The resulting charts look something like this. Before talking about the results on this Xbar / R chart, I want to discuss the basic components of the chart.
Linda : The green line down the center represents the process average for the data collected.
Linda : The red lines above and below that are control limits, meaning that if the data is inside these limits, the process is in control - with certain exceptions that I'll talk about in a minute. Control limits can be calculated, based upon a formula that uses the process average and sample size; however, in Minitab the lines appear by default at plus and minus three-sigma around the centerline. The plus and minus 3 sigma has become accepted practice. Be careful not to confuse control limits with specification limits. These lines do not have any association with what the customer wants, they are based purely on the data that has been collected, so keep in mind that a process could be in control and still not be meeting the customer's expectations.
Linda : And, each data point on the chart represents the average or range, as the case may be, of one data sample.
Linda : Knowing that, what can we tell about the temperatures on the extruder? Do you think they are they staying in control?

Linda : This is what a process in control would look like,
Linda : it shows only random variation around the centerline.
Linda : On the other hand, there are several significant patterns that can appear in the data to indicate an out of control state. These patterns fall into the three basic categories shown on screen. Click on each set of images to hear a description of the problem. Keep in mind that these are general concepts for process control; each GE business has its own guidelines for determining adequate process control. Please check with your MBB for guidance.
Linda : In the first examples you see data points that have gone above or below the control limits. Those extreme values indicate a special cause is effecting the process and should be investigated.
Linda : The second set of examples shows several data points in a row on one side of the centerline. This indicates a potential process shift. Analysis should be performed to confirm this possibility, and to identify when the trend began.
Linda : The third set indicates another type of trend, which is 6 or more points in a row that show a steady downward or upward progression. Like the second example, knowing the time trend began can be useful in analysis of the problem.

Linda : Returning to the charts on extruder temperatures, what, if any problems do you see in the data based on the Minitab rules.

Linda : It's been a while since we talked about the Rockledge case, but I hope you didn't forget that we have a job to do! Before we can claim success, we've got to put a control system in place there. Let's take our X's one at a time.
Linda : There is something you need to know that will help us decide the control strategy for this improvement: A torque wrench can be set by the manufacturer to operate only within a certain range of torque. Based on that information, what is the best strategy to use?

Linda : Since Mistake Proofing is the best option, I'd like you to take a minute to think about ways to mistake proof our other X, use of the right nut type. Type your ideas in the text box, then click Done.
Linda : There are a several approaches to mistake proofing the nut type. I think the most thorough is simply to remove the old nut type from the plant so that it cannot be accidentally used. However, there could be other uses for the old nut type that makes it impossible to eliminate, so another option is color coding the nut, placing documentation at each gas turbine indicating that only the blue nuts should be used on this machine, and note this change in existing quality plans. These are a couple of my ideas, you may have thought of some other good solutions.

Linda : Now let's review what you've learned in this step.
Linda : You can now describe the Risk Management role and function in the control phase.
Linda : The concept of Mistake Proofing,
Linda : And finally, the use of statistical process control charts --
Linda : Particularly the X bar and R charts.
Linda : Reviewing the key parts of a process control system, you'll see that having completed step 12, we can now finalize it for the Rockledge case.
Linda : We know our process controls, in both cases we are able to mistake proof the X's
Linda : we have decided on what documentation is required
Linda : and we have already modeled the data collection in the pilot environment, so data on the fully implemented process can be collected in the same fashion. That plan should be documented at this stage.

Linda : Congratulations! You've accomplished your learning goals for this step and have concluded the final step in the Rockledge Case.

Master : Well, kid, just when I was getting to like you, this is our last visit. I've taught you all I can, now its time for you to get out there on your own. But before you go, let's review this last phase you went through, the control phase.
Master: In step one, you started learning about the components of a process control system, including the need for an implementation plan, documentation and training, as well as the requirement that you re-evaluate process capability to confirm the improvements. And you were reminded that the measurement system for the project improvements should be validated before going any further with the implementation.

Master : Then in step 2, you reviewed the process capability analysis. In order to statistically confirm the improvements it should be completed both in the pilot and once the improved process is fully implemented.

Master: Finally in step 3 you completed the process control system by choosing between a risk management system, mistake proofing and statistical process control charting.

(Illustration) Confirmation of the improvements

Confirmation of the improvements

Linda : The measurement system validation in step 1 gave us final confirmation of the tolerance range established by the D O E. Now, the goal in step 2 is to statistically confirm that the improvements have positively impacted the nut removal process.

Linda : Confirmation in Six Sigma means statistics that will back up your decisions. I know not everyone loves stats, but the good news is, in step 2, we are using calculations that you have already learned!
Linda : When you get finished with this step you will be able to apply the process capability and hypothesis testing that you learned in Analyze to the Control phase.

Linda : You may be thinking that it's been a while since Analyze and it's not entirely clear why these tests are repeated during Control.
Linda : All previous steps have led us to believe that the nut removal process at Rockledge will be improved by using New Torque Master Nuts and by setting the torque level on the wrench to 17,000 foot pounds during installation.
Linda : But remember that reaching Six Sigma requires in-depth statistical analysis. Based on the six sigma process, you believe that those improvements will have a beneficial impact on your project Y of reducing nut installation time, but have you statistically confirmed that it does?
Linda : Process capability is the measure for how a process is performing, so to verify that our process is doing better, we need to re-calculate that number now.
Linda : You'll actually recalculate during the pilot phase to see if the capability has improved, then calculate it again after the improvement has gone live in the workplace. The second "real-world" calculation should only happen after enough time has passed to allow sufficient sampling and the process is believed to be in control. For the purpose of this training, that means after you have completed the control tasks presented in Step three.
Linda : A second type of improvement evidence is the result from a hypothesis test. In the Rockledge case that will mean hypothesizing that there has been a change in the nut removal process versus no change in the process.
Linda : Since this means comparing the mean of the original data collected on the nut removal process with data collected after the improvement, and this is continuous data, a two-sample T test is the best choice of analysis.
Linda : Now that you understand why we are performing these analyses, let's get to it!.

Linda : Since we haven't decided on our control strategies in the workplace yet, we are going to be evaluating the capability of the pilot process.
Linda : As always, we've got to begin with the data. This data set was collected over the course of three scheduled outages at the pilot site. The time was measured for removing twenty-two randomly selected bolts on a different gas turbine during each outage.
Linda : Generating the process capability report for this data in Minitab -- as you learned to do in the Analyze phase -- we get the following summary of the Sigma values.
Linda : And, comparing those numbers to the original Z-bench scores for this nut removal process, has the process improved?
Linda : There is an over four-sigma improvement in the process capability and, most importantly, the Defects per Million Opportunites has dropped from around one hundred forty thousand to zero. This is statistical confirmation that in the pilot testing environment, the improvements made to the X's have had a positive impact on the project Y. This report should be generated once again on measurements of the process in its full implementation for confirmation of the process improvement in the real world.

Linda : The final confirmation of success in the Rockledge case is the result from a hypothesis test, because it provides 95% confidence in our decision that we've made an improvement. Which answer best describes our hypothesis for this test?

Linda : To review what we covered in this lesson, you should now be able to apply what you learned in the analyze phase,
Linda : to evaluate the process capability and hypothesis test results for statistical confirmation of the process improvements.

Linda : And in the Rockledge Case, with a dramatically higher sigma score and the definitive results of a hypothesis test, we can now confirm that the process improvements made during the Improve phase, have had a positive impact on the project goal of reducing nut removal time.

Linda : Well, time flies when you are having fun -- I told you I enjoyed my work, didn't I!? We've reached the end of step 2 and you are almost at the end of Duh-may-ic.

(Illustration) Validate Measurement System

Validate Measurement System

Master :Now that the improved process is established, I'll show you how to keep it in place by following the steps of Control.
Master : Step one is validating the measurement system. To assure that the improved process continues working, you often have to measure it. As you may recall, the measurement system can potentially enter variation into your data, so you need to validate it first.
Master: Step two is determining process capability. Part of completing a project is documenting that the process has improved; to do this you need to re-calculate the process capability.
Master: And, step three is to implement a process control system and project closure. You need to make sure that the improved process stays in control, so you document the appropriate procedures for the process, including how to react if it goes out of control, and finalize a plan for checking the process control. Development of the process control system really gets started in step 1, but is implemented business-wide in step 3.

Master : Remember that an improvement is only valuable if it is consistently implemented. So, your job isn't over until a control system has been put in place!
Master : Linda, the control expert, will be helping you with this phase.
Master : So here is Linda to get you started.
Linda : Thanks Master. Before we jump into the Control steps, I want to tell you why I enjoy working with teams at this stage. I find it very rewarding to see improvement visions become reality in the work environment and to establish methods for keeping them in place.

Linda : Like almost everything in Six Sigma, a process control system generally includes taking some measurements to statistically verify your conclusions. And, making sure those measurements tell the truth about a process means first validating the measurement system. So our task in this step will be to perform another Measurement System Analysis.

Linda : Let's begin by discussing what you'll learn in this lesson. Before taking on the primary task for this step, I want you to understand where it fits in the control phase of the six sigma process.
Linda : So first you should be able to describe why and how a control system is established,
Linda : And also the role of a quality plan in the control process.
Linda : And finally, be able to apply the knowledge you gained to verify that you can take accurate measurements of those components.

Linda : Why is a process control system necessary?
Linda : Once the Improve phase is over, the chosen improvement has been shown to work, right? Unfortunately, processes have a tendency to degrade over time, particularly if it's assumed that they'll function in the real world just as they did in a pilot.
Linda : Also, at this stage, the process is generally moving beyond the hands of the Six Sigma team. Those who are responsible for continuing it need a clear understanding of how to implement it consistently and steps to take if it gets out of control.
Linda : Therefore, as part of the Process Control System the Six Sigma team needs to create an implementation plan that includes a strategy for controlling each improved sub-process.
Linda : And, the improved process needs to be communicated to all involved parties through documentation and training.
Linda : A data collection plan is also necessary to test the improved process and confirm that the solutions are indeed having positive impact.

Linda : For many processes GE already has in place what are called "quality plans" to ensure each product characteristic or sub-process stays in conformance with their overall process.
Linda : There are a couple of reasons that you should take into consideration any existing quality plans as part of establishing a process control system for your project. One, the plan may include process procedures and tolerances, as well as items to be monitored for control and response plans in the event of a process breakdown. These can inform your own control plan.
Linda : And two, your improved sub-process may have an impact on the quality plan, so you need to include changes to it as part of your documentation. For now that's enough background on process control, you'll learn more about general control strategies in Steps 2 and 3.

Linda : We currently know that the nut removal process at Rockledge can be improved by using a new nut type and torque setting, and we are getting ready to move into full-scale implementation of those solutions.
Linda : Another way of saying that is "based on our Design of Experiment we have determined the tolerances for the X's that will provide a positive impact on our project Y."

Linda : The overall goal of the control phase is to control the X's, so we must come up with a system to assure that the torque settings are being made correctly and the right nuts are being used. Step 1 is titled Validate Measurement System, and you may be wondering how that fits into the Control phase goal.
Linda : At this step, we haven't decided how to control our X's -- we will make that decision in step 3 -- for the moment, just be aware that because the torque setting is continuous data, it might involve taking ongoing measurements. As you now know, before using a measurement system, you have to validate it. So, that is one reason you perform this task in step 1.
Linda : A second reason is, whether or not we end up collecting data as part of our control system, before going any further, we must verify that the tolerances established in Step 9 were not influenced by any measurement system variation. This really should be done prior to conducting the DOE, but now is your absolute last chance.
Linda : That concludes your briefing. To validate the measurement system you should use the same process that you learned in Measure Step. The key difference is that in measure step the Y was measured, but in this Step it is the X that is being measured.

Linda : Remember the Measurement System Analysis Checklist you used back to guide your assessment? We'll walk through it again as we validate the torque setting measurement system.
Linda : The first couple of items look at the measurement procedure. Torque wrenches have a gauge that displays the torque that will be applied to a nut in foot- pounds. In this case, the measurement procedure would be for the operator to read the torque setting on the wrench, prior to installing each nut.
Linda : Items three, four, and five ask you to consider the three types of gauge error. In this case, the torque wrench has been well calibrated by the manufacturer. The setting is exact within plus or minus five percent. This is acceptable.
Linda : Looking at the last item, because the measurement procedure in this case is so straightforward and the manufacturer has guaranteed that the gage is accurate and precise, we will not be running a Gage R& R.

Linda : Before moving on to step 2, let's review what we have covered.
Linda : In step 1, you learned the importance of a process control system
Linda : and the role of a quality plan.
Linda : Finally, once you had that background knowledge, we validated the measurement system for one of the X's that are being improved by this project. In step two, you'll review how to evaluate if that improvement is having an effect.

Linda : And, that brings us to the end of this Step for the Rockledge case. By going through the Measurement System Analysis checklist, we now know that we have a valid measurement system for recording the torque applied to the nuts.

Extract the Advantages of the Project

For more objectives what the advantages of our project, we can breakdown the advantages by the value, cost saving, defect decreasing, increasing of productivity, cost down of material cost, accuracy time services, etc. There are some tangible advantages can be represent in Money if possible. But, we can extract also the intangible advantages of our project, such as creating new value, creating website as the information system, etc. As long as we can extract the advantages of our project, its mean that our project right to be implemented.

Monitoring the Improvement

Besides we have standardization for implementation of improvement, we also have a monitoring system to control the improvement. Monitoring commonly use the graphical chart such as control chart, etc. Monitoring by using control chart aim to quickly detect the occurrence of assignable causes of process shift so that investigation of the process and corrective action may be undertaken before many nonconforming units are occurred. Monitoring implementation must be sustained in order to gaining success of improvement cycles.

In this phase, monitoring activities will focus on the result (Y) of the process. But, better result we must also control the factors (X) after improvement. Such as analyze concept, to control Y, we must control X’s.

Setup of control chart same like we get the data of capability process. Rational sub grouping needed to get the data point summary (as the representative of the groups, mean or range). Conducting Rational sub grouping is not a ‘must’ but ‘recommended’ in order to get better result. Subgroup size usually have a sample around 4 ~ 5.

Picture C.2 Outlook of Control Chart (Monitoring System)

Control chart will automatically set the control limit as +/- 3 sigma. We expect that this control limit is lower than product/services spec because inside of control limit is process in control equal that this data still inside the spec. But, if data is out of control limit, it’s not meaning out of spec, but the data get closer to the spec limit so we need quick action to investigate and finding the problem in order to not reach the spec limit.

Based on area limit; control chart has three main areas. Area one sigma called save area. We may not fully concern if data spread in this area. Second areas are 2 sigma area or Warning Limit area. If data spread in this area, we must be aware of data spreading and anticipate the action. Third area is +/- 3 sigma area or Action Limit area. If data spread in this area, we must investigate about the causes and finding the solution to control that. In other words, each step in control limit (control chart) makes us to be aware of the data spreading. This activity to ensure whether our improvement run well as the plan and ensure that organization sustain implementing improvement as the result of Improvement phase.

How to detect the uncontrolled data point of the Control Chart?

By using control chart as the main tools to monitoring system, we must know-how to use this tool. We must know how to interpreting data in the control chart. To know whether data is controllable or not, we can perform test of our control chart. There are eight tests to perform control chart monitoring.

1. 1 point more than 3s from center line

2. 9 point in a row on same side of center line

3. 6 point in a row, all increasing or all decreasing

4. 14 points in a row, alternating up and down

5. 2 out of 3 points > 2s from center line (same side)

6. 4 out of 5 points > 1s from center line (same side)

7. 15 points in a row within 1s of center line (either side)

8. 8 points in a row > 1s from center line (either side)

Let us check of control chart bellow:

Picture C.3 Test Performance of Control Chart (1)

Test Results for I Chart of Weight

TEST 1. One point more than 3.00 standard deviations from center line.

Test Failed at points: 14, 23, 30, 31, 44, 45

TEST 2. 9 points in a row on same side of center line.

Test Failed at points: 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 33, 34, 35, 36

TEST 5. 2 out of 3 points more than 2 standard deviations from center line (on one side of CL).

Test Failed at points: 24, 30, 31, 45

TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL).

Test Failed at points: 5, 6, 7, 29, 30, 31, 32, 45

Interpreting the results

The individuals chart shows six points outside the control limits and 22 points inside the control limits exhibiting a nonrandom pattern, suggesting the presence of special causes (Unusual occurrences that are not normally part of the process). See the Session window results for a list of the points that failed each test.

Picture C.4 Test Performance of Control Chart (1)

TEST 6. 4 out of 5 points more than 1 standard deviation from center line (on one side of CL).

Test Failed at points: 5

Interpreting the results

Subgroup 5 failed Test 6, meaning it is the fourth point in a row in Zone B (1 to 2 standard deviations from the center line). This suggests the presence of special causes

Type of Control Chart

Type of control chart is varying. The usages of each type must be applied properly based on the data type and other option rule. Bellow the summary of the Control Chart Type.

Picture C.5 The Application of Control Chart

The application of control chart in general divided due to the type of the data, attribute or continuous data. More detail cases and application of control chart can be learned in Tool Categories.

Create Standardization of Implementation of the Improvement

Standardization is the one of key in controlling phase. Creating standardization will minimize error of uncontrollable process. If we not conduct the standardization, the big opportunity the process will raise variation in process again, not repeatable benefits of the improvement, not changed working method, increase time of maintenance, etc. and the end of the error will increase customer dissatisfaction. (Without standardization, the improvement result from project may not be observed in the real field)

How to create the standardization?

Standardization is the executable and valuable for the organization. Standardization must be detailed explanation and understandable by every member of the organization. Besides that, standardization should be simple and clear based on the working flows and procedure. Also important that it must agreed by the law, national standard or organization policy.

Control Matrix

In the Control phase, the activities, objectives and tools that will be used to break control the improvement application. Detail of Control phase activities are drawn Matrix bellow:

Picture C.1 Control Matrix

The baseline to control of our improvement has some activities that must be implemented. Creating standardization and Monitoring the result is the key activities in this phase. Tighten of controlling will minimize the error repeated again.