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control chart interpretation, and other quality metrics.

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Control Charts

Control charts: Does your data represent a process that is stable and in control?

Control charts are the best way to learn how a process is running. They are used to reduce the chance of making one of two kinds of mistakes:

  1. Overcontrolling
    Also called a Type I error, this refers to adjusting the process when nothing out of the ordinary has occurred.
  2. Undercontrolling
    Also called a Type II error, this refers to the failure to adjust the process when something out of the ordinary has occurred

If you are not sure which chart to use for your data, review the brief descriptions on data analysis tools.

Control charts - See an example of a control chart

Frequently-asked questions about control charts

  1. Which control chart should you use?
  2. Multiple control limits: A long shot, or just a bad slice?
  3. When should you recalculate limits?
  4. Testing a theory about your data

For more on control charts and how they can help you, view a 4-minute video.

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X-bar and sigma

What is it?

An X-bar and s (sigma) chart is a special purpose variation of the X-bar and R chart. Used with processes that have a subgroup size of 11 or more, X-bar and s charts show if the system is stable and predictable. They are also used to monitor the effects of process improvement theories. Instead of using subgroup range to chart variability, these charts use subgroup standard deviation. Because standard deviation uses each individual reading to calculate variability, it provides a more effective measure of the process spread. X-bar and sigma charts To create an X-bar and sigma chart using software, download a copy of SQCpack.

What does it look like?

The X-bar chart, on top, shows the mean or average of each subgroup. It is used to analyze central location. The sigma chart, on the bottom, shows how the data is spread and used to study system variability.

g-chart

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X-MR Chart

What is it?

An individuals and moving range (X-MR) chart is a pair of control charts for processes with a subgroup size of one. Used to determine if a process is stable and predictable, it creates a picture of how the system changes over time. The individual (X) chart displays individual measurements. The moving range (MR) chart shows variability between one data point and the next. Individuals and moving range charts are also used to monitor the effects of process improvement theories.

What does it look like?

The individuals chart, on top, shows each reading. It is used to analyze central location. The moving range chart, on the bottom, shows the difference between consecutive readings. It is used to study system variability.

g-chart

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X-MR Chart

What is it?

An individuals and moving range (X-MR) chart is a pair of control charts for processes with a subgroup size of one. Used to determine if a process is stable and predictable, it creates a picture of how the system changes over time. The individual (X) chart displays individual measurements. The moving range (MR) chart shows variability between one data point and the next. Individuals and moving range charts are also used to monitor the effects of process improvement theories.

What does it look like?

The individuals chart, on top, shows each reading. It is used to analyze central location. The moving range chart, on the bottom, shows the difference between consecutive readings. It is used to study system variability.

g-chart

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np-chart

What is it?

An np-chart is an attributes control chart used with data collected in subgroups that are the same size. Np-charts show how the process, measured by the number of nonconforming items it produces, changes over time. The process attribute (or characteristic) is always described in a yes/no, pass/fail, go/no go form. For example, the number of incomplete accident reports in a constant daily sample of five would be plotted on an np-chart. Np-charts are used to determine if the process is stable and predictable, as well as to monitor the effects of process improvement theories. Np-charts can be created using software programs like SQCpack.

What does it look like?

The np-chart shows the number of nonconforming units in subgroups of set sizes.

np control chart

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p-chart

What is it?

A p-chart is an attributes control chart used with data collected in subgroups of varying sizes. Because the subgroup size can vary, it shows a proportion on nonconforming items rather than the actual count. P-charts show how the process changes over time. The process attribute (or characteristic) is always described in a yes/no, pass/fail, go/no go form. For example, use a p-chart to plot the proportion of incomplete insurance claim forms received weekly. The subgroup would vary, depending on the total number of claims each week. P-charts are used to determine if the process is stable and predictable, as well as to monitor the effects of process improvement theories. P-charts can be created using software programs like SQCpack.

What does it look like?

The p-chart shows the proportion of nonconforming units in subgroups of varying sizes.

p control chart

When is it used?

Use a p-chart when you can answer “yes” to all these questions:

1. Do you need to assess system stability?

2. Does the data consist of counts that can be converted to proportions?

3. Are there only two outcomes to any given check?

4. Has the characteristic being charted been operationally defined prior to data collection?

5. Is the time order of subgroups preserved?

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c-chart

What is it?

A c-chart is an attributes control chart used with data collected in subgroups that are the same size. C-charts show how the process, measured by the number of nonconformities per item or group of items, changes over time. Nonconformities are defects or occurrences found in the sampled subgroup. They can be described as any characteristic that is present but should not be, or any characteristic that is not present but should be. For example a scratch, dent, bubble, blemish, missing button, and a tear would all be nonconformities. C-charts are used to determine if the process is stable and predictable, as well as to monitor the effects of process improvement theories. C-charts can be created using software products like SQCpack.

What does it look like?

The c-chart shows the number of nonconformities in subgroups of equal size.

c control chart

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u-chart

What is it?

A u-chart is an attributes control chart used with data collected in subgroups of varying sizes. U-charts show how the process, measured by the number of nonconformities per item or group of items, changes over time. Nonconformities are defects or occurrences found in the sampled subgroup. They can be described as any characteristic that is present but should not be, or any characteristic that is not present but should be. For example, a scratch, dent, bubble, blemish, missing button, and a tear are all nonconformities. U-charts are used to determine if the process is stable and predictable, as well as to monitor the effects of process improvement theories. U-charts can be created using software programs like SQCpack.

What does it look like?

The u-chart shows the proportion of nonconformities units in subgroups of varying sizes.

g-chart

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control chart interpretation, and other quality metrics.

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Histogram: Study the shape

A histogram can be created using software such as SQCpack. How would you describe the shape of the histogram?

Bell-shaped: A bell-shaped picture, shown below, usually presents a normal distribution.

Bimodal: A bimodal shape, shown below, has two peaks. This shape may show that the data has come from two different systems. If this shape occurs, the two sources should be separated and analyzed separately.

Skewed right: Some histograms will show a skewed distribution to the right, as shown below. A distribution skewed to the right is said to be positively skewed. This kind of distribution has a large number of occurrences in the lower value cells (left side) and few in the upper value cells (right side). A skewed distribution can result when data is gathered from a system with has a boundary such as zero. In other words, all the collected data has values greater than zero.

Skewed left: Some histograms will show a skewed distribution to the left, as shown below. A distribution skewed to the left is said to be negatively skewed. This kind of distribution has a large number of occurrences in the upper value cells (right side) and few in the lower value cells (left side). A skewed distribution can result when data is gathered from a system with a boundary such as 100. In other words, all the collected data has values less than 100.

Uniform: A uniform distribution, as shown below, provides little information about the system. An example would be a state lottery, in which each class has about the same number of elements. It may describe a distribution which has several modes (peaks). If your histogram has this shape, check to see if several sources of variation have been combined. If so, analyze them separately. If multiple sources of variation do not seem to be the cause of this pattern, different groupings can be tried to see if a more useful pattern results. This could be as simple as changing the starting and ending points of the cells, or changing the number of cells. A uniform distribution often means that the number of classes is too small.

Random: A random distribution, as shown below, has no apparent pattern. Like the uniform distribution, it may describe a distribution that has several modes (peaks). If your histogram has this shape, check to see if several sources of variation have been combined. If so, analyze them separately. If multiple sources of variation do not seem to be the cause of this pattern, different groupings can be tried to see if a more useful pattern results. This could be as simple as changing the starting and ending points of the cells, or changing the number of cells. A random distribution often means there are too many classes.

Follow these steps to interpret histograms.

  1. Study the shape.
  2. Calculate descriptive statistics.
  3. Compare the histogram to the normal distribution.