1. Method Name

Histogram

2. Alternative Names

Frequency Distribution Chart

3. Brief Description

A histogram is a bar chart that visually represents the distribution of continuous data. It shows how often values occur within predefined intervals (classes or “bins”), thereby revealing the shape, center, and spread of the data set.

4. Purpose / When to Use

It is used to understand process variability. It helps answer questions such as: Is the process stable and predictable? Is it capable of meeting customer requirements (specification limits)? Are there any unusual patterns in the data? It is one of the seven basic quality tools.

5. Procedure / How to Apply It

1. Collect data: Obtain a sufficient amount of continuous data from the process (typically at least 50–100 values). Example: measurements of the diameter of manufactured shafts, the time required to fulfill a request.
2. Determine the number of classes (intervals/bins): Decide into how many columns you will divide the data. A common rule is to use the square root of the number of data points (√n).
3. Calculate the class width: Find the maximum and minimum values in the data (range) and divide it by the number of classes. Round the result to a practical value.
4. Create a frequency table: Count how many data points fall into each interval.
5. Draw a histogram
: - Plot the intervals (classes) on the horizontal axis (x-axis).
- Plot the frequency (number of occurrences) on the vertical axis (y-axis).
- For each interval, draw a bar with a height corresponding to its frequency. Unlike a standard bar chart, the bars touch one another.

6. A Real-World Example

The manufacturer fills 500-ml bottles. The customer’s specification limits are 495 ml to 505 ml. After collecting volume data from 100 bottles, they created a histogram. Shape analysis
: - Normal distribution (bell curve): The process is centered around the mean value of 501 ml and is stable.
- Bimodal (two bells): This may indicate that the data comes from two different processes (e.g., two filling lines, two shifts with different settings).
- Asymmetric (skewed): The process tends to produce values closer to one of the limits.
- Outlier (isolated bar): Indicates an unusual event or a measurement error.

7. Benefits

- Quick visualization of variability: Shows at a glance how the process is performing
.- Provides an overview of process capability: By comparing the histogram with specification limits, you can quickly assess whether the process is capable of producing the required quality.
- Pattern identification: Reveals unusual patterns (e.g., a bimodal distribution) that indicate hidden problems in the process.
- Easy to create: It can be easily created in standard spreadsheet software (e.g., Excel).

8. Risks / Limits

- Dependence on the number of classes: The shape of a histogram can change significantly depending on the chosen number and width of the intervals. An incorrect choice can lead to misinterpretation.
- Static view: A histogram displays data for a specific period but does not show how it changes over time. Control charts or run charts are used for this purpose.
- Need for a sufficient amount of data: A sufficient number of data points is necessary for a reliable histogram. Valid conclusions cannot be drawn from a small sample.

9. Practical Tips

- Histogram vs. Bar Chart: A histogram is used for continuous data (measurements), and its bars are connected. A bar chart is used for discrete data (categories, e.g., number of defects by type), and the bars are separated.
- Add specification limits: Whenever possible, plot the upper and lower specification limits (USL/LSL) on the histogram. This immediately shows how many products are outside the tolerance range
.- Experiment with the number of classes: Try changing the number of classes to see if a different, more meaningful pattern emerges.