This month’s Tip of the Month focuses on
Control Charts.
This discussion will help you understand strategies and techniques you can use to improve the performance of your company's operations and focus your scarce resources on the areas where real improvements can be made.
Arch + Beam newsletters cover business topics that will get you thinking about ways to improve your business. You won't be able to use all of the suggestions, but for about fifteen minutes of reading, we hope you will get some good ideas each month.
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The Expert: Stabilizing Out-of-Control Processes
Using Statistical Process Control ("SPC") |
You know something isn't right. Your customers
are complaining about your quality and responsiveness. Your employees
are pointing fingers. Your managers are giving your anecdotal evidence
of the problems, but you're not sure what to believe.
You don't have a lot of extra time or resource to go
off and do a large root-cause analysis, but you know that you need to get
the problem fixed. You want data not opinions.
You want to fix the root cause and not the symptom.
There are many Six Sigma / quality tools that you can
use to help you and, if used correctly, they are very powerful. One such
tool for statistical process control is the Control Chart.
Control Charts are simple graphs used to study how a process changes over time. Some characteristics about control charts include:
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Control charts use historical data to develop
the boundaries of what it means for the process to be "in control" and
"out-of-control". This allows you to see if a process is performing
normally or if there is a problem that needs further investigation because it cannot be explained by normal causes.
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Control Charts help you see what is the best possible performance for a given process (in its current design) and helps you strive for that level of performance. If that "best level of performance" is not good enough, it then creates a data based rationale for redesigning the process for better performance.
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Control Charts
can be used for both continuous data (e.g. time, dollars, length) or
attribute data (e.g. pass/fail, small/medium/large, yes/no), although the
control chart formulas and usage will be different.
For the purpose of this newsletter, we will use a
hypothetical business situation. Keep in mind that the results of
statistical process control are only as good as the data and the
appropriateness of the analysis methods used, so it is important that you work with
an expert in quality and operations improvement to utilize these tools
correctly. For the purpose of brevity, we are oversimplifying some of
the concepts and are making certain assumptions.
Situation:
Customer Service Hold Times
In this situation, we will be using Control Charts to
help us analyze a call center.
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Step 1: Define which process will be controlled or monitored.
Customer Service Hold Time: Customer calls a toll-free number, and after exhausting the self-help options, is put in a hold queue to wait for the next customer service representative.
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Step 2: Determine how the data will be collected (e.g. what the measurement system will be)
Phone system has the ability to report the time for each call from when the caller was first put into the hold queue until a Customer Service representative answered the call.
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Step 3: Create the control charts
See "Quant Guru" section.
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Step 4: Collect the data using rational subgroups
In order to avoid inaccurate distortions of the data, it is important to collect measurements in small "subgroups". These subgroups should consist of at least 3 to 5 individual measurements that are taken as close as possible to one another. Then, subgroups should be taken across many different shifts, hours of the day, etc. For this example, one rational subgroup would be to measure 5 customer call hold times in a row. Then, make sure that you collect subgroups from varying times during the day and across multiple shifts.
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Step 5: Interpret the control charts and take action based on them
See "Quant Guru" section.
From all this, we will then analyze two control charts that are usually paired together: an averages chart and a ranges chart.
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Averages Control Chart: seeks to answer "has something special (in SPC language "special cause variation") caused the central tendency of this process to change over time?"
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Range Control Chart: seeks to answer "has something special caused the process to become more or less consistent?
Benefits of Control Charts
From the analysis, you then look for specific patterns
or data points that cannot be explained by normal process variation (in SPC language "common cause variation). It is in these areas that you then can focus further analysis efforts to see what caused the "special" variation.
The Control Chart analysis also allows you to predict what the expected range of outcomes would be from the process.
Finally, often times, you find that while your process is "in control" it is not meeting customer expectations (in SPC language "not meeting customer specification limits"). If you find this to be the case, then despite the fact that your process is consistent, it is consistently not meeting customer expectations and so you need to redesign the process. This is a key to control charts. They don't tell you if you are meeting what the customer wants, they just tell you if the process is in control or not. In many cases, you first must get a process "in control" before you can then decide whether redesign is necessary.
For those of you who prefer to leave the math to the
statisticians, stop reading here. For the rest of you, let's jump into the
numbers below.
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The Quant Guru: Continuous Data Control Chart
How to create and interpret control charts |
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To help us analyze our customer hold time data, we will
create and analyze an "Average and Range" Control Chart.
Start with the
Data
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Collect your data in rational subgroups. For example,
you would measure that five customers in a row experienced the following hold
times (in seconds): 72, 66, 45. 22, 11. To calculate one subgroup
average (called "X-Bar"), you
would then average these numbers together to get 43 as the average (=
(72+66+45+22+11/5) and 61 as the subgroup Range (= largest "72" minus smallest "11").
Do this at least 25 more times collecting these subgroups from five customer
hold times in a row but with the subgroups from varying times of day and different work shifts.
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Calculate the grand mean (= "X-Double-Bar") of all subgroups. This would involve summing all the individual X-Bars together and dividing by 25, assuming you had 25 subgroups. This is an average of averages.
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Calculate the average Range (= "R-Bar") by adding together all the subgroup ranges and then divide by 25, assuming again that you had 25 subgroups.
Create the Control
Chart
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A standard control chart will have a format similar to this:
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Use the following formulas to calculate the Average ("X-double bar") and Range ("R-bar"). Then calculate the Upper Control Limit ("UCL") and Lower Control Limit ("LCL"). You will note that a part of the formula is based on constants that are found in any statistics textbook. These constant values change based on the subgroup size.
Analyze the Control Chart
Your analysis of the Control Charts is now looking for certain patterns that show you that the process is not in control or showing other distinct attributes. In order to do this analysis, we must split the Control Chart into a series of "zones" and then examine what the chart shows us.
A typical Control Chart should be split into six zones, each one sigma (= standard deviation) wide. This can be done using statistical software (e.g. Minitab) or certain Excel models available commercially.
Why six sigma (standard deviation) zones (3 above and 3 below the mean)?
Because a wise statistician determined that a subgroup that falls outside of plus or minus 3 standard deviations would have such a low probability of having been caused by the normal "common cause variation" that it must be caused by something special (called "special cause variation"). This standard is used pretty consistently on most control charts. "
You are looking for any of the following:
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Any one point beyond Zone A (= higher than the upper control limit or below the lower control limit)
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Two out of any three points in a row in Zone A or beyond, with all three on the same side of the average
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Four out of five in a row in Zone B or beyond, and all five on the same side of the average
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Fifteen points in a row in Zone C, above or below the process average
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... others you can discover in any good book on Statistical Process Control
Averages and Ranges Chart
Below is a typical pairing of the Averages (X-Bar) and Ranges (R) Chart. This chart was generated using the statistical software Minitab.
The Averages (X-Bar) chart shows how the process average changes. The Ranges (R) chart shows how the variation of the process changes.
What to look for
The idea is to use these control charts to help you identify what might be happening, such as:
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The process is stable and therefore you can use the control chart to predict the likely future performance of the process. If this performance isn't good enough, then you may need to consider redesigning the process, as it won't get much better on its own.
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The process is out of control meaning that there were certain subgroups that varied so much that they could not be explained by how much we would normally expect this process to vary. So, you should do further analysis to investigate the root cause of the specific instances that are out-of-control. Perhaps a new product was released with a lot of bugs and this created the longer hold times or perhaps the flu hit a large number of the call center agents and the managers had to step in leading to a change in productivity.
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The process is going through a cycle which indicates that there must be a special cause for this repetitive cycle.
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The process is trending downward or upward. You should investigate why this trend exists and determine if action needed to be taken.
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The process is showing many consecutive data points on the same side of the mean. Perhaps the process has gone through a change that is more permanent. You may need to recalculate all your control charts if this is the case, as they would now be out-of-date.
Value of Control Charts
With all the math and charting behind us, what is the value of Control Charting?
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Control charts help you identify processes that are not performing well and provides you with the trigger to go perform root cause analysis to find these "special causes."
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Control charts also stop you from wasting your time trying to find the root cause of variations that are caused by things that are out of your control and that you cannot impact.
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Control charts help you identify what a particular process is capable of, and after comparing this to your Customer's expectations, you can determine whether a process just needs to be better controlled or whether it needs to be completely redesigned in order to meet your Customer's needs.
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Finally, control charts are useful both to improve processes as well as to maintain / control processes, so they are a multi-use tool.
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The Naysayer
All the reasons it won't work |
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As the saying goes "garbage in garbage out".
The problem with control charts is that it is really easy to use them incorrectly and then to draw false conclusions from the outputs. Below are some areas that you should consider when creating control charts:
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Non-random subgroups: the reason that subgroups are used is to avoid distortions caused by individual measurements. Based on something called the "central limit theorem", it is important to use subgroups that are large as possible and where the measurements are taken close together and are basically random. Taking all measurements right after lunch and then trying to extrapolate the results to the entire 24 hours of the process would obviously be flawed. Don't treat the process with abnormal care while doing your measurements or your results will be invalid.
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Using the wrong control chart formulas: you have to admit that after reading about these control charts you are wondering whether you have the time to figure out what constants to use or which formulas are appropriate. This newsletter has only touched on control charts for continuous data and then it only talked about the "Average and Range" chart. For larger subgroup sizes (greater than 10), the "Average and Standard Deviation" chart is usually used. And, if you are charting attribute data, such as the proportion defective or the number of defects per unit, you have to use completely different formulas.
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Get Range Chart in Control Before Interpreting Average (X bar) Chart: this is due to the fact that the control limits of the X bar chart are calculated from the observed variation in the ranges. So, get R chart in control first, and then interpret the X bar chart.
So, the key message is to take care when using control charts. They can be incredibly powerful when used correctly, and can be a waste of your time when not.
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For more information, please Contact Us to discuss
your specific needs. |
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Reading Tips |
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Read about our Monthly Tip from Three Different
Perspectives
The
Expert who describes the improvement idea in detail
The Quant
Guru who provides the formulas or math behind the topic
The
Naysayer who tells the reasons it won't work (so you
can avoid them)
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