Statistical process control (SPC)

Statistical process on control (SPC) is a tool to control and monitor a process. To control the process important process parameters must be measured and analyzed. With SPC the goal is to detect when a process is out of control to minimize the amount of wrong products.

Tools

Control Chart

The important tool of SPC is the Control Chart.

The control chart can help

• To prevent that a process is going out of control.
• To determine the range of a process.
• Monitor change in process over time (wear out of production equipment).
• Snapshot of a production period.
  

UCL and LCL are not the specification limits!!


Data File

Common Control Chart interpretation (WECO) rules

• A point falls outside the UCL or LCL (3 sigma lines).
• Two out of three successive points are outside the 2 sigma line (second gray line under or above the mean).
• Four out of five successive points are outside the 1 sigma line (first gray line under or above the mean).
• Eight successive points are on one side of the mean line.

When one of these rules happens it will be visible as a red dot in the plot. If needed corrective actions must be taken to restore the process. Keep in mind a point outside the ULC and LCL will can occur in about 1 in the 371 data-points.

Calculations

UCL = Mean + 3 x STDEV
LCL = Mean - 3 x STDEV

Cp and Cpk

To check if the production process is capable to produce within specification limits the Cp and Cpk are calculated.

The higher the Cpk value the better a product is within specification.

Example

With a Cpk of 1.17 is 0.05% out of tolerance (5 on 100 products).

Two sided table
Cpk	Sigma level	% out of tolerance	PPM out of tolerance
0.33	1.0	31.73	317310.508
0.50	1.5	13.36	133614.403
0.67	2.0	4.55	45500.264
0.83	2.5	1.24	12419.331
1.00	3.0	0.27	2699.796
1.17	3.5	0.05	465.258
1.33	4.0	0.01	63.342
1.50	4.5	0.001	6.795
1.67	5.0	0.0001	0.573
1.83	5.5	0.000004	0.038
2.00	6.0	0.0000002	0.002