Full Answer
What is X-bar and Sigma?
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.
What is the difference between Sigma chart and X bar R control chart?
Selection of appropriate control chart is very important in control charts mapping, otherwise ended up with inaccurate control limits for the data. Manually it is very easy to compute X Bar R Control chart, where as sigma chart may be difficult due to tedious calculations and large sample size.
What does the X-bar chart show?
X-bar chart: The mean or average change in process over time from subgroup values. The control limits on the X-Bar brings the sample’s mean and center into consideration.
What is a sigma chart?
A free online reference for statistical process control, process capability analysis, measurement systems analysis, control chart interpretation, and other quality metrics. What is it? An X-bar and s (sigma) chart is a special purpose variation of the X-bar and R chart.
What are X Bar R Control Charts?
X Bar R charts are the widely used control chart for variable dat a to examine the process stability in many industries (like Hospital patients’ blood pressure over time, customer call handle time, length of the part in production process etc.,).
X Bar R Control Chart Definitions
X-bar chart: The mean or average change in process over time from subgroup values. The control limits on the X-Bar brings the sample’s mean and center into consideration.
Use X Bar R Control Charts When
Even very stable process may have some minor variations, which will cause the process instability. X bar R chart will help to identify the process variation over the time
How to Interpret the X Bar R Control Charts
To correctly interpret X bar R chart, always examine the R chart first.
Steps to follow for X bar R chart
Determine the objective of the chart and choose the important variables
Important notes
A process is “in control” that indicates means of the process is stable and it can be predictable
Authors
I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!
What are X Bar S Control Charts?
X Bar S charts often used control chart to examine the process mean and standard deviation over the time. These charts are used when the subgroups have large sample size and S chart provides better understanding of the spread of subgroup data than range.
X Bar S Control Chart Definitions
X-bar chart: The mean or average change in process over time from subgroup values. The control limits on the X-Bar brings the sample’s mean and center into consideration.
Use X Bar S Control Charts When
The sampling procedure is same for each sample and is carried out consistently.
How to Interpret the X Bar S Control Charts
To correctly interpret X bar S chart, always examine the S chart first.
Steps to follow for X bar S chart
Determine the objective of the chart and choose the important variables
Important notes on X Bar S Control Charts
A process is “in control” that indicates means of the process is stable and it can be predictable
Authors
I originally created SixSigmaStudyGuide.com to help me prepare for my own Black belt exams. Overtime I've grown the site to help tens of thousands of Six Sigma belt candidates prepare for their Green Belt & Black Belt exams. Go here to learn how to pass your Six Sigma exam the 1st time through!
Example One
The Xbar chart below shows an out of control process. The R chart appears to be in control.
Using Minitab
As revisions are released the menu's may change from that shown below however, the general path is likely to remain similar.
Example Two
Using the data set in Excel in the .zip file below, copy and paste the information into statistical software and the following charts are generated. The data and results is also shown at the bottom of this page in a picture format.
Behavior of the Sample Mean (x-bar)
LO 6.22: Apply the sampling distribution of the sample mean as summarized by the Central Limit Theorem (when appropriate). In particular, be able to identify unusual samples from a given population.
EXAMPLE 9: Behavior of Sample Means
Birth weights are recorded for all babies in a town. The mean birth weight is 3,500 grams, µ = mu = 3,500 g. If we collect many random samples of 9 babies at a time, how do you think sample means will behave?
The Sampling Distribution of the Sample Mean
If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
EXAMPLE 10: Using the Sampling Distribution of x-bar
Household size in the United States has a mean of 2.6 people and standard deviation of 1.4 people. It should be clear that this distribution is skewed right as the smallest possible value is a household of 1 person but the largest households can be very large indeed.
What is X-Bar?
Before discussing x-bar, some prerequisite information is needed about populations and samples in statistics. Here are a few definitions that are needed:
What Does X-Bar Mean?
In statistics, an estimate is a number that approximates a population parameter that is found from some sample. A point estimate is a single number that is the best estimate for some population parameter.
