Assignable Cause
Published: November 7, 2018 by Ken Feldman
Assignable cause, also known as a special cause, is one of the two types of variation a control chart is designed to identify. Let’s define what an assignable cause variation is and contrast it with common cause variation. We will explore how to know if your control is signaling an assignable cause and how to react if it is.
Overview: What is an assignable cause?
A control chart identifies two different types of variation: common cause variation (random variation resulting from your process components or 6Ms ) and assignable or special cause variation.
Assignable cause variation is present when your control chart shows plotted points outside the control limits or a non-random pattern of variation. Since special cause variation is unexpected and due to some factor other than randomness, you should be able to assign a reason or cause to it.
When your control chart signals assignable cause variation, your process variable is said to be out of control, or unstable. Assignable cause variation signals can be identified by use of the Western Electric rules, which include:
- One point outside of the upper control limit or lower control limit
- A trend of 6 or 7 consecutive points increasing or decreasing
- A cycle or repeating pattern
- A run of 8 or more consecutive points on either side of the average or center line.
Assignable cause variation can be attributed to a defect, fault, mistake, delay, breakdown, accident, and/or shortage in the process. Or it can be a result of some unique combination of factors coming together to actually improve the process. When assignable causes are present, your process is unpredictable. The proper action and response is to search for and identify the specific assignable cause. If your process was improved as a result of your assignable cause, then incorporate it so that the cause is retained and improvement maintained. If your process was harmed by the assignable cause, then seek to eliminate it.
3 benefits of an assignable cause
Assignable causes can be good or bad. They are signals that something unexpected happened. Listen to the signal.
1. Signals something has happened
Special or assignable cause variation signals that something unexpected and non-random has occurred in your process.
2. Specific cause
By investigating and identifying the specific cause of your signal, you can narrow in on your next steps for bringing the process back into control.
3. Can become common cause variation
Good news! You found that your assignable cause for lowered production was due to a power outage. Unfortunately, you may not be able to stop power outages in your community. If nothing is done, your assignable cause becomes a common cause.
You might not be able to stop power outages, but could you install a back-up generator? Then, if the generator doesn’t kick on, you will have an assignable cause you can do something about.
Why is an assignable cause important to understand?
Interpreting what an assignable cause tells you is important to understand.
Provides direction for action
Since an assignable cause can be a signal of something good or bad, you need to understand the different actions. Don’t ignore special or assignable causes.
Not every unusual point has an assignable cause
While at your favorite casino, you may throw a pair of dice at the craps table. Is there an assignable cause for throwing an 11 or a 10, or is it random variation? No, you would expect the process of rolling a fair pair of dice to show 10s and 11s. What about a 13? That would be unexpected and probably the result of something unusual happening with the dice. The same is true for your process. Don’t assume an assignable special cause unless your control chart signals it.
Useful for determining whether your improvements worked
When you improve the process, your control chart should send signals of special cause variation — hopefully in the right direction. If you can link that signal to the specific assignable cause of your improvement, then you know it worked.
An industry example of an assignable cause
The accounts receivable department of a retail chain started to get complaints from its customers about overbilling. Fortunately, the manager of the department had participated in the company’s Lean Six Sigma training and had been using a control chart for errors.
Upon closer review, she noticed that errors seemed to occur more on Fridays than the rest of the week. In fact, the chart showed that almost every Friday, the data points were outside the upper control limit. She was concerned that nobody was identifying that as a signal of special cause.
She put together a small team of clerks to identify why this was happening and whether there was an assignable reason or cause for it. The assignable cause was determined to be the extra work load on Fridays.
The team recommended a change in procedure to better balance the workload during the week. Continued monitoring showed the problem was resolved. She also held an all-hands meeting to discuss the importance of not ignoring signals of special cause variation and the need to seek out an assignable cause and take the appropriate action.
3 best practices when thinking about an assignable cause
Signals of special cause variation require you to search for and identify the assignable cause.
1. Document your search
If you’ve identified the assignable cause, document everything. If this cause happens again in the future, people will have some background to act quickly and eliminate/incorporate any actions.
2. Quickly identify the cause
Time is of the essence. If the cause is resulting in a deteriorating process, act quickly to identify and eliminate the cause. The recommendation is the same if your cause made the process better, otherwise, whatever happened to improve the process will be lost as time goes by.
3. Don’t ignore signals of assignable cause
Even if you get a single signal of special cause, search for the assignable cause. You may choose not to take any action in the event it is a fleeting cause, but at least try to identify the assignable cause.
Frequently Asked Questions (FAQ) about an assignable cause
1. is an assignable cause always bad .
No. It is an indication that something unexpected happened in your process. It could be a good or bad thing. In either case, search for and identify the assignable cause and take the appropriate action.
2. What are some sources of an assignable cause?
Some sources may be your process components such as people, methods, environment, equipment, materials, or information. Your process variation can come from these items and can be the assignable cause of a signal of special cause variation.
3. How do I tell if I should look for an assignable cause?
Control charts were developed to distinguish between common and special cause variation. If they signal special cause variation in your process, seek out an assignable cause and take the appropriate action of either eliminating or incorporating your assignable cause.
Final thoughts on an assignable cause
All processes will exhibit two types of variation. Common cause variation is random, expected, and a result of variation in the process components. Special cause variation is non-random, unexpected, and a result of a specific assignable cause.
If you get a signal of special cause variation, you need to search for and identify the assignable cause. Once found, you will either seek to incorporate or eliminate the cause depending on whether the cause improved or hurt your process.
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Assignable Cause
Last updated by Jeff Hajek on December 22, 2020
An assignable cause is a type of variation in which a specific activity or event can be linked to inconsistency in a system. In effect, it is a special cause that has been identified.
As a refresher, common cause variation is the natural fluctuation within a system. It comes from the inherent randomness in the world. The impact of this form of variation can be predicted by statistical means. Special cause variation, on the other hand, falls outside of statistical expectations. They show up as outliers in the data .
Variation is the bane of continuous improvement . It decreases productivity and increases lead time . It makes it harder to manage processes.
While we can do something about common cause variation, typically there is far more bang for the buck by attacking special causes. Reducing common cause variation, for example, might require replacing a machine to eliminate a few seconds of variation in cutting time. A special cause variation on the same machine might be the result of weld spatter from a previous process. The irregularities in a surface might make a part fit into a fixture incorrectly and require some time-consuming rework. Common causes tend to be systemic and require large overhauls. Special causes tend to be more isolated to a single process step .
The first step in removing special causes is identifying them. In effect, you turn them into assignable causes. Once a source of variation is identified, it simply becomes a matter of devoting resources to resolve the problem.
One of the problems with continuous improvement is that the language can be murky at times. You may find that some people use special causes and assignable causes interchangeably. Special cause is a far more common term, though.
I prefer assignable cause, as it creates an important mental distinction. It implies that you…
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- Assignable Cause
A control chart can identify one of two types of variation: assignable cause (also known as a special cause) and common cause. Let’s look at what assignable cause variation looks like and compare it to common cause variation. This article will explain how to determine if your control signals, and how to respond if it does.
What is an assignable cause?
A control diagram shows two types of variation. common cause variation is a random variation that results from process components or 6Ms. Special cause variation can be assigned.
If your control chart has plotted points that are not within the limit or show a non-random pattern in variation, this is considered assignable cause variation. You should be able to cause it. Special cause variation is unpredicted and caused by something other than randomness.
Your process variable is considered unstable or out of control when your control chart signals assignable causes variation. The Western Electric rules can help you identify signals of assignable cause variation. They include:
- One point beyond the upper limit or below limit
- A trend that has 6 or 7 points consecutively increasing or decreasing
- A repeating or cycle
- A series of 8 or more points consecutively on either side of the average or center line.
Assignable cause variation may be due to a defect or fault, mistake, delay in processing, accident, or shortage. It could also be due to a unique combination of factors that work together to improve the process. Your process can be unpredictable if there are no assignable causes. Your process may have been improved by your assignable cause. If so, you should incorporate it into your process to ensure that improvement is maintained and retained.
A case study from the industry of an assignable cause
Overbilling began to be a problem for the accounts receivable department at a retail chain. The department manager had taken part in Lean Six Sigma training at the company and was using a control chart to correct errors.
On closer inspection, she discovered that Fridays were the most common day for errors. The chart revealed that nearly all data points exceeded the upper limit on Fridays. She was worried that no one was recognizing that as a sign of special cause.
To determine the cause of this, she assembled a small group of clerks. It was Friday’s extra work load that was the cause.
To better balance the work week, the team suggested a change to the procedure. The problem was found and fixed by continued monitoring. An all-hands meeting was also held to discuss the importance of not ignoring signals of special cause variation, the need to search for an assignable cause, and the necessary action to take.
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Assignable causes of variation have an advantage (high proportion, domination) in many known causes of routine variability. For this reason, it is worth trying to identify the assignable cause of variation, in such a way that its impact on the process can be eliminated, of course, assuming that project managers or members are fully aware of the assignable cause of variation. Assignable causes of variation are the result of events that are not part of the normal process. Examples of assignable causes for variability are (T. Kasse, s.237):
- incorrectly trained people
- broken tools
- failure to comply with the process
Identify data of assignable causes
The first step you need to take when planning data collection for assignable causes is to identify them and explain your goals . This step is to ensure that the assignable causes data that the project team gathers provides the answers that are needed to carry out the ' process improvement ' project efficiently and successfully. The characteristics that are desirable and most relevant for an assignable causes are for example: relevant, representative, sufficient. In the planning process for collecting data on assignable causes, the project team should draw and mark a chart that will provide the findings before actual data collection begins. This step gives the project team an indication of what data that can be assigned is needed (A. van Aartsengel, S Kurtoglu, s.464).
Types of data for assignable causes
There are two types of data for assignable causes, qualitative and quantitative . Qualitative data is obtained from deseriography resulting from observations or measures of different types of characteristics of the results of the process in terms of narrative words and statements. However, the next group of data, which are quantitative data on assignable causes, are derived from the description of observations or measures of process result characteristics in terms of measurable quantity in which numerical values are used (A. van Aartsengel, S. Kurtoglu, s.464).
Determining the source of assignable causes of variation in an unstable process
If an unstable process occurs then the analyst must identify the sources of assignable cause variation. The source and the cause itself must be investigated and, in most cases, unfortunately also eliminated. Until all such causes are removed, then the actual capacity of the process cannot be determined and the process itself will not work as planned. In some cases, however, assignable cause variability can improve the result, then the process must be redesigned (W. S. Davis, D. C. Yen, s.76). There are two possibilities for making the wrong decision, which concerns the appearance of assignable cause variations: there is no such reason (or it is incorrectly assessed) or it is not detected (N. Möller, S. O. Hansson, J. E. Holmberg, C. Rollenhagen, s.339).
Examples of Assignable cause
- Poorly designed process : A poorly designed process can lead to variation due to the inconsistency in the way the process is operated. For example, if a process requires a certain step to be done in a specific order, but that order is not followed, this can lead to variation in the results of the process.
- Human error : Human error is another common cause of variation. Examples include incorrect data entry, incorrect calculations, incorrect measurements, incorrect assembly, and incorrect operation of machinery.
- Poor quality materials : Poor quality materials can also lead to variation. For example, if a process requires a certain grade of material that is not provided, this can lead to variation in the results of the process.
- Changes in external conditions : Changes in external conditions, such as temperature or humidity, can also cause variation in the results of a process.
- Equipment malfunctions : Equipment malfunctions can also lead to variation. Examples include mechanical problems, electrical problems, and computer software problems.
Advantages of Assignable cause
One advantage of identifying the assignable causes of variation is that it can help to eliminate their impact on the process. Some of these advantages include:
- Improved product quality : By identifying and eliminating the assignable cause of variation, product quality will be improved, as it eliminates the source of variability.
- Increased process efficiency : When the assignable cause of variation is identified and removed, the process will run more efficiently, as it will no longer be hampered by the source of variability.
- Reduced costs : By eliminating the assignable cause of variation, the cost associated with the process can be reduced, as it eliminates the need for additional resources and labour.
- Reduced waste : When the assignable cause of variation is identified and removed, the amount of waste produced in the process can be reduced, as there will be less variability in the output.
- Improved customer satisfaction : By improving product quality and reducing waste, customer satisfaction will be increased, as they will receive a higher quality product with less waste.
Limitations of Assignable cause
Despite the advantages of assigning causes of variation, there are also a number of limitations that should be taken into account. These limitations include:
- The difficulty of identifying the exact cause of variation, as there are often multiple potential causes and it is not always clear which is the most significant.
- The fact that some assignable causes of variation are difficult to eliminate or control, such as machine malfunction or human error.
- The costs associated with implementing changes to eliminate assignable causes of variation, such as purchasing new equipment or hiring more personnel.
- The fact that some assignable causes of variation may be outside the scope of the project, such as economic or political factors.
Other approaches related to Assignable cause
One of the approaches related to assignable cause is to identify the sources of variability that could potentially affect the process. These can include changes in the raw material, the process parameters, the environment , the equipment, and the operators.
- Process improvement : By improving the process, the variability caused by the assignable cause can be reduced.
- Control charts : Using control charts to monitor the process performance can help in identifying the assignable causes of variation.
- Design of experiments : Design of experiments (DOE) can be used to identify and quantify the impact of certain parameters on the process performance.
- Statistical Process Control (SPC) : Statistical Process Control (SPC) is a tool used to identify, analyze and control process variation.
In summary, there are several approaches related to assignable cause that can be used to reduce variability in a process. These include process improvement, control charts, design of experiments and Statistical Process Control (SPC). By utilizing these approaches, project managers and members can identify and eliminate the assignable cause of variation in a process.
- Davis W. S., Yen D. C. (2019)., The Information System Consultant's Handbook: Systems Analysis and Design , CRC Press, New York
- Kasse T. (2004)., Practical Insight Into CMMI , Artech House, London
- Möller N., Hansson S. O., Holmberg J. E., Rollenhagen C. (2018)., Handbook of Safety Principles , John Wiley & Sons, Hoboken
- Van Aartsengel A., Kurtoglu S. (2013)., Handbook on Continuous Improvement Transformation: The Lean Six Sigma Framework and Systematic Methodology for Implementation , Springer Science & Business Media, New York
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Special Causes of Variation | Assignable causes | Types of variations
Special Causes of Variation are also known as Assignable Causes (un natural) of variation.
If Special cause of variations are present in a process, then the voice of the process is neither stable nor predictable and is said to be out of statistical control.
SPC technique uses Control Charts to monitor and control the Special Cause of variations present in the manufacturing process.
Control Chart is considered as one of the Seven Basic Quality Tools used for product and process improvement.
Table of Contents
Special Causes (Assignable causes)
- Special cause of variation are not always acting on the process.
- Process is not under Statistical control.
- Process output is unpredictable.
- Process is not stable over time.
- Erratic fluctuations and Shift occurred in process.
Type of Special Causes of Variation
- Extreme Variations
- Erratic Fluctuations
- Indication of Trend
Extreme Variations : Extreme variation is recognized by the points falling outside the Upper and Lower control limits.
Causes of Extreme Variations:
- Error in measurements and calculations.
- Wrong setting of machine, tools etc.
- Samples chosen at the start or at the end of an operation.
Erratic Fluctuations : Erratic fluctuation is characterized by ups and downs. This may be due to single cause or a group of causes affecting the process.
Causes of Erratic Fluctuations:
- Frequent adjustment of machine.
- Change in Man, machine , method and material etc.
- Processing of different types of material.
Shift : When a series of consecutive points fall above or below the centre line on the control chart then it is assumed that shift in the process has taken place. It is generally assumed that when 7 consecutive points lie above or below the centre line, the shift is occurred.
Causes of Shift:
- Change in Machine setting.
- Change in Material.
- Loose fixture etc.
- Change in Operator, Inspector and Inspection equipment.
- Unskilled or New operator or carelessness of the operator.
Indication of Trend : If the consecutive points on control chart tend to move steadily either towards Upper Control Limits (UCL) or Lower Control Limit (LCL), then it can be assumed that process is indicating a ‘Trend’ i.e. change is taking place slowly.
Causes of Trend:
- Wear of thread on clamping device
- Clogging of fixtures and holes
- Effect of temperature and humidity.
Common Causes Vs Special Causes
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What is Statistical Process Control (SPC)?
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ASSIGNABLE CAUSES OF VARIATIONS
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Assignable causes of variation are present in most production processes. These causes of variability are also called special causes of variation ( Deming, 1982 ). The sources of assignable variation can usually be identified (assigned to a specific cause) leading to their elimination. Tool wear, equipment that needs adjustment, defective materials, or operator error are typical sources of assignable variation. If assignable causes are present, the process cannot operate at its best. A process that is operating in the presence of assignable causes is said to be “out of statistical control.” Walter A. Shewhart (1931) suggested that assignable causes, or local sources of trouble, must be eliminated before managerial innovations leading to improved productivity can be achieved.
Assignable causes of variability can be detected leading to their correction through the use of control charts.
See Quality: The implications of W. Edwards Deming's approach ; Statistical process control ; Statistical...
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Deming, W. Edwards (1982). Out of the Crisis, Center for Advanced Engineering Study, Massachusetts Institute of Technology, Cambridge, Massachusetts.
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Difference Between , Qualitypedia , Six Sigma
- Special Cause vs. Common Cause Variation
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What is the variation?
Whatever measurement we take, there is always a variation between these measurements. No two items or measurements are precisely the same.
The problem with the variation is that it is the enemy of quality. Variation and quality do not go hand in hand. Variation reduction is one of the significant challenges of quality professionals.
Two types of variation, and why is it important to differentiate?
When dealing with variation, the challenge quality professionals face when to act and when not to act. Because if you act on each and every variation in the process and adjust the process, this will be a never-ending process. Dr. Deming called this "tempering the process." Rather than improving the quality, tempering, in fact, reduces the quality. Deming demonstrated the effect of tempering with the help of a funnel experiment.
The causes of variation can be classified into two categories:
- Common Causes
- Special Causes
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Common Cause Vs Special Cause: Types of Variation
Common cause variation is the natural variation in the process. It is a part of the process. There are "many" causes of this type of variation, and it is not easy to identify and remove these. You will need to live with them unless drastic action is taken, such as process re-engineering.
Common causes are also called n atural causes, noise, non-assignable and random causes .
Special cause variation, on the other hand, is the unexpected variation in the process. There is a specific cause that can be assigned to the variation. For that reason, this is also called as the assignable cause . You are required to take action to address these variations.
Special causes are also called assignable causes .
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Control Charts to identify special causes
If the measurements of a process are normally distributed, then there is a 99.73% chance that the measurement will be within plus and minus three standard deviations. This is the basis of control charts.
If you plot the measurements on a Control Chart, then any measurements which are outside the plus and minus three standard deviation limits are expected to be because of a special cause. These limits are called as the Upper Control Limit (UCL) and the Lower Control Limits (LCL), Once you get such measurement, you are expected to investigate, do the root cause analysis , find out the reason for such deviation and take necessary actions.
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What are the Basic Statistical Concepts
What Shewhart discovered in the ’20s is that variability is as normal to a manufacturing process as it is to natural phenomena like the movement of molecules in a jar of fluid. No two things can ever be made exactly alike, just as no two things are alike in nature. The key to success in manufacturing is to understand the causes of variability and to have a method that recognizes them. Shewhart found two basic causes of variability: common causes and assignable causes.
Common Causes of Variability
Probability and chance.
If we flip a coin and count the number of heads versus tails, at first we may get a few more of one than the other but over the long run, they will be fairly even (Figure 1.3.1). We say that the probability of heads in a coin toss is 50% or 0.5. Probability is a statistic. For a few coin flips, this probability may not be a reliable indicator of the outcome, but it tends to be more reliable as larger groups of coin tosses are counted. Coin tosses may vary purely by chance, and chance is what is known as a common cause of variability.
Unequal Frequency Distribution
Another example of common causes at work is the throw of the dice. If we repeatedly throw a pair of dice and record the totals, we will get an unequal distribution of results. The possible outcomes are the numbers 2 through 12, but as any craps game player will tell us, the frequency of their occurrence varies. Dice pair combinations total some numbers more frequently than others, as shown in Figure 1.3.2. The number 7 will occur in six combinations whereas the number 12 has only one. Over the long run, the probability of the number 7 occurring is .167 or about 17%, which is greater than the number 2, which is about 3%. A pair of dice produces an example of an unequal frequency distribution, but it is entirely due to common causes.
Constant-Cause System
Whenever the outcomes of a process can be expressed in probabilities, and we are certain about the distribution of outcomes over the long run, we have what is known as a constant-cause system.
As you may have guessed, manufacturing processes sometimes behave like constant-cause systems. The causes of variation are commonplace like dice throws. If left to produce parts continually without change, the variation would remain. It cannot be altered without changing the process itself. Statistics provide us with ways of recognizing variation due to common causes. The main one is the control chart. By using a control chart we can separate common causes from the second type, which are called assignable causes.
Assignable Causes of Variability
A change of materials, excessive tooling wear, a new operator — these types of things would produce variation in a process that is different from variation due to common causes. They disturb a process so that what it produces seems unnatural. A loaded pair of dice is another example. Since we know what a regular pair of dice produces over a large number of rolls, we can be reasonably sure a pair of dice is loaded if, after a large number of rolls, we have more 12s than 7s.
When we look for problems in a process we are usually just looking for these assignable causes of variability. Assignable causes produce erratic behavior for which a reason can be identified. One might ask why we are going through all the trouble. Why separate assignable causes from common causes when we have to compare parts to a specification anyway? One reason is that we can minimize variability when we know its causes. The less variability we have in our parts, and the closer they are to the target, the happier our customers will be. They will be confident in our ability to supply a good, consistent product with few or no parts out of specification. On the other hand, large variability may result in parts being out of specification.
Choices for many parts of the specification
If there are many parts out of specification, we have three choices: 1) continually inspecting all parts and using the good ones, 2) improving the process until most or all parts are good, or 3) scrapping the process and building a better one. Since 100% inspection is expensive and inefficient in most cases, we are better off trying to improve the process and reducing our inspection load — which brings us back to the process. There is no sense in trying to improve a process that won’t do the job for us. Also, we don’t want to scrap a process that potentially could work like a charm. Therefore, we need a way to determine whether the process can consistently produce good parts. The only reliable method is through the use of control charts to find and eliminate the assignable causes of variation.
Basic Statistical Terms
Before we go on to the basic statistical concepts presented in the following sections, there are some terms that we need to discuss. Refer to Figure 1.3.3 as these terms are presented.
Sample Term
As we collect data, we pull samples from the process. A sample is an individual piece of measurement that we collect for analysis. Samples are usually pulled in rational groups called subgroups. Groups of samples that are pulled in a manner that shows little variation between parts within the group, such as consecutive parts off a manufacturing line, are considered rational subgroups.
Once we have collected the samples that make up our subgroup, we can calculate the average of this data, otherwise called the mean. The symbol used to represent the mean is x, pronounced x-bar. We can continue to collect our subgroups at regular intervals. Once we have collected a number of subgroups and calculated the mean of each one, we can also calculate the overall average of the data. This is called the grand average and is represented by X. As we have been collecting data, we have pulled just a few samples from all of the parts we manufacture. All of the parts we make constitute a population or universe. It would be very difficult and time-consuming to measure every part manufactured, so we use the samples and statistical analysis to give us an idea of what all of the parts in our universe look like. The statistical concepts that are used to make conclusions about the universe are introduced in the following sections of this chapter and the remaining chapters.
Measures of Central Tendency
Many processes are set up to aim at a target dimension. The parts that come off the process vary, of course; but we always hope they are close to the nominal and that very few fall outside of the high and low specifications. Parts made in this way exhibit what is called a central tendency. That is, they tend to group around a certain dimension (Figure 1.3.4).
The most useful measure of central tendency is the mean or average. To find the mean of measurement data, add the data together and divide by the number of measurements taken. The formula would be:
Each x is a measurement and n is the number of measurements. In statistics, the average is symbolized by x. If we use the Greek letter for summation ∑, the formula can be written as:
There are two additional measures of central tendency that can be used. The first is the median, which is the middle of our data. The median splits our data in half, so 50% of our parts are above the median, and 50% are below. The second measure of central tendency is the mode, which is the most frequently occurring value in our data.
Figure 1.3.5 is a histogram showing one dimension and its variation among 50 parts. The histogram shows the frequency of parts at each dimension by the height of the bars. Notice that the x is not at the most frequent value. The most frequent value (mode) is just to the left of it. Now, look at Figure 1.3.6. The mean value in this histogram seems to be among the least frequent values that occurred. Obviously, without some kind of statistic that tells us about the spread or dispersion of our data, the mean does not tell us enough. Averages are used in many sports, from bowling to baseball. When we know someone’s bowling average or baseball hitting average we have some indication of how good that person is, but not really enough information about consistency. Lurking behind a low average could be a lot of great games and a few very bad ones. A good average could merely be the work of an average player with a few lucky games.
Range and Standard Deviation (Sigma)
Two measures of dispersion are used in statistics, the range and the standard deviation.
Range Formula
The range tells us what the overall spread of the data is. To get the range, subtract the lowest from the highest measurement. The symbol for range is R. The formula is:
This formula simply tells us to subtract the smallest measurement from the largest. Now that we have a measure of spread and a measure of central tendency, why do we need a third statistic? What does standard deviation tell us that range and average do not? To help answer this, we need to look at Figure 1.3.7. Two different histograms are pictured. Rather than bars, continuous lines are used to show the shape of the distributions. We can imagine that if enough data was collected, and if the data was represented by bars of very narrow width, a bar histogram would look nearly like the curves shown here.
Standard Deviation Formula
The two histograms have different shapes, yet the ranges and averages are the same. This is when we use the standard deviation. Standard deviation uses all of the data displayed on the histogram, not just the highest and lowest points, and gives us a better idea of what the distribution looks like.
The standard deviation of a population (universe) is called sigma in statistics and is symbolized by the Greek letter σ. Sigma can be calculated using this formula:
µ is the mean of the data, x is an individual measurement, and N is the total number of measurements in the universe. It is not very often that we calculate the sigma because measuring all of the parts in the universe is very time-consuming. Instead, we estimate the population standard deviation by pulling samples and calculating the sample standard deviation s. The formula for s is:
This formula is called the n-1 formula because of its denominator. The more classic standard deviation formula uses n instead of n-1. The n-1 formula will be used here because it provides a closer approximation of the standard deviation of samples coming from a process that is producing continually. Continuous processes are the most common type used in manufacturing. Sigma has a special relationship to the distribution shown in Figure 1.3.8. It is called the normal distribution, and its properties are described in the next paragraph.
The Normal Distribution
There is one type of distribution that can be described entirely by its mean and standard deviation. It is the normal (Gaussian) distribution or bell-shaped curve. It has these characteristics (Figure 1.3.9):
- The mean equals the mode, which equals the median.
- It is symmetrical about the mean.
- It slopes downward on both sides to infinity. In other words, it theoretically has an infinite range.
- 68.25% of all measurements lie between x – σ and x + σ. See Figure 1.3.8.
- 95.46% of all measurements lie between x – 2σ and x + 2σ.
- 99.73% of all measurements lie between x – 3σ and x +3σ.
The equation for a bell-shaped curve is:
The normal distribution is a valuable tool because we can compare the histogram of a process to it and draw some conclusions about the capability of the process. Before making this type of comparison, however, a process must be monitored for evidence of stability over time. This is done by taking small groups of samples at selected intervals, measuring them, and plotting their averages and ranges on a control chart. The control chart provides us with an indication of whether we have stable variation — in other words, a constant-cause system — or a lack of stability due to some assignable causes. Chapter 2 describes the making and using of x & R charts in more detail. The reason they work has to do with the central limit theorem and the normal distribution curve.
Central Limit Theorem
Shewhart found that the normal distribution curve appears when the averages of subgroups from a constant-cause system are plotted in the form of a histogram. The constant-cause system does not itself have to be a normal distribution. It can be triangular, rectangular, or even an inverted-pyramid shape like dice combinations, as long as the sample size is reasonably large. The averages of different-sized subgroups selected from these distributions, or universes, as they are called in statistics, will show a central tendency. The variation of averages will tend to follow the normal curve. This is called the central limit theorem.
How Stewhart Demonstrated Central Limit Theorem
Shewhart demonstrated this by using numbered chips and a large bowl. His normal bowl had 998 chips, his rectangular bowl had 122, and his triangular bowl had 820. The rectangular universe had chips bounded by a certain range and in equal numbers, like in Figure 1.3.10. The triangular universe had unequal numbers of various chips, as shown in Figure 1.3.11. Shewhart took each chip out of the bowl one at a time, recorded the number, and put it back. He then mixed the bowl before choosing another. He averaged every four. The points he plotted fell within or along the edges of the bell-shaped curve. What this meant to him is that a process can be monitored over time by measuring and averaging a standard subgroup of parts. The subgroup could be 2, 4, or even 20. The frequency could be once per hour, or once per day, depending upon the output. If the process was a constant-cause system, these averages would fall within a normal curve. One could conclude that the process was stable. By stable, we mean that the variability was entirely due to common causes. Statisticians also use the phrase in control to refer to a process that has stable variability over time.
Frequently checking the averages of subgroups also provides a way to discover when assignable causes are present in a process. When assignable causes appear, they will affect the averages to the point where these averages will probably not fit within a normal curve. Once the stable variation of the process is known, the assignable causes will appear in averages of subgroups taken periodically.
How To Calculate the Standard Deviation
We can calculate the standard deviation of the averages and, if compared to the standard deviation of the individual samples, we will find it is smaller, as shown in Figure 1.3.12. σx is the symbol we use to represent the standard deviation of the averages. It is related to the standard deviation of the individuals by the formula:
σ x is the standard deviation of the individuals, and n is the number of samples in the subgroup. Control charts work because, in the real world, measurements of the same feature on a number of parts tend to cluster about a fixed value in a manner described by the central limit theorem. The charting of averages has this particular advantage over the charting of individual data points. The charting of ranges is also used because subgroup ranges will also show stability if a constant-cause system exists.
The SPC concepts presented here will be explained further throughout Part I. Chapters 2 through 5 will deal specifically with some of these concepts and how they are implemented with SPC.
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Six Sigma Study Guide
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Posted by Ted Hessing
Variation is the enemy! It can introduce waste and errors into a process. The more variation, the more errors. The more errors, the more waste.
What is Variation?
Quick answer: it’s a lack of consistency. Imagine that you’re manufacturing an item. Say, a certain-sized screw. Firstly, you want the parameters to be the same in every single screw you produce. Material strength, length, diameter, and thread frequency must be uniform. Secondly, your customers want a level of consistency. They want a certain size of screw all to be the same. Using a screw that’s the wrong size might have serious consequences in a construction environment. So a lack of consistency in our products is bad.
We call the differences between multiple instances of a single product variation .
(Note: in some of Game Change Lean Six Sigma’s videos, they misstate six sigma quality levels as 99.999997 where it should be 6 sigma = 99.99966 % )
Why Measure Variation?
We measure it for a couple of reasons:
- Reliability: We want our customers to know that they’ll always get a certain level of quality from us. Also, we’ll often have a Service Level Agreement or similar in place. Consequently, every product needs to fit specific parameters.
- Costs: Variation costs money. So to lower costs, we need to keep levels low.
Measuring Variation vs. Averages
Once, companies tended to measure process performance by average. For example, average tensile strength or average support call length. However, a lot of companies are now moving away from this. Instead, they’re measuring variation. For example, differences in tensile strength or support call lengths.
Average measurements give us some useful data. But they don’t give us information about our product’s consistency . In most industries, focusing on decreasing fluctuations in processes increases performance. It does this by limiting factors that cause outlier results. And it often improves averages by default.
How Do Discrepancies Creep into Processes?
Discrepancies occur when:
- There is wear and tear in a machine.
- Someone changes a process.
- A measurement mistake is made.
- The material quality or makeup varies.
- The environment changes.
- A person’s work quality is unpredictable.
There are six elements in any process:
- Mother Nature, or Environmental
- Man or People
- Measurement
In Six Sigma, these elements are often displayed like this:
Discrepancies can creep into any or all elements of a process.
To read more about these six elements, see 5 Ms and one P (or 6Ms) .
For an example of changing processes contrarily causing variation, see the Quincunx Demonstration .
Process spread vs. centering
Types of Variation
There are two basic types that can occur in a process:
- common cause
- special cause
Common Cause
Common cause variation happens in standard operating conditions. Think about the factory we mentioned before. Fluctuations might occur due to the following:
- temperature
- metal quality
- machine wear and tear.
Common cause variation has a trend that you can chart. In the factory mentioned before, product differences might be caused by air humidity. You can chart those differences over time. Then you can compare that chart to weather bureau humidity data.
Special Cause
Conversely, special cause variation occurs in nonstandard operating conditions. Let’s go back to the example factory mentioned before. Disparities could occur if:
- a substandard metal was delivered.
- one of the machines broke down.
- a worker forgot the process and made a lot of unusual mistakes.
This type of variation does not have a trend that can be charted. Imagine a supplier delivers a substandard material once in a three-month period. Subsequently, you won’t see a trend in a chart. Instead, you’ll see a departure from a trend.
Why is it Important to Differentiate?
It’s important to separate a common cause and a special cause because:
- Different factors affect them.
- We should use different methods to counter each.
Treating common causes as special causes leads to inefficient changes. So too, does treating a special cause like a common cause. The wrong changes can cause even more discrepancies.
How to Identify
Use run charts to look for common cause variation.
- Mark your median measurement.
- Chart the measurements from your process over time.
- Identify runs . These are consecutive data points that don’t cross the median marked earlier. They show common cause variation.
Control Charts
Meanwhile, use control charts to look for special cause variation.
- Mark your average measurement.
- Mark your control limits. These are 3 standard deviations above and below the average.
- Identify data points that fall outside the limits marked earlier. In other words, above the upper control limit or below the lower control limit. These show special cause variation.
Calculating
Variation is the square of a sample’s standard deviation .
How to Find the Cause of Variation
So far, you’ve found any significant variation in your process. However, you haven’t found what its cause might be. Hence, you need to find the source.
You can use a formal methodology like Six Sigma DMAIC, Use a multi vari chart to identify the source of variation.
How to Find and Reduce Hidden Causes of Variation
DMAIC methodology is the Six Sigma standard for identifying a process’s variation, analyzing the root cause, prioritizing the most advantageous way to remove a given variation, and testing the fix. The tools you would use depend on the kind of variation and the situation. Typically we see either a “data door” or a “process door” and the most appropriate use techniques.
For a smaller, shorter cycle methodology, you could try Lean tools like Kaizen or GE’s Work Out.
How to Counter Variation
Once you identify its source, you need to counter it. As we implied earlier, the method you use depends on its type.
Counter common cause variation using long-term process changes.
Counter special cause variation using exigency plans.
Let’s look at two examples from earlier in the article.
- Product differences due to changes in air humidity. This is a common cause of variation.
- Product differences due to a shipment of faulty metal. This is a special cause variation.
Countering common cause variation
As stated earlier: to counter common cause variation, we use long-term process changes. Air humidity is a common cause. Therefore, a process change is appropriate.
We might subsequently introduce a check for air humidity. We would also introduce the following step. If the check finds certain humidity levels, change the machine’s temperature to compensate. The new check would be run several times a day. Whenever needed, staff would change the temperature of the machine. These changes then lengthen the manufacturing process slightly. However, they also decrease product differences in the long term.
Countering special cause variation
As mentioned earlier, we need exigency plans to counter special cause variation. These are extra or replacement processes. We only use them if a special cause is present, though. A large change in metal quality is unusual. So we don’t want to change any of our manufacturing processes.
Instead, we implement a random check of quality after every shipment. Then, an extra process to follow if a shipment fails its quality check. The new process involves requesting a new shipment. These changes don’t lengthen the manufacturing process. They do add occasional extra work. But extra work happens only if the cause is present. Then, the extra process eliminates the cause.
Combining Variation
Rather than finding variation in a single sample, you might need to figure out a combined variance in a data set. For example, a set of two different products. For this, you’ll need the variance sum law .
Firstly, look at whether the products have any common production processes.
Secondly, calculate the combined variance using one of the formulas below.
No shared processes
What if the two products don’t share any production processes? Great! Then you can use the simplest version of the variance sum law.
Shared processes
What if the two processes do share some or all production processes? That’s OK. You’ll just need the dependent form of the variance sum law instead.
Calculate covariance using the following formula.
- μ is the mean value of X.
- ν is the mean value of Y.
- n = the number of items in the data set.
Additional Resources
ANOVA Analysis of Variation
What You Need to Know for Your Six Sigma Exam
Combating variation is integral to Six Sigma. Therefore, all major certifying organizations require that you have substantial knowledge of it. So let’s walk through how each represents what they expect.
Green Belts
Asq six sigma green belt.
ASQ requires Green Belts to understand the topic as it relates to:
Exploratory data analysis Create multi vari studies . Then interpret the difference between positional, cyclical, and temporal variation. Apply sampling plans to investigate the largest sources. (Create)
IASSC Six Sigma Green Belt
IASSC requires Green Belts to understand patterns of variation. Find this in the Analyze Phase section.
Black Belts
Villanova six sigma black belt.
Villanova requires Black Belts to understand the topic as it relates to:
Six Sigma basic premise
Describe how Six Sigma has fundamentally two focuses– variation reduction and waste reduction that ultimately lead to fewer defects and increased efficiency. Understand the concept of variation and how the six Ms have an influence on the process . Understand the difference between assignable cause and common cause variation along with how to deal with each type.
Multi vari studies
Create and interpret multi vari studies to interpret the difference between within piece, piece to piece, and time to time variation.
Measurement system analysis
Calculate, analyze, and interpret measurement system capability using repeatability and reproducibility , measurement correlation, bias, linearity, percent agreement, precision/tolerance (P/T), precision/total variation (P/TV), and use both ANOVA and c ontrol chart methods for non-destructive, destructive, and attribute systems.
ASQ Six Sigma Black Belt
ASQ requires Black Belts to understand the topic as it relates to:
Multivariate tools
Use and interpret multivariate tools such as principal components, factor analysis, discriminant analysis, multiple analysis of variance, etc to investigate sources of variation.
Use and interpret charts of these studies and determine the difference between positional, cyclical, and temporal variation.
Attributes data analysis
Analyze attributes data using logit, probit, logistic regression , etc to investigate sources of variation.
Statistical process control (SPC)
Define and describe the objectives of SPC, including monitoring and controlling process performance, tracking trends, runs, etc, and reducing variation in a process.
IASSC Six Sigma Black Belt
IASSC requires Black Belts to understand patterns of variation in the Analyze Phase section. It includes the following:
- Multi vari analysis .
- Classes of distributions .
- Inferential statistics .
- Understanding inference.
- Sampling techniques and uses .
Candidates also need to understand its impact on statistical process control.
ASQ Six Sigma Black Belt Exam Questions
Question: A bottled product must contain at least the volume printed on the label. This is chiefly a legal requirement. Conversely, a bottling company wants to reduce the amount of overfilled bottles. But it needs to keep volume above that on the label.
Look at the data above. What is the most effective strategy to accomplish this task?
(A) Decrease the target fill volume only. (B) Decrease the target fill variation only. (C) Firstly, decrease the target fill volume. Then decrease the target fill variation. (D) Firstly, decrease the target fill variation. Then decrease the target fill volume.
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Comments (4)
Ijust wanted to thank you Ive been calling and searching reading etc never could find one source to stay focused on to study. Thanks to you now I have found that course and plan to stay on track any recommendations Thanks for helping and taking the time to help people I really appreciate this really thanks any suggestioins you have for me I appreciate.
May God bless you and thanks
Again, you’re welcome, Anthony. I have a write up on how to approach any Six Sigma exam here.
If during Analyze phase of DMAIC the team undersands that the process has many common causes of variation and the process should be redesigned, can the team switch to DMADV?
Absolutely. Pivoting is essential in many cases as new information is discovered.
I would caution that clear communication with your stakeholders is essential here. You want to ensure that the cost to redesign & deploy the new process doesn’t exceed the benefit you’d achieve.
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Statistical Process Control 101
- Understanding Process Variation
Types of Process Variation
- Common cause variation is inherent to the system. This variation can be changed only by improving the equipment or changing the work procedures; the operator has little influence over it.
- Assignable cause variation comes from sources outside of the system. This variation can occur because of operator error, use of improper tooling, equipment malfunction, raw material problems, or any other abnormal disruptive inputs.
Control versus capability
Example of special cause variation.
- Why Use SPC in Manufacturing?
- Statistical Process Control (SPC) Implementation
- The Problem with Tampering
- Distributions
- Populations and Sampling
- Process Behavior and Control
- Specification and Control Limits
- SPC Control Charts
- SPC Charting Examples
- Capability and Cpk Manufacturing Charts
- Overcoming Obstacles to Effective SPC
- Statistical Process Control FAQs
Take the first step from quality to excellence
IMAGES
VIDEO
COMMENTS
Assignable cause, also known as a special cause, is one of the two types of variation a control chart is designed to identify. Let's define what an assignable cause variation is and contrast it with common cause variation. We will explore how to know if your control is signaling an assignable cause and how to react if it is.
What is the Assignable Cause? • An "Assignable Cause" relates to relatively strong changes, outside the random pattern of the process. • It is "Assignable", i.e. it can be discovered and corrected at the machine level. • Although the detection of an assignable cause can be automated, its identification and correction often requires
Assignable cause variation may be due to a defect or fault, mistake, delay in processing, accident, or shortage. It could also be due to a unique combination of factors that work together to improve the process. Your process can be unpredictable if there are no assignable causes.
An assignable cause is a type of variation in which a specific activity or event can be linked to inconsistency in a system. In effect, it is a special cause that has been identified. As a refresher, common cause variation is the natural fluctuation within a system. It comes from the inherent randomness in the world.
Common causes [ edit] Inappropriate procedures Poor design Poor maintenance of machines Lack of clearly defined standard operating procedures Poor working conditions, e.g. lighting, noise, dirt, temperature, ventilation Substandard raw materials Measurement error Quality control error Vibration in industrial processes
Assignable cause variation may be due to a defect or fault, mistake, delay in processing, accident, or shortage. It could also be due to a unique combination of factors that work together to improve the process. Your process can be unpredictable if there are no assignable causes. Your process may have been improved by your assignable cause.
Assignable causes of variation have an advantage (high proportion, domination) in many known causes of routine variability. For this reason, it is worth trying to identify the assignable cause of variation, in such a way that its impact on the process can be eliminated, of course, assuming that project managers or members are fully aware of the assignable cause of variation.
Assignable causes: A) are not as important as natural causes. B) are within the limits of a control chart. C) depend on the inspector assigned to the job. D) are also referred to as "chance" causes. E) are causes of variation that can be identified and investigated. E Control charts for variables are based on data that come from:
A process is said to be in statistical control when assignable causes are the only sources of variation. F 5. Mistakes stemming from workers' inadequate training represent an assignable cause of variation. T 6. Averages of small samples, not individual measurements, are generally used in statistical process control. T 7.
The purity of the Patagonian salt, or absence from it of those other saline bodies found in all sea-water, is the only assignable cause for this inferiority: a conclusion which no one, I think, would have suspected, but which is supported by the fact lately ascertained, [3] that those salts answer best for preserving cheese which contain most ...
Special Causes of Variation are also known as Assignable Causes (un natural) of variation. If Special cause of variations are present in a process, then the voice of the process is neither stable nor predictable and is said to be out of statistical control.
Then, the following causes seem possible for any data point to appear on the list. A new operator was running the process at the time. The raw material was near the edge of its specification. There was a long time since the last equipment maintenance. The equipment maintenance was just performed prior to the processing.
Assignable causes of variation are present in most production processes. These causes of variability are also called special causes of variation ( Deming, 1982 ). The sources of assignable variation can usually be identified (assigned to a specific cause) leading to their elimination.
Where we put these limits will determine the risk of undertaking such a search when in reality there is no assignable cause for variation. Since two out of a thousand is a very small risk, the 0.001 limits may be said to give practical assurances that, if a point falls outside these limits, the variation was caused be an assignable cause.
There is a specific cause that can be assigned to the variation. For that reason, this is also called as the assignable cause. You are required to take action to address these variations. Special causes are also called assignable causes. Seven Basic Quality Tools Get this $135 course for just $13.99 today! 3+ hours of videos, slides & quizzes
Common Cause: A cause of variation in the process is due to chance but not assignable to any factor. It is the variation that is inherent in the process. Likewise, a process under the influence of a common cause will always be stable and predictable. Assignable Cause: It is also known as "special cause". The variation in a process that is ...
These causes are sporadic, and they are a result of a specific change that is brought about in a process resulting in a chaotic problem. It is not usually part of your normal process and occurs out of the blue. Causes are usually related to some defect in the system or method.
It cannot be altered without changing the process itself. Statistics provide us with ways of recognizing variation due to common causes. The main one is the control chart. By using a control chart we can separate common causes from the second type, which are called assignable causes. Assignable Causes of Variability
Counter special cause variation using exigency plans. Let's look at two examples from earlier in the article. Product differences due to changes in air humidity. This is a common cause of variation. ... Understand the difference between assignable cause and common cause variation along with how to deal with each type.
Common cause variation is inherent to the system. This variation can be changed only by improving the equipment or changing the work procedures; the operator has little influence over it. Assignable cause variation comes from sources outside of the system. This variation can occur because of operator error, use of improper tooling, equipment ...