# How to determine if an engineering process is stable and capable?

Mostly interested in understanding how engineers determine if an engineering process is stable and capable, particular in design for manufacturing (DFM) frame work for components. Some example components to consider are:

• Flow rate for Solenoid Valve
• Torque for a Brushless DC Motor
• Capacitance for a Capacitor

Note: There are infinite amount of examples.

How does an engineer confirm if a vendor has a stable and capable process (incoming material)? To be cost competitive it is important to have the least amount (optimal) manufacturing test and inspection processors yet ensure the end product meets specification. How does an engineer ensure the final product meet specification (outgoing material)?

• I think you are asking "How can I know if my vendor has a decent quaility control?" or do I misunderstand you?
– mart
Commented Mar 23, 2015 at 10:10
• Could this be what you are looking for: en.wikipedia.org/wiki/Control_theory ? Commented Mar 26, 2015 at 18:01
• @MatsGranvik I don't think that's what Mahendra is referring to. Control theory is the programming behind your thermostat, or the cruise control on your car. This sounds more like process engineering, dealing with quality control. Both types of control, but distinct concepts. Commented Mar 26, 2015 at 21:10

## 1 Answer

One possible method to determine stability and capability is using control charts. Below is an example control chart representing an unstable process. The data points are represented in blue, which include few data points above the upper control limit (UCL - Purple line) and below the low control limit (LCL - Red line).

Below is data for the above chart. The data is Apple stock price for 15 days. Data is for illustration purpose only.

\begin{array}{| l | l | l | l | l | l | l | l | l | l |} \hline & & & & & & & \bar{X} Chart & \bar{X} Chart & \bar{X} Chart\\ Date & Open & High & Low & Close & \bar{X} & R & LCL & CL & UCL \\ \hline 3/19/2015 & 126.7& 127.2& 125.4& 125.5& 126.2& 1.8& 124.1& 126.1& 128.2 \\ 3/18/2015 & 126.0& 128.6& 125.3& 127.4& 126.7& 2.7& 124.1& 126.1& 128.2 \\ 3/17/2015 & 125.9& 127.2& 124.6& 127.0& 126.2& 2.6& 124.1& 126.1& 128.2 \\ 3/16/2015 & 123.8& 124.9& 123.3& 125.4& 124.4& 2.0& 124.1& 126.1& 128.2 \\ 3/13/2015 & 124.9& 125.9& 122.5& 123.5& 124.2& 3.3& 124.1& 126.1& 128.2 \\ 3/12/2015 & 123.3& 125.9& 122.6& 125.4& 124.3& 3.2& 124.1& 126.1& 128.2 \\ 3/11/2015 & 126.7& 126.2& 124.1& 123.7& 125.2& 3.0& 124.1& 126.1& 128.2 \\ 3/10/2015 & 126.4& 127.2& 123.8& 124.5& 125.4& 3.4& 124.1& 126.1& 128.2 \\ 3/9/2015 & 127.9& 129.5& 125.0& 127.1& 127.4& 4.5& 124.1& 126.1& 128.2 \\ 3/6/2015 & 128.4& 129.3& 126.2& 126.6& 127.6& 3.1& 124.1& 126.1& 128.2 \\ 3/5/2015 & 128.5& 128.7& 125.7& 126.4& 127.3& 2.9& 124.1& 126.1& 128.2 \\ 3/4/2015 & 128.1& 129.0& 126.8& 128.5& 128.1& 2.2& 124.1& 126.1& 128.2 \\ 3/3/2015 & 126.9& 128.0& 125.5& 127.3& 126.9& 2.4& 124.1& 126.1& 128.2 \\ 3/2/2015 & 126.2& 127.2& 125.3& 126.0& 126.2& 1.9& 124.1& 126.1& 128.2 \\ & & & & & 126.1& 2.8 \\ & & & & & \bar{\bar{X}} & \bar{R} \\ \hline \end{array}

Steps for the Chart

1. $\bar{X}$, Average of observation
2. $R$, Range , Max - Min
3. $\bar{\bar{X}}$, $\bar{R}$, Average of $\bar{X}$ and Average of Range
4. The center line of $\bar{X} Chart$ is $\bar{X}$
5. LCL and UCL lines for $\bar{X} chart$ use $\bar{X}$ equation

Below is a control chart representing a stable process. All data points are between LCL and UCL.

Note: The data has been adjusted to illustrate a stable process

If the specification limits (Upper specification limit: USL and low specification limit: LSL) are outside of both the LCL and UCL then the process is considered a capable process.

• Y-axis are not labeled. Also I fail to see the connection to the question, but I don't understand the question anyway.
– mart
Commented Mar 26, 2015 at 20:42
• @mart the Y-axis can be any measurement type. Example: flow rate, voltage, pressure. For illustration purpose the data is apple stock price. Open close high and low. Commented Apr 6, 2015 at 21:23