You create a control chart by plotting data points over time and adding center lines and control limits to monitor process stability and identify unusual variations. Here's a breakdown of the process:
Steps to Create a Control Chart
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Collect Your Data: Gather a relevant dataset of measurements taken over time. The data should represent the characteristic you want to monitor (e.g., product dimensions, process temperature, service time).
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Calculate the Center Line: Determine the average of your collected data. This average is represented as a horizontal line in the middle of your chart and serves as a baseline for your process.
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Calculate Control Limits: Control limits are the upper and lower boundaries that define the expected range of variation for your process. They're typically calculated as follows:
- Upper Control Limit (UCL): The upper limit of acceptable variation.
- Lower Control Limit (LCL): The lower limit of acceptable variation.
The specific formulas for calculating UCL and LCL depend on the type of data you're analyzing (e.g., continuous data, attribute data). Common control charts and their formulas are:
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X-bar and R Charts (for continuous data): Used to monitor the mean and range of samples. The formulas use factors based on sample size (n), typically found in statistical tables or software:
- UCL (X-bar): X-double bar + A2 * R-bar
- LCL (X-bar): X-double bar - A2 * R-bar
- UCL (R): D4 * R-bar
- LCL (R): D3 * R-bar
Where:
- X-double bar is the average of sample averages.
- R-bar is the average of sample ranges.
- A2, D3, and D4 are constants based on sample size (n).
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Individual and Moving Range (I-MR) Charts (for continuous data, when n=1): Used for individual measurements.
- UCL (Individual): X-bar + 2.66 * MR-bar
- LCL (Individual): X-bar - 2.66 * MR-bar
- UCL (MR): 3.267 * MR-bar
- LCL (MR): 0
Where:
- X-bar is the overall average.
- MR-bar is the average moving range (difference between consecutive points).
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p-Chart (for attribute data - proportion defective):
- UCL: p-bar + 3 sqrt((p-bar (1 - p-bar)) / n)
- LCL: p-bar - 3 sqrt((p-bar (1 - p-bar)) / n)
Where:
- p-bar is the average proportion defective.
- n is the sample size.
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c-Chart (for attribute data - number of defects):
- UCL: c-bar + 3 * sqrt(c-bar)
- LCL: c-bar - 3 * sqrt(c-bar)
Where:
- c-bar is the average number of defects.
Commonly, control limits are set at +/- 3 standard deviations (3σ) from the center line. This is based on the assumption of normally distributed data.
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Plot the Data: Create a chart with time on the x-axis and your measurements on the y-axis. Plot each data point and draw horizontal lines for the center line, UCL, and LCL. Use different colors or line styles to distinguish the lines.
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Analyze the Chart: Look for "out-of-control signals," which indicate that your process might be unstable or experiencing special cause variation. Common rules for identifying out-of-control signals include:
- A single point falls outside the control limits.
- Two out of three consecutive points fall beyond 2 standard deviations from the center line.
- Four out of five consecutive points fall beyond 1 standard deviation from the center line.
- Eight consecutive points fall on one side of the center line.
- Unusual patterns or trends.
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Take Action: When you identify an out-of-control signal, investigate the cause and take corrective action to bring the process back into control. This might involve identifying and eliminating special causes of variation.
Example
Suppose you're monitoring the weight of cereal boxes filled by a machine. You collect data on the weight of 5 boxes every hour for 24 hours. You would then calculate the average weight (X-bar) and range (R) for each hour, then calculate X-double bar and R-bar across all 24 hours to establish your center lines. Using the appropriate A2, D3, and D4 constants (depending on your sample size of 5), you can calculate the UCL and LCL for both the X-bar and R charts. Plotting these values allows you to visually monitor the process and identify hours where the weight is outside acceptable control limits, prompting investigation into the cause of the variation.
Importance
Control charts are vital tools for statistical process control (SPC). They help you:
- Distinguish between common cause and special cause variation.
- Monitor process stability over time.
- Identify areas for improvement.
- Reduce defects and improve quality.
- Make data-driven decisions.
