Statistical Process Control

 

Self-use Tool

 

Sample - Continuous Data

Sample - Attribute Data

 

Let us consider a process of manufacturing a Tube of length 100 cm and two scenarios below. 

 

  • Tube is consistently made at 95 cm, without much variation in the length.
  • Tube is made on an average at 100 cm, however ranging between 110 cm to 90 cm. 

 

In the first case, although the process is highly predictable (always delivers at 95 cm), it lacks accuracy. In the next case, although it meets the target of 100 cm several times (is accurate), it lacks precision as shown by very high variance. Accuracy is impacted by the Output Mean, and Precision is impacted by Output Variance. And we certainly do not want any of these in our processes. The first case could be result of a wrong setting in machine and second case could be due to lack of standard training to workers. Hence we would strive to control our process by making it more Accurate as well Precise, by means of Standardization etc. 

 

Variation is inherent in every process, and no process output would be bang-on target every time. No matter how controlled our process is, time to resolve a customer complaint can never be always 10 hours or a tube can never be always 100 cm in length. We expect some amount of variation, which should be totally random in nature, without any pattern. This is known as Non-assignable cause variation, as we can not really attribute any cause to the random variations. 

 

If time taken to resolve customer complaints, received on Wed and Thu, is always high, then there must be a Special Cause for this pattern. Perhaps, a rookie Customer Service personnel works on these two days and he or she takes more time than an experienced personnel. 

 

The length of Tubes cut from a particular machine is always off-target, then there must be a Special Cause for this pattern. The machine may have a calibration problem, and it always cut 2 cm less than the prescribed length. 

 

Statistical Process Control (SPC) refers to identifying these Special Cause Variations, performing a Root-cause-analysis, and controlling or mitigating these Special Causes. SPC is the cornerstone of Six Sigma Framework, one of the most widely used Total Quality Management tool.

 

We would be concerned about the following. 

  • Inability to meet the Target (Output Mean different than Target)
  • Too much of variation (Output Variance more than a specified tolerance)
  • Presence of a definite trend, indicating a Special Cause variation. 

 

Our process deliverable could be a numeric value (Length, Diameter, No. of days etc.) or it could be Pass/Fail or Defective/Non-defective kind of scenario. Accordingly we deal with Continuous Data or Attribute Data respectively for these 2 cases. 

 

To be precise, there are 8 tests which are used to detect Assignable (Special) Cause Variation. These tests are shown in the picture below.

8 tests to detect out-of-control process

  • 1 point beyond Upper or Lower Control Limits
  • 7 consecutive points on the same side of Centerline
  • 6 consecutive points all either increasing or decreasing
  • 14 consecutive points alternating up and down
  • 2 out 3 points > 2 Std. Dev. From Centerline on the same side
  • 4 out 5 points > 1 Std. Dev. From Centerline on the same side
  • 15 consecutive points with +/1 1 Std. Dev. From centerline on either side
  • 8 consecutive points >1 Std. Dev. From centerline on either side