Statistics in Engineering: Statistical Process Control (Part 7 of 8)

Preface
This series is aimed at providing tools for an electrical engineer to gain confidence in the performance and reliability of their design. The focus is on applying statistical analysis to empirical results (i.e. measurements, data sets).

Introduction
Now that we are familiar with all the basic statistical methods we can look at using them in the manufacturing space to monitor a process for error.

Generally a process is made of two steps: establishing the process and then monitoring it. It is common to see the use of ANOVA for establishing a process or optimizing a process and SPC for maintaining and monitoring that process.

If you are not familiar with statistics or need a brush up I recommend Schaum's Statistics. It provides a good overview of material without a lot of time spent on proofs and lots of examples.

Concepts
Statistical Process Control (SPC): A method of quality control using statistical processes.
4-M: The four conditions which a process can be broken into: man, machine, material and method.
Common Causes: Think of this as the normal variation encountered in a functioning process.
Special Causes: These causes are outside of the normal variation and indicate a failure in the process that must be corrected.
Control Chart: A way of visualizing and monitoring a process. Generally by plotting sampled values or sampled means along an x axis (the y being the magnitude). Also along the x-axis are a center line and the LCL and UCL.
LCL: This is the lower limit which differentiates special causes from common causes in a control chart.
UCL: This is the upper limit which differentiates special causes from common causes in a control chart.
Process Spread: Essentially just the set points for the LCL and UCL. Often set to +/-3 sigmal.
Detection Rules: The LCL and UCL can be thought of as detection rules. Rules that indicate a failure in the process. There are other rules which can detect failures earlier and before an LCL or UCL violation. These can be tests for steadily increasing or decreasing, oscillations, positive or negative offset, etc. This could possibly save money by reducing maintenance or material costs or I imagine increased operator safety.
Process Capability Index, C_p: A processes potential for meeting specifications and is defined as (UCL-LCL)/6sigma.
C_pk Index: Measures the process performance and is defined as min((UCL-mu)/3sigma,(mu-LCL)/3sigma).

Monitoring a process

1. Once the process is established you should have enough data to establish a centerline (mu) and LCL and UCL (using the standard deviation, sigma).
2. Determine what kind of chart you're going to use. Is this sampled data? Counted data?
3. Establish your process limits. Usually +/-3sigma.
4. Establish your test rules.
5. Monitor your output. Compute your C_p.

Next Up
Next article we wrap up the series and establish a decision tree for applying the right statistical method for the right situation.