Table of Contents
What Is SMPX?
SMPX (Sample Mean Plus X standard deviations) is a statistical calculation used in quality control and process monitoring. It computes control limits by adding or subtracting a specified number of standard deviations (k) from the sample mean. This approach is fundamental to Shewhart control charts and the empirical rule in statistics.
The most common multiplier is k=3, which captures 99.73% of values for normally distributed data (the basis of Six Sigma methodology). Using k=2 captures approximately 95.45% of values. These bounds help identify unusual observations and out-of-control processes in manufacturing and laboratory settings.
Formula
Applications
| k Value | Coverage (Normal) | Use Case |
|---|---|---|
| 1 | 68.27% | General variation band |
| 2 | 95.45% | Warning limits |
| 3 | 99.73% | Control limits (3-sigma) |
| 6 | 99.9999998% | Six Sigma specification |
Frequently Asked Questions
Why is k=3 the standard for control charts?
Walter Shewhart chose 3 standard deviations because it provides a good balance between detecting real process changes and minimizing false alarms. With k=3, only 0.27% of points would fall outside the limits by chance when the process is in control, giving a false alarm rate of about 1 in 370 samples.
Can I use SMPX with non-normal data?
Yes, but the percentage coverage will differ from the normal distribution values. Chebyshev's inequality guarantees that at least (1 - 1/k^2) of values fall within k standard deviations for any distribution, regardless of shape. For k=3, this gives at least 88.9% coverage even for non-normal data.