homeworks1,2, and 3
Johnnetwork 
Formulasandexamples.pptxControl Charts
Variables Control Charts
Formulas
Procedure to create control charts
Collect the data
Run the process untouched to gather initial data for control limits.
Generally, collect 20-25 subgroups (100 total samples) before calculating the control limits.
Each time a subgroup of sample size n is taken, an average is calculated for the subgroup and plotted on the control chart.
Control Charts
Determine trial centerline
The centerline should be the population mean,
Since it is unknown, we use X double bar, or the grand average of the subgroup averages.
Where
Xbar is the average of the sample
Xbarbar is the grand average, this will be used as the center line on the Xbar Chart
m is the number of samples
n is the sample size
Determine trial control limits - Xbar chart
The normal curve displays the distribution of the sample averages.
A control chart is a time-dependent pictorial representation of a normal curve.
Processes that are considered under control will have 99.73% of their graphed averages fall within six standard deviations.
Control Charts
UCL and LCL calculation
Control Charts
Determining an alternative value for the standard deviation
Where
R is the range between of the sample
R = xmax – xmin
R = Difference between the largest and smallest observations
Determine trial control limits - R chart
The range chart shows the spread or dispersion of the individual samples within the subgroup.
If the product shows a wide spread, then the individuals within the subgroup are not similar to each other.
Equal averages can be deceiving.
Calculated similar to x-bar charts;
Use D3 and D4
Control limits for the R chart
R-bar chart exceptions
Because range values cannot be negative, a value of 0 is given for the lower control limit of sample sizes of six or less.
Control Charts
Example #1. Create a
Variables Control Chart Xbar and R. Determine the number of observations in each sample n=
What is the measurable variable?
To determine the value for n, the number of subgroups
In order to determine the upper (UCL) and lower (LCL) limits for the x-bar charts, you need to know how many subgroups (n) there are in your data.
Once you know the value of n, you can obtain the correct constants (A2, A3, etc.) to complete your control chart.
The value of n is the number of subgroups within each data point. For example, if you are taking temperature measurements every min and there are three temperature readings per minute, then the value of n would be 3. And if this same experiment was taking four temperature readings per minute, then the value of n would be 4. Here are some examples with different tables of data to help you further in determining n:
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deviation
standard
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LCL
3
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UCL
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