We would like to get created a PHP class for the statistical management of an array of data to generate XmR control charts. We don't need any graphical work. Just the statistical calcualtions.
Detailed information on how to do these kind of statistical calculations is available at [url removed, login to view]:_Basic_control_charts:_theory_and_construction,_sample_size,_x-bar,_r_charts,_s_charts. A simplified example in excel file is also attached. Take into account that some calculations in the excel file have been simplified.
1. Basic calculations based on the input array that the PHP class has to provide:
- Central line
- σ, 2σ and 3σ of the central line
- Moving ranges
- Average moving range
- Upper range limit
- Lower natural process limit
- Upper natural process limit
- Target lower limit
- Target central line
- Target upper limit
2. Interpret signals in the data
- Detect outliers: A point outside the natural process limits indicates something unusual happened.
- Detect Long runs: 8 consecutive points running on one side of the central line (or 10 in 12, or 12 in 14)
- Detect Short runs: At least 3 out of 4 consecutive points closer to the control limit than to the central line.
In general, these four rules have to be checked:
- Any point falls beyond 3σ from the central line (this is represented by the upper and lower control limts).
- Two out of three consecutive points fall beyond 2σ on the same side of the central line.
- Four out of five consecutive points fall beyond 1σ on the same side of the central line.
- Nine or more consecutive points fall on the same side of the central line.
3. Recalculation of central line and limit
If there is a long run or a short run that continues up to 5 values, the central line and the natural process limits have to be recalculated.
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