A standard set of graphical methods for improving quality.

The seven basic tools of quality are a standard set of graphical methods for improving quality. They can help with understanding variation and determining the root cause of errors in processes. The seven basic tools are most commonly used within lean manufacturing. All of the tools are graphical methods that do not require much knowledge of statistics. Among them, they can solve most problems within quality improvement.

The set of seven tools became established in Japanese manufacturing during the post-war period, when W. Edwards Deming was promoting statistical quality control methods in Japan. The full set of statistical methods Deming taught included more advanced methods, such as design of experiments and hypothesis testing. These were too challenging for many production workers. Manufacturers, therefore, started trying to use simpler graphical methods whenever possible.

The seven basic tools are:

1. **Check sheet**: A standard form that allows information to be quickly entered by making checks, for example, a checklist or a tally chart.

2. **Histogram**: A histogram is a way of graphically representing the probability distribution for a reasonably large dataset.

3. **Run chart**: A scatter plot with the sample number on the x-axis and measured value on the y-axis, presenting a view of how a process changes over time.

4. **Control chart**: A special type of run chart with control limits and other information added to identify whether a process is in-control.

5. **Pareto chart**: A combination of two charts for the same data—an ordered bar chart and a line chart giving the cumulative percentage. This gives a clear indication of which items have a significant impact on the total.

6. **Fishbone diagram**: A hierarchical diagram, similar to a tree or mind map, with standard headings used to analyze the root cause of a defect. It is also known as an Ishikawa diagram.

7. **Scatter diagram**: A plot involving two or more variables, represented on perpendicular axes, used to determine correlations between them.

### Check Sheets

Check sheets are a simple yet important tool for quality. They are a basic form laid out to allow the user to enter information quickly, predominantly by making checkmarks, rather than writing words or numbers. Check sheets can take many forms, such as checklists or tally charts. A checklist is a useful method to ensure that a process is followed correctly. Each step in the process is listed as a line item, and the user simply checks the item as it is completed. Checklists are particularly useful when carrying out quality control checks on an output or safety checks, for example, preflight aircraft checks. Most check sheets, however, provide a means of quickly and intuitively entering data as it is observed.

A frequency distribution check sheet can be used to record variable data while simultaneously building up an intuitive understanding of the probability distribution. This enables the user to make a quick judgement on whether the data is normally distributed without having to perform any calculations or create a separate histogram. The form is a table with two axes. Along the horizontal axes are listed values that the variable might take. On the vertical axis, the frequency of each value is recorded. Each time the user observes a value, they place a mark in the column for the corresponding value. The marks start on the bottom row and stack up when multiple observations of the same value are made. This results in bars with heights that represent the frequency with which each value is observed. When there is sufficient data, this presents a visualization of the frequency distribution that is representative of the underlying probability distribution, much like a histogram. The user can clearly see when a reasonable amount of data has been collected and whether the data is approximately normal.

Other commonly used check sheets are used to count defects. These can be divided into:

**Defect type**: A simple tally chart used to count the number of defects of each type.**Defect cause**: This is similar to a defect type check sheet. Instead of listing the type of defect, the cause is listed.**Defect location**: A diagram of the object being checked, typically shown from a number of directions, onto which the defect locations can be marked. An everyday example of a defect location check sheet is used when a hire car is returned.

### Histogram

A histogram is a way of graphically representing the distribution of values within a dataset. If the sample is large enough, it provides a reasonable approximation for the underlying probability distribution. It is one of the original statistical tools developed by Karl Pearson, the founder of modern statistics. It produces a result similar to a frequency distribution check sheet but can be applied to large datasets.

Before the histogram can be created, the data must first be grouped into *bins*, a series of intervals, and how many values are within each interval counted. The bins are typically of equal size. If the same is large, more bins can be used. For example, if you had 1,000 values ranging between zero and 100, you might create 10 bins. The bins would be 0-10, 11-20 and so forth. Once the bins have been created, the histogram is simply a bar chart giving the frequency of values within each bin.

Many different software applications have tools for creating histograms. The COUNTIFS function can be used to directly count the values in bins using Excel. If the histogram doesn’t give a clear picture of the frequency distribution, it may be because the bin ranges have been selected poorly or because there is insufficient data.

### Run Chart

A run chart is a scatter plot of the process output. The sample number is given on the x-axis, and the observed value of the process output is given on the y-axis. This gives a clear indication of how the process is varying with respect to time. For example, the user can see if the output is getting progressively bigger or smaller, or if it oscillating between two extreme values. Ideally, there should be no clearly discernible pattern in the data, indicating that the variation is caused by random influences.

It presents a view of how the process changes over time. For example, in the below run chart, the process appears to have drifted with seven values getting progressively smaller before returning to a random state.

Run charts can be a really useful way to get a quick indication of how a process is behaving. They provide temporal information that a frequency plot or histogram cannot provide. This is because in a frequency distribution, there is no indication of which values occurred first. The clear downward trend seen in the above run chart would, therefore, not be apparent.

### Control Chart

A control chart is essentially just a run chart with some added information. It includes a number of horizontal lines indicating the control limits and possibly also a number of zones within these limits. Typically, control limits would be set at +/- 3 standard deviations with horizontal red lines used to indicate them. The control limits do not relate to the product tolerance or specification for the process. They only relate to the baseline level of variation observed in the process. However, it is assumed that the process variation has been compared with the specification to ensure that the process is capable. Different sampling strategies are used to create different types of control charts depending on the measurements used. For example, for regular samples, an X-bar R or X-bar S control chart is used. For individual real-time measurements, one should use anIndividuals with Moving Range (IMR) control chart.

The area within the control limits may be further divided into three zones designated as A, B and C. Horizontal lines marking +/-1 and +/-2 standard deviation may be used to define these zones with Zone C being the region within one standard deviation of the mean, Zone B being made up of the two regions between one and two standard deviations from the mean, and Zone A being made up of the two regions between two and three standard deviations from the mean. Because the number of standard deviations is frequently referred to, it is often simply referred to as *sigma.*

Use of these zones allows simple rules to be applied to determine when statistically significant data has been observed that indicate either the random variation is increasing in magnitude or special cause variation has become an issue. In such a case, further action should be taken to determine the root cause of these changes. When there is only random variation within the control limits, the process is said to be “in-control.”Common rules used to determine when a process is out of control include a single point outside the control limits, a number of points in one of the outer zones or a number of points heading in the same direction.

### Pareto Chart

A Pareto chart combines two charts, one over the other, to show which factors make a significant contribution to a total value. The frequency of each type of defect, or the value for each factor, is given on a bar chart with the values sorted in descending order. The cumulative percentage of each value is also given as a line chart. Because the values are listed in descending order, the line chart starts at the top of the first bar and increases with a convex curvature. If the total is dominated by a few values, the line will be highly convex and flatten toward the right side. If all the values are of similar magnitude, the line will be approximately linear.

It is important to realize that a Pareto chart only gives a valid representation of the impact of each effect if they can be regarded as having an equal impact on the total quality or performance of the process. In other words, the quality is the sum of each individual effect. For example, imagine a chart was being used to consider the impact of crime in an area. The chart might include columns for littering, jaywalking, shoplifting, assaults and murders. Because the frequency of littering and jaywalking is much higher than assaults and murders, the Pareto chart would suggest that efforts should be focused on reducing littering and jaywalking. Clearly, this is an absurd idea. Although there are far fewer murders, they have a much greater impact on the community. This is an extreme example, but it illustrates the care that must be taken when comparing the causes or types of defects using a Pareto chart.

### Fishbone Diagram

A fishbone diagram is a hierarchical diagram, similar to a tree or mind map, with standard headings used to analyze the root cause of a defect. The diagram is arranged to look like a fish with the problem or effect at the head, a spine running horizontally and the main categories of causes radiating out on both sides like fish bones. This type of diagram is also known as an Ishikawa diagram or cause-and-effect diagram. Pre-printed forms may be used with standard headings for classes of defect or cause. The most common classification is the 5 M’s: machine, method, material, manpower and measurement. These headings can help simulate thought and generate possible causes beyond initial assumptions.

Although a fishbone diagram is traditionally used to analyze the root cause of a defect, other hierarchical structures can be just as useful. They may actually be easier to use, enabling a particular thought to be expanded by exploring the underlying root cause for a superficial cause. This concept of going deeper into each cause has been referred to as “asking the five whys.” Going five levels into a particular cause is difficult using a fishbone diagram.Variation breakdown, or a thought map, is now often preferred.

### Scatter Diagram

A scatter diagram, or scatter plot, is used to plot two, or sometimes more, variables against each other. It is one of the most fundamental tools used in science and engineering to understand the correlation between variables. A typical scatter diagram has a horizontal and a vertical axis, each representing a different variable. Points are plotted within the area according to the value of each variable for the given observation. If the points are all clustered together, along a straight line or curve, this indicates a correlation, or relationship, between the variables. If the points are randomly scattered over the area, there is no correlation.

If different colors or symbols are used, an additional variable can be represented on a two-dimensional diagram. The symbols can be used for either a discrete or continuous variable. In the example below, the horizontal axis is used to represent age while the vertical axis is used to represent height. These are both continuous variables. Different symbols are used to represent sex, a random variable. A clear correlation can be seen between age and height. It is more difficult to see if there is a correlation between sex and height, although it does appear that there is some correlation.

It is conventional to place the independent variable, or cause, on the horizontal axis, and the dependent variable, or effect, on the vertical axis. Oftentimes, the direction of causality is not known when plotting the data but is none-the-less arranged according to the suspected cause.

The seven basic tools of quality are graphical tools that can be used to gain a great deal of understanding about variation and the cause of defects. They are intuitive and require little knowledge of statistics. Despite this, they are able to solve most problems within quality improvement.