X-bar chart
Encyclopedia
In industrial statistics
, the X-bar chart is a type of Shewhart
control chart
that is used to monitor the arithmetic mean
s of successive samples of constant size, n. This type of control chart is used for characteristics that can be measured on a continuous scale, such as weight, temperature, thickness etc. For example, one might take a sample of 5 shafts from production every hour, measure the diameter of each, and then plot, for each sample, the average of the five diameter values on the chart.
For the purposes of control limit
calculation, the sample means are assumed to be normally distributed, an assumption justified by the Central Limit Theorem
.
The X-bar chart is often used in conjunction with a variation chart such as the R-chart or s-chart. The R-chart shows sample ranges (difference between the largest and the smallest values in the sample), while the s-chart shows the samples' standard deviation
. The R-chart was preferred in times when calculations were performed manually, as the range is far easier to calculate than the standard deviation; with the advent of computers, ease of calculation ceased to be an issue, and the s-chart is preferred these days, as it is statistically more meaningful and efficient. Depending on the type of variation chart used, the average sample range or the average sample standard deviation
is used to derive the X-bar chart's control limits.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the X-bar chart is a type of Shewhart
Walter A. Shewhart
Walter Andrew Shewhart March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.W...
control chart
Control chart
Control charts, also known as Shewhart charts or process-behaviour charts, in statistical process control are tools used to determine whether or not a manufacturing or business process is in a state of statistical control.- Overview :...
that is used to monitor the arithmetic mean
Arithmetic mean
In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...
s of successive samples of constant size, n. This type of control chart is used for characteristics that can be measured on a continuous scale, such as weight, temperature, thickness etc. For example, one might take a sample of 5 shafts from production every hour, measure the diameter of each, and then plot, for each sample, the average of the five diameter values on the chart.
For the purposes of control limit
Control limits
Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic from the statistic's mean....
calculation, the sample means are assumed to be normally distributed, an assumption justified by the Central Limit Theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
.
The X-bar chart is often used in conjunction with a variation chart such as the R-chart or s-chart. The R-chart shows sample ranges (difference between the largest and the smallest values in the sample), while the s-chart shows the samples' standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
. The R-chart was preferred in times when calculations were performed manually, as the range is far easier to calculate than the standard deviation; with the advent of computers, ease of calculation ceased to be an issue, and the s-chart is preferred these days, as it is statistically more meaningful and efficient. Depending on the type of variation chart used, the average sample range or the average sample standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
is used to derive the X-bar chart's control limits.