STATISTICAL INFERENCE

STATISTICAL CONTROL CHARTS

Summary

• Control charts are constructed by periodically collecting "rational subgroups" or special samples of a few items from production and plotting summary results, such as the sample average and sample range, for the subgroup against the time of sampling. Limits are included on the charts to indicate instability in the process.
• Purpose of Control Charts
  • To learn, in a systematic data based manner, the relationships between process variables and product quality characteristics through the examination of a large number of small (typically 3 to 9) samples on a regular basis over time.
  • To provide a timely signal of the presence of instability in a process and thus to indicate when and where to look for causes of instability so that prompt corrective action can be taken.
  • To achieve and maintain stability or statistical control.
  • To pave the way towards the assessment of process capability.
• Process capability describes the behaviour of a process when it is operating in a state of statistical control (stability).
  • the ability of a process to turn out items with the greatest possible consistency.
  • the best distribution of that can be expected of the process.
  Stability does not mean that the process is producing only good products.
• The inherent variation present in a stable process is called common cause variation.
  • common cause variation accounts for about 85% of process problems. Statistical techniques can indicate the magnitude of common cause variation.
  • a reduction in common cause variation requires a change of the process itself (not an adjustment to the process) and is normally the responsibility of management.
  • the adjustment of a stable process leads to overcontrol and thus inflates variability.
• The causes of instability in a process are called special or assignable causes.
  • they account for about 15% of process problems.
  • statistical techniques indicate when they are present.
  • they can often be removed by local action.
• Control charts are designed to balance economically the risks of:
  • Overcontrol- taking action when the process is stable and no action is necessary, thus inflating the variation in a process and
  • Undercontrol- failing to take action when special causes are present and action should be taken to identify and eliminate them.
• Two types of action should be taken:
  • action on the process to identify and remove special causes.
  • action on product to determine if it is out of specifications.
• It is much easier to find special causes "on-the-spot" than to try to reconstruct circumstances later.
• Measurement of the product quality characteristics should be made as close to the potential source of problems as possible. Do not wait until the product is completely fabricated or assembled.
• Remember that control limits reflect the natural tolerance of the process and have nothing to do with specifications. Thus
  • a stable process may be producing items that are consistently out of specifications.
  • an out of control process may not be producing any items that are out of specifications.