A free online reference for statistical process control, process capability analysis, measurement systems analysis, control chart interpretation, and other quality metrics.
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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.
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.
A median chart is a special purpose variation of the X-bar chart. This chart uses the median instead of the subgroup average to show the system’s central location. The median is the middle point when data points are arranged from high to low. The chart shows all the individual readings. Use charts to determine if the system is stable and predictable or to monitor the effects of process improvement theories.
Although median charts show both central location and spread, they are often paired with range charts.
The median chart shows each reading in a subgroup. Subgroup medians are connected by the data line and are used to analyze the central location.
Use the median chart when you want to plot all the measured values, not just subgroup statistics. This may be the case when subgroup ranges vary a great deal, as showing all the points will emphasize the spread. It shows users that individual data points can fall outside the control limits, while the central location is within the limits.
Use the median chart when you can answer yes to these questions:
Collect as many subgroups as possible before calculating control limits. With smaller amounts of data, the median chart may not represent variability of the entire system. The more subgroups you use in control limit calculations, the more reliable the analysis. Typically, twenty to twenty-five subgroups will be used in control limit calculations.
Median charts have several applications. When you begin to improve a system, use them to assess the system’s stability.
After the stability has been assessed, determine if you need to stratify the data. You may find entirely different results between shifts, among workers, among different machines, among lots of materials, etc. To see if variability on the median chart is caused by these factors, you should collect and enter data in a way that lets you stratify by time, location, symptom, operator, and lots.
You can also use median charts to analyze the results of process improvements. Here you would consider how the process is running and compare it to how it ran in the past. Do process changes produce the desired improvement?
Finally, use median charts for standardization. This means you should continue collecting and analyzing data throughout the process operation. If you made changes to the system and stopped collecting data, you would have only perception and opinion to tell you whether the changes actually improved the system. Without a control chart, there is no way to know if the process has changed or to identify sources of process variability.
Variables data is normally analyzed in pairs of charts which present data in terms of location or central location and spread. Location, usually the top chart, shows data in relation to the process average. It is presented in X-bar, individuals, or median charts. Spread, usually the bottom chart, looks at piece-by-piece variation. Range, sigma, and moving range charts are used to illustrate process spread. Another aspect of these variables control charts is that the sample size is generally constant.
Use the following types of charts and analysis to study variables data:
These charts, and more, can be created easily using software packages such as SQCpack.
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.
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.
An X-bar and R (range) chart is a pair of control charts used with processes that have a subgroup size of two or more. The standard chart for variables data, X-bar and R charts help determine if a process is stable and predictable. The X-bar chart shows how the mean or average changes over time and the R chart shows how the range of the subgroups changes over time. It is also used to monitor the effects of process improvement theories. As the standard, the X-bar and R chart will work in place of the X-bar and s or median and R chart. To create an X-bar and R chart using software, download a copy of SQCpack.
The X-bar chart, on top, shows the mean or average of each subgroup. It is used to analyze central location. The range chart, on the bottom, shows how the data is spread. It is used to study system variability.
You can use X-bar and R charts for any process with a subgroup size greater than one. Typically, it is used when the subgroup size falls between two and ten, and X-bar and s charts are used with subgroups of eleven or more.
Use X-bar and R charts when you can answer yes to these questions:
Collect as many subgroups as possible before calculating control limits. With smaller amounts of data, the X-bar and R chart may not represent variability of the entire system. The more subgroups you use in control limit calculations, the more reliable the analysis. Typically, twenty to twenty-five subgroups will be used in control limit calculations.
X-bar and R charts have several applications. When you begin improving a system, use them to assess the system’s stability.
After the stability has been assessed, determine if you need to stratify the data. You may find entirely different results between shifts, among workers, among different machines, among lots of materials, etc. To see if variability on the X-bar and R chart is caused by these factors, collect and enter data in a way that lets you stratify by time, location, symptom, operator, and lots.
You can also use X-bar and R charts to analyze the results of process improvements. Here you would consider how the process is running and compare it to how it ran in the past. Do process changes produce the desired improvement?
Finally, use X-bar and R charts for standardization. This means you should continue collecting and analyzing data throughout the process operation. If you made changes to the system and stopped collecting data, you would have only perception and opinion to tell you whether the changes actually improved the system. Without a control chart, there is no way to know if the process has changed or to identify sources of process variability.
Variables data is data that is acquired through measurements, such as length, time, diameter, strength, weight, temperature, density, thickness, pressure, and height. With variables data, you can decide the measurement’s degree of accuracy. For example, you can measure an item to the nearest centimeter, millimeter, or micron.
Variation is inherent to any system, and the data collection process is no exception. However, excessive variation in the data collection process will appear as variation on the control chart and can have a negative effect on process analysis. In addition to using operational definitions to ensure measurement consistency, you should periodically perform repeatability and reproducibility tests and recalibrate gages.
Gage R&R refers to testing the repeatability and reproducibility of the measurement system. Repeatability is the variation found in a series of measurements that have been taken by one person using one gage to measure one characteristic of an item. Reproducibility is the variation in a series of measurements that have been taken by different people using the same gage to measure one characteristic of an item.
Gage R&R studies let you address two major categories of variation in measuring systems: gage variability and operator variability. Gage variability refers to factors that affect the gage’s accuracy, such as its sensitivity to temperature, magnetic and electrical fields and, if it is mounted, how tight or loose the mount is. Operator variability refers to variation caused by differences among people. It can be caused by different interpretations of a vague operational definition, as well as differences in training, attitude, and fatigue level.
Performing gage R&R studies can be made easier by using software such as GAGEpack.
An operational definition, when applied to data collection, is a clear, concise detailed definition of a measure. The need for operational definitions is fundamental when collecting all types of data. It is particularly important when a decision is being made about whether something is correct or incorrect, or when a visual check is being made where there is room for confusion.
For example, data collected will be erroneous if those completing the checks have different views of what constitutes a fault at the end of a glass panel production line. Defective glass panels may be passed and good glass panels may be rejected. Similarly, when invoices are being checked for errors, the data collection will be meaningless if the definition of an error has not been specified.
When collecting data, it is essential that everyone in the system has the same understanding and collects data in the same way. Operational definitions should therefore be made before the collection of data begins.
Any time data is being collected, it is necessary to define how to collect the data. Data that is not defined will usually be inconsistent and will give an erroneous result. It is easy to assume that those collecting the data understand what and how to complete the task. However, people have different opinions and views, and these will affect the data collection. The only way to ensure consistent data collection is by means of a detailed operational definition that eliminates ambiguity.
The above article is an excerpt from the “Operational definition” chapter of Practical Tools for Continuous Improvement: Volume 1 – Statistical Tools. The full chapter provides more details on creating operational definition.
A resource for data collection tools, including how to collect data, how much to collect, and how frequently to collect it.
Sampling is a tool that is used to indicate how much data to collect and how often it should be collected. This tool defines the samples to take in order to quantify a system, process, issue, or problem.
To illustrate sampling, consider a loaf of bread. How good is the bread? To find out, is it necessary to eat the whole loaf? No, of course not. To make a judgment about the entire loaf, it is necessary only to taste a sample of the loaf, such as a slice. In this case the loaf of bread being studied is known as the population of the study. The sample, the slice of bread, is a subset or a part of the population.
Now consider a whole bakery. The population of interest is no longer a loaf, but all the bread that has been made today. A sample size of one slice from one loaf is clearly inadequate for this larger population. The sample collected will now become several loaves of bread taken at set times throughout the day. Since the population is larger, the sample will also be larger. The larger the population, the larger the sample required.
In the bakery example, bread is made in an ongoing process. That is, bread was made yesterday, throughout today, and will be made tomorrow. For an ongoing process, samples need to be taken to identify how the process is changing over time. Studying how the samples are changing with control charts will show where and how to improve the process, and allow prediction of future performance.
For example, the bakery is interested in the weight of the loaves. The bakery does not want to weigh every single loaf, as this would be too expensive, too time consuming, and no more accurate than sampling some of the loaves. Sampling for improvement and monitoring is a matter of taking small samples frequently over time. The questions now become:
These two questions, “how much?” and “how often?” are at the heart of sampling.
Begin by answering the question, “How many items does this process produce during the frequency interval (per hour, week, etc.)?” When that number is determined, the sample size should be at least the square root of that number. For instance, if a purchasing department processes 100 purchase orders per week, an appropriate sample size would be 10 purchase orders per week (the square root of 100 is 10.)
The above article is an excerpt from the “Sampling” chapter of Practical Tools for Continuous Improvement: Volume 1 – Statistical Tools. The full chapter provides more details on sampling.
Tools for analyzing and interpreting data so that areas to improve become apparent.
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Consists of measurements of a characteristic, such as length, weight, density, time, or pressure.
Consists of defects per item (nonconformities) or the number of defective items (nonconforming). For example, the number of non-working parts in sample or the number of blemishes counted on an individual part.
Consists of a count of items or occurrences, such as the number of defective items, the number of scratches on a door panel, or how often a specific problem occurs.
Use this when other control charts are not effective to determine if your process is stable.
Answer “yes” or “no” to a series of questions about your control charts.
Follow these steps to interpret histograms.