Key Points
- LCLs are the lowest limit available before data departs from the standard deviation.
- They are used throughout control charts when conducting data analysis.
- LCLs can fall out of the possible data range of a given dataset.
Virtually all processes exhibit variation, and we hope that such variation is constant and due only to common causes. However, identifying special cause variation and lack of process stability is critical to success, and the lower control limit is a fundamental part of identifying special cause variation.
Overview: What Is a Lower Control Limit (LCL)?
On a control chart, the lower control limit is a line below the centerline that indicates the number below which any individual data point would be considered out of statistical control due to special cause variation. It is typically set to three standard deviations below the centerline for charts plotting central tendency, and some multiple of the centerline for charts plotting variation.
In the case of charts for central tendency, it is critical to utilize the correct estimate of standard deviation in calculating the lower control limit. A measure of short-term or “within subgroup” variation is utilized to identify the presence of special causes that appear over time, and these estimates are often adjusted by an unbiasing constant.
1 Benefit and 1 Drawback of a Lower Control Limit
The lower control limit is a critical value as it allows for the most commonly used detection rule to be used on values below the center of the data.
1. It Identifies Unusually Low Values
The rule used to determine an unusually low value in a dataset is a point below the lower control limit. When this is observed, we typically determine it to be due to special cause variation and an indication that the process lacks stability.
2. It May Fall Outside of the Possible Data Range
For certain datasets, and especially when utilizing individual control charts or charts for variation such as MR, R, and S, the calculation of the lower control limit may result in a value that is at or beyond the natural range of the process.
For example, a chart plotting cycle time may have a negative value for the lower control limit even though we cannot record negative times. In this case, the lower control limit will not be useful in detecting special cause variation causing unusually low values, and alternative rules must be used.
Why Is a Lower Control Limit Important to Understand?
Process stability is critical to the improvement of the process, and the lower control limit is a fundamental part of assessing stability.
It Helps Avoid Tampering
By calculating a control limit based on statistical probability, we can identify whether a point lower than usual was to be expected given the common cause variability in the process or is an indication of something unusual happening. This, in turn, can help us avoid putting resources toward identifying the cause of points that were not indicative of a process shift.
It Identifies Individual Events
While other rules exist to identify more sustained shifts in a process, the control limits help us identify if a single point was likely due to special cause variation even if the process itself has not shifted.
Why It Matters
You’re going to do a fair bit of data analysis throughout the development of any project. While you’re likely familiar with the UCL, having the LCL on hand helps make sure your production is staying within ideal parameters. Values out of those measurements indicate some extreme occurrences are happening throughout your production line.
An Industry Example of a Lower Control Limit
A manufacturer of food must take precautions to ensure that their products weigh, on average, at least as much as the declaration on the label. A control chart is made to identify whether the weights are stable by collecting packages five at a time each hour:
The lower control limit, labeled LCL on the graph, indicates that on this Xbar chart, any group of five packages averaging under 41.7503g is an indication that the process is unstable and special cause variation exists.
Best Practices
While using the lower control limit may seem straightforward, there are some ways in which it is misused.
Use a Logical Estimate of the Standard Deviation
When constructing a chart, we typically utilize only the variation within subgroups or short-term variation (such as the moving range) to eliminate as many possible special causes of variation as possible and only capture the common cause variation. The overall standard deviation of the entire dataset should not be used as it is more likely to contain special cause variation.
Verify the Value Is Within the Range of a Dataset
On some charts and with some datasets, the lower control limit might fall outside of the range of values the process can produce. In this case, other rules should be utilized to detect special cause variation below the centerline.
Other Useful Tools and Concepts
While we’ve explored LCL at length, that isn’t all there is to know about the Six Sigma methodology. Understanding the role of the stakeholder in your project management is key. These individuals can help secure funding and set the milestones you need to achieve throughout a project.
Additionally, having subject matter experts on hand can improve corporate culture thanks to their knowledge. Learn how these experts can influence process improvement, process design, and more in our comprehensive guide on the subject.
Defining What Too Low Is
While processes produce a range of data, the lower control limit is a formal definition for the point at which we consider the data to be too low to have been due to common cause variation. Understanding the need for this formally and avoiding process tampering when there is no indication of special cause variation helps reduce noise and gain process stability.
