How to detect common cause and special cause process variation

From my previous article,  we know that there are 2 types of process variations , common cause and special cause present in manufacturing process which impact product quality differently.  As those variations are not  tangible and visible in the process therefore how do we detect those variations. 

In a low volume manufacturing environment we can use preset rules by count of reject per shift or per lot to determine if there could be possibility of special cause exist.  Under  common cause influence,  we would need to know usual reject count per lot or per shift. 

Let’s say we have lot size 100 pcs and usually there is only 2-3 rejects per lot when there is common cause variation.  Certain reject symptom would not happen at all  and other not critical reject symptom would only 1 or 2 pcs.  From the information,  we already know the reject behavior of common cause process.  Then we set rules for triggering for possibility of special cause existence per guidance table below.

Per shift

Common cause process behaviour

Special cause process behaviour

Reject count	1-   4	>4
Reject count for critical defect	0	>1
Reject count for major defect	1	>2

Per table above we set rules for triggering for possibility of special cause

1.   If reject count is more than 4 parts,

2.   If reject count for critical reject is 1 or more (example wrong component in PCBA SMT process)

3.   If reject count for major defect is 2 or more (such as missing component on PCBA)

We can also use preset reject rules in high volume manufacturing process if  all finished parts is measured or tested or inspected 100%.

Some quality characteristics are time consuming to measure or it is not possible to measure 100% as some measurement process is a destructive process. 

Therefore in 1920s Walter  Shewart (1891-1967)  founded the concept of statistical process control (SPC) chart where we can detect  process is normal under common cause variations or change through small sampling to understand production trend .  Process changes is usually associated to presence of special cause.

In a paper cutting factory we need to  collect sample data of finished product paper length  as this is critical to quality feature per customer definition.

We can plot the paper length data collected to become a run chart over time with sample size of 1 piece per hour .  This chart will only give us some idea if we are meeting the customer requirement per below.  We can further enhance the run chart to become a control chart using SPC method.

Figure a.  Run chart  of paper length  versus time of  production

Control chart is actually a run chart over time with 3 horizontal lines, upper control limit,  data average center line and lower control limit. 

Figure b.  Control chart structure

To plot a control chart we only need a small sample size measurement data over time and plot the data to study their trend with reference to center line (CL), lower control limit (LCL) and upper control limit (UCL)  to know if there  is process operating under common cause or special cause. 

Let’s explore a bit of theory behind the control chart and its control limit.

Most of measurement data would form a continuous normal distribution if we plot at least 30 data collected (Figure b).  In a normal distribution, two important parameter which characterize the normal distribution  process average,µ  and process variation/spread, s which means  how is far is the spread from process average. 

 

Figure c.  30 data collected and plot into histogram will form a normal distribution

The upper and lower control limit in control chart represent process spread and Dr Shewart had chosen +/- 3 sigma spread from process average to generate control limit.  Computation of  process average from sample data collected over time and control limit are widely available in the web and most text books about  SPC.

Figure d.  +/- 3 sigma spread from process average use to generate upper and lower control limit

A process is said to be in control if operating under common cause variation when

a.   all of the plotted points on the process control charts are between the upper and lower control limits

b.   forms a random pattern

For paper cutting example,  we have plotted the 3 horizontal lines,  LCL,  CL and UCL (figure).  Now we can study the plotted trend better with presence LCL, CL and UCL as a reference. 

The trend of the plotted points in Figure e shows  the paper cutting process is operating under common cause variation where .

• All of the plotted points on the process control charts are between the upper and lower control limits
• Forms a random pattern

Figure e :  Control chart for cut paper length operating under common cause variation (in control)

If there is sudden change in process then the control chart will show a different pattern or out of control signal. Figure e show that one point at 23:00 above the upper control limit (UCL), this means that there could be presence of special cause variation.

Figure f.  One point above control limit, out of control situation.  There could be presence of  special cause

The illustration above  only show one of the several out of control trends which show that there could be special cause exist by reviewing the control chart.  

There a few pattern is which judge a presence of special cause or process change per below.

Rule	Interpretation	Chart pattern
1 point beyond the upper or lower control limits	Indicates a shift in the mean or an increase in the variation of the process
9 in a row on one side of the center line	Detects a stable run with a different process mean
6 in a row increasing or decreasing	Indicates a shift in the mean or an increase in the variation of the process
14 points in a row alternating up and down	Indicates systematic effects such as two alternating machines, shifts, vendors, operators, etc..
2 out of 3 points in a row in Zone A or beyond	Detects a shift in the process average or increase in the variation
4 out of 5 points in Zone B or beyond	Detects a shift in the process mean

The two methodologies that are commonly used to detect any process changes associated to presence of special cause are :-

Preset rules for reject count  can use in both high and low volume production for 100% inspection of parts

Statistical process control chart (SPC) use in high volume production for sampling of parts to study trend and understand all parts trend.

There could be other methods available some would more involve automatic triggering which could use preset rules or SPC principles. 

It is very important we have a clear criteria to define process is "normal" and any deviation form norm could be due to presence of special cause.  Once we are able to detect common and special cause variation,  then we can address both type of variations using different approaches.  We shall discussed more in the future.