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

Question

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)?

Answer 1

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.