Process Stability refers to the consistency of the process to stay within Upper Control Limit (UCL) and Lower Control Limit (LCL). The outputs of any process will have a mean value. Then the control Limits for the process are defined as follows:
Upper Control Limit (UCL) = Mean + 3 sigma
Lower Control Limit (LCL) = Mean - 3 sigma
If the process behaves consistently over time, i.e. the outputs fall within the range UCL to LCL called process width, then the process is said to be stable or in control.
If the Outputs are spread across outside the limits, then the process is Unstable or Out of Control.
Process Capability is a measure of the ability of the process to meet customer specifications. The measure tells how good each individual output is. An estimation of the ppm (defective parts per million) is a method to measure process capability.
Capability Indices (Cp, Cpk) are metrics used to measure the process capability. It indicates how capable the process is in terms of meeting customer requirements.
Customers provide Upper Specification Limit (USL) and Lower Specification Limit (LSL) within which they want the product value to exist. This is called the tolerance or Allowed variation. (E.g. A customer of a Building Management system may want his air conditioning such that room temperature is 20 +/- 2 (deg C) i.e. with USL =24 deg C and LSL = 18 deg C)
The air-conditioning process may have its own Mean/Average temperature say, 21 deg. C
Cp = Tolerance/ Process Width = (USL-LSL) / (UCL-LCL)
Cpk = min(Cpu,Cpl) where Cpu measures the closeness between process mean and USL; Cpl measures the closeness between process mean and LSL. Cpk accounts for change is process mean.
A simplistic example: In an exam if the passing mark is 40 (USL = not specified; LSL = 40) and a student if 5 continuous attempts get 30,30.5,31,32,30 then we can say he is Stable(consistent) but not Capable.
Is Process Stability supposed to be a pre-requisite for all type of processes?
Any manufacturing /production process should be stable before being released to the production environment. Many customers request that their suppliers submit process capability data to qualify the supplier process. Any estimate of process capability depends entirely on where the process happens to be when the data is collected. For an unstable process, the mean shifts about over time. So, stability would be prerequisite for such process, as the process capability can only be estimated for stables processes.
But, I believe, processes involved in Research and Development, Innovation would be inherently unstable. These process may not need a Capability estimation , so stability will not be a prerequisite.