What Are Control Charts Types Formulas and Solved Examples
What is the Process?
By its general term, process means a series of actions or steps that is taken in order to achieve a particular end or goal. For example, filling out an expense report, checking into a hospital or filling a prescription. Whenever we execute such actions, there is always a strong motive at the back of our head i.e., to generate an output, be it a product or service, and in the process, we also most importantly generate data. This data is beneficial to control and improve the process as it works on four dimensions: quality, quantity, timeliness and cost. It would not be wrong to say that control charts are the heart of statistical process control (SPC).
What is a Control Chart?
Control charts are also known as Shewhart charts, named after Walter A. Shewhart. It is a statistical process controlling tool which helps to monitor the improvements in the process over time. For example, hospital management decides to reduce the time taken to admit someone to the hospital and thus use a solving methodology. They start by developing the process flow diagram on how people are admitted to the hospital. Next, they measure the average time taken to admit a patient each day. And finally, plot the process variables on a control chart over time.
The objective of this control chart would be to find any "special" causes of variation as well as to reflect the process improvements that have been made. Again, to effectively use control charts, understanding the information in variation is a must.
It will be more appropriate to say that the control charts are the graphical device for Statistical Process Monitoring (SPM). Control charts perpetually monitor quality depending on the number of process characteristics to be monitored. A control chart always includes a limit such as the central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. On comparing the current data to these lines, we can draw conclusions regarding whether the process variation is in control or out of control. A control chart provides us with a picture of the process variable over time and lets us know the type of variation we are dealing with as we move forward with continuous improvement. This understanding of variation is the key to using control charts effectively.
Types of Control Charts
Since now that we fully understand what a control chart means, we shall jump directly into its types.
There are Two Types of Control Charts:
1) Univariate Control Chart: As we all know ‘uni’ means one, thus a, is a graphical display (chart) of one quality characteristic is called univariate control chart.
2) Multivariate Control Chart: It is also a graphical display of a statistic that summarizes or represents more than one quality characteristic.
When to Use a Control Chart?
A control chart can be helpful to control any ongoing processes. It finds and corrects the problem as they appear.
A control chart plays an outstanding role in predicting the expected range of outcomes from a process.
It also helps in determining whether a process is in statistical control.
Control charts help to analyze the pattern of process variation from either special causes or common causes.
Lastly, it is of great help in determining whether the quality improvement project should target to prevent specific issues or to make fundamental changes to the process.
What are the Basic Procedures?
The basic procedures can be explained in the following steps:
Step 1: An appropriate control chart for the data is to be selected.
Step 2: For the collection and plotting of data an appropriate time period is to be determined.
Step 3: In this step, collection and analysis of data and construction of the chart is to be done.
Step 4: “Out of control signals” on the control chart is to be kept in mind and once it is identified, it needs to be marked on the chart and further investigation of the cause is needed.
Step 5: Keep an account of the things learnt, the cause and how it was corrected.
Step 6: The data generated needs to be plotted and with every new data, a check for new out-of-control signals.
Step 7: In case you start a new control chart and the process may be out of control, the first 20 points calculated from the control limits will be the conditional limits. You will have to recalculate the control limits if you get at least 20 sequential points from a period when the process is operating in control.
Benefits of Process Control Charts
Control charts are used by Organizations for continuous quality improvement in the following ways:
Control charts provide a simple and common language for dealing with process performance and behavior.
It aware us with decisions about which processes to leave alone and which to subject to an improvement cycle
It Limits the need for inspection.
Control charts help to determine process capability based on past performance and trends.
It can also predict future performance if the system is stable and in control.
Control charts also assess the impact of process changes.
It visualizes the performance of the process over time.
It creates a baseline for future improvements.
Communicating the performance of a process is also influenced by control charts.
FAQs on Control Charts in Statistics and Quality Control
1. What is a control chart in statistics?
A control chart is a statistical process control (SPC) tool used to monitor whether a process is stable over time. It displays data points plotted in time order along with a center line (CL), an upper control limit (UCL), and a lower control limit (LCL).
- The center line represents the process mean.
- The control limits are typically set at ±3 standard deviations (σ) from the mean.
- If points fall outside the limits or show unusual patterns, the process may be out of control.
2. What are the components of a control chart?
The main components of a control chart are the center line, upper control limit, lower control limit, and plotted data points. These include:
- Center Line (CL): The process average (mean).
- Upper Control Limit (UCL): Typically mean + 3σ.
- Lower Control Limit (LCL): Typically mean − 3σ.
- Time-ordered data points representing sample statistics.
3. How do you calculate control limits for a control chart?
Control limits are calculated using the process mean and standard deviation, usually as UCL = μ + 3σ and LCL = μ − 3σ. The steps are:
- Calculate the process mean (μ).
- Find the standard deviation (σ).
- Apply the ±3σ formula.
4. What is the difference between control limits and specification limits?
The key difference is that control limits are statistically calculated from process data, while specification limits are set by customer or design requirements. Specifically:
- Control limits reflect natural process variation (±3σ).
- Specification limits define acceptable product performance.
- A process can be in statistical control but still not meet specifications.
5. What are the different types of control charts?
The main types of control charts are variable charts and attribute charts. Common examples include:
- X̄-chart: Monitors sample means.
- R-chart: Tracks sample ranges.
- S-chart: Tracks sample standard deviations.
- p-chart: Monitors proportion of defects.
- c-chart: Tracks number of defects per unit.
6. What is an X-bar and R control chart?
An X̄-R chart is a pair of control charts used together to monitor the process mean and variability for small sample sizes. It consists of:
- X̄-chart: Tracks changes in the sample mean.
- R-chart: Monitors the range (max − min) within samples.
7. How do you interpret a control chart?
A control chart is interpreted by checking whether data points fall within control limits and whether any non-random patterns appear. Look for:
- Points outside UCL or LCL.
- Seven or more consecutive points on one side of the mean.
- Trends increasing or decreasing consistently.
8. Why are control charts set at 3 sigma limits?
Control charts use 3σ limits because about 99.73% of normally distributed data lies within ±3 standard deviations of the mean. This means:
- Only about 0.27% of points fall outside limits by chance.
- Points beyond ±3σ likely indicate special cause variation.
9. Can you give an example of a control chart calculation?
Yes, for a process with mean 100 and standard deviation 5, the control limits are calculated using ±3σ. Calculation:
- UCL = 100 + (3 × 5) = 100 + 15 = 115
- LCL = 100 − (3 × 5) = 100 − 15 = 85
10. What is the purpose of a control chart in quality control?
The purpose of a control chart is to monitor process stability and detect unusual variation before defects occur. It helps to:
- Identify special causes of variation.
- Maintain consistent product quality.
- Support data-driven decision making.
- Improve continuous process performance.
