When analyzing a control chart a process is considered in statistical control when?
Control Charts were first developed by Walter A. Shewhart during his time at Bell Labs as a graphical method to measure, communicate & control process variation. In developing this tool, Shewhart recognized that there are 2 types of variation within any process; Normal Process Variation also called Common Cause Variation &
Special Cause Variation. Control charts are utilized to clearly distinguish between common variation and special cause variation. As I said above, the most important benefit of a control chart is that is graphically displays your data in such a way that the special cause variation becomes readily apparent, but there are other additional benefits that Control Charts provide, such as: Shewart knew that every normal process had a certain amount of expected variation, and he also
knew that processes occasionally experience Special Cause Variation. He needed a method to separate these two types of variation and using by a Control Chart he was able to graphically display this data in such a way that the Special Cause Variation became very easy to identify. This original concept of a control chart has now become a basis for the concept of Statistical Process Control. Control Charts often depend on process to be “Normal”. This
means that the process output, or whatever is being measured, is normally distributed. As you may already know about Normal Distributions, they can be fully characterized by two features, their mean and their standard deviation. For some control charts, instead of the standard deviation, your control limits will be based on the range of the data. This is normally when the sample size of your subgroup is between 1 to 10 samples. Similar to
Normal Distributions, Control Charts rely heavily on the process output mean and the process output standard deviation (or range) to determine if a process is in-control or out of control. The most important element of a control chart is the Mean. This is the average expected value for a process output. The 2nd most important element of a control chart is the Control Limits. Every Control Chart has an Upper Control Limit (UCL) and a Lower Control Limit
(UCL). These limits are used to determine if a process is in-control or out-of control. So, A process is considered in-control if all the data points collected fall within the Control Limits of a Control Chart (more on trending below). The last major element of your control chart are your axes. The X-Axis for most Control Chart represent things like units, subgroups or time. The Y-Axis of your control chart represents the value you’re measuring. Once you’ve defined all the major elements of your control chart, the next step is deciding what type of data you plan on collecting & analyzing. There are 2 major types of Quantitative data; continuous (variable) data & discrete (attribute) data. The next data element to consider is sample size & sub-grouping. The data points on your control chart can be individual data points or they can be the average of a sample of data, this is an important concept in Control Charts called Sub-Grouping. For example, let’s say you build 10 discrete lots of a certain product every day where each lot has 100 units of product. From
each of those 10 lots, you pull 5 samples to destructively test. Those 5 samples are considered your sub-group. The sample size of this subgroup is 5 and is important to note as it will assist you in selecting the right control chart. [table id=3 /] Then from this data you can calculate the Lot Average (X-Bar) and the Lot Range (R). [table id=4 /] We can also use this data to calculate the Grand Average (1.2612) and the Grand Range (0.40) of the entire data set which is
used to create our control limits. More on this below. It is very important that you select the correct control chart! Selecting the incorrect control chart might lead you to incorrectly analyze your data, miss special cause variation or take action on variation that you think is special cause when it’s actually common cause. As you may have seen, Control Charts are also commonly paired together. For example, the X-Bar R (Range) Chart pairs
together a control chart for X-Bar (Average) with a control chart for the Range (R) of the data. This pairing allows you to study the variation between data points (X-Bar graph) AND the variation within a subgroup (range graph). There are many different control charts which have been created to properly analyze different data types. For example, there are different charts between continuous data and discrete data. There are also different control charts depending on the sample size
of the subgroup that you’re measuring. If you’re sub-grouping, it’s important to remember that the Grand Average, Grand Range & Grand Standard Deviation is just the Average, Range & Standard Deviation of the entire population of data that you’ve measured. Note: These values should only be calculated from the process when it is considered “in control”. I’ve put together a step-by-step guide to go along with the flowchart below to help you select the right
Control Chart. In the situation where multiple defects can occur on any given unit or sample, choose a C-chart or U-Chart based on the consistency of the sample size. In the situation where only 1 defect can occur on any given unit or sample, choose an NP-chart or P-Chart based on the consistency of the sample size. See the chart above for guidance. Before you’re able to accurately set the limits on your control chart, it’s important to collect data from the
process for a time period, or a defined number of samples where you believe the process is in control. Additionally, the limits on your control chart depend on the type of control chart that you need to use. The most common limits used on control charts is 3 times the standard deviation. For more information on setting limits on your control chart, I highly recommend checking out this post on
iSixSigma. In determining whether your process is in control or not there are a number of rules that have been developed to detect a trend. These trend rules are what indicate that special cause variation is effecting the process. It are these special causes that must be eliminated from your process. [table id=2 /] Here’s a quick explainer video about control charts from Keith Bower. You can check out more CQE related videos on my YouTube Channel. Here’s a short quiz that should challenge your understanding of the Control Chart! What is the Primary purpose of a Control Chart: To collect raw data from a process for further analysis To diagram the flow of information or material through a process To plot 2 variables against each other to determine the level of correlation between the 2. To Graphically display process data in such a way that Special Cause Variation becomes readily apparent. Which of the following are Secondary Benefits of Control Charts:
What is the difference between Common Cause & Special Cause Variation: Special Cause Variation can be attributed/assigned to a particular deviation in the process while Common Cause Variation is random and normal to the process. Common Cause Variation is small, while Special Cause Variation is very large. Common Cause Variation is a bad thing, while Special Cause Variation is neither good nor bad because it is infrequent. Common Cause Variation can be attributed to a particular deviation in the process while Special Cause Variation is random. Which 2 Statistics can fully define a Normal Distribution: The Upper & Lower Control Limits The Mean & Standard Deviation The Mean & Control Limits The Average & the Range If received the following feedback from the customer regarding your product: “It is the best device I’ve ever used” Would that data be considered Qualitative or Quantitative? Let’s say your data tracks a linear dimension on a critical feature and the output of that measurement is the following value: 12.146″ Is that data point considered Discrete or Variable Data? Let’s say your measured 5 samples from 3 consecutive lots from your process and came up with the following data: [table id=5 /] What would your Sub-Group Averages be for your 3 Lots? Lot 1: 2.5 Lot 1: 3 Let’s say your measured 5 samples from 3 consecutive lots from your process and came up with the following data: [table id=5 /] What would your Sub-Group Range be for your 3 Lots? Let’s say your measured 5 samples from 3 consecutive lots from your process and came up with the following data: [table id=5 /] What would your Grand Average & Range be for your 3 Lots? Grand Average: 8 Grand Average: 7 Grand Average: 7 Grand Average: 8 How should Baseline Averages, Ranges & Standard Deviations be established: Quickly and Arbitrarily Baseline data should only be established after sufficient data has been collected, where the process is believed to be in control. Baseline data should be established by the process Subject Matter Expert alone. For Continuous Data with a sub-group sample size of 20, what Control Chart should you use: NP Chart P Chart Xbar-S Chart I-MR Chart For Discrete Data with a Constant Sample Size and only 1 possible defect per unit, which Control Chart should you use? NP Chart P-Chart C-Chart U-Chart The I in I-MR Chart stands for: Instant Irrational Idea Individual The XBar in Xbar – R Chart is equivalent too: Sub-Group Average Grand Average Sub-Group Variation Grand Control Limit The S in Xbar-S stands for: Succinct Start Standard Deviation Safety External Links:I wanted to include some links to some other good, free online resources for Control charts.
Other Cool StuffWanna do me a favor? I’ve created a quick, 3 minute survey to get your feedback! CQE Academy Survey <- Thanks!!! Want to continue learning? Continuous Improvement, Product and Process Control, Product & Process Design. Have General questions about the CQE Exam, check out my FAQ. Want to learn more about me or CQE Academy, check the About Me page. Thanks, Andy What does it mean when a process is in statistical control?A process is said to be in control or stable, if it is in statistical control. A process is in statistical control when all special causes of variation have been removed and only common cause variation remains.
What is the statistical process chart used to control?The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit.
What is statistical process control quizlet?Statistical Process Control (SPC) A method of quality control that uses statistical methods in order to monitor and control a process. Control Charts. Graphical tool that uses actual variation in observed data to determine if a process is 'in control' or 'out of control'.
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