V4 - Control Charts

• Process that is operating in the presence of assignable/systematic causes of variation => is out of control when it does not follow a random pattern

  • sources of variability that are not part of the chance causes

  • Process variability in this cases is significantly higer

• three “Ms”: method, measurement, milieu

  • 1) improperly adjusted or controlled machines (or failures)

  • 2) operator errors (manpower);

  • 3) defective raw materials.

• center line (CL)

• upper (UCL) and lower control limit (LCL)

  • typically 3 sigma

• upper (UWL) and lower warning limit (LWL)

  • tipically 2 sigma

• no

• Control charts make it possible to identify when the process is out of control (abnormal conditions)

  • This does NOT mean out of specifications.

• These conditions are not correlated:

  • A process can be out of control, but within specification limits => typically, if NT<<S.

  • A process can be in control, but out of specification limits => typically, when the process natural variability is too large

• A point that plots within the control limits represents a necessary (but not sufficient) condition for saying that the process is in control.

  • No action is necessary

  • A point that plots outside the control limits is evidence that the process is out of control

• In the presence of random/chance causes of variation only => plotted points should exhibit a random pattern

• Hp0 => the process is in control state.

• Possible outcomes are

  • (1) failing to reject Hp0

  • (2) rejecting Hp0

• If Hp0 is rejected => investigation and corrective action are required to find and eliminate assignable cause(s)

  • Out of control situations trigger investigation.

• for variables

  • quality characteristics measured on a continuous numerical scale

  • e.g. geometrical dimensions, weights

• for attributs

  • quality characteristics assuming only 2 states

  • these can be seen as binary quality characteristics

    • defective/non-defective

    • conforming/non-conforming

  
  

Several criteria can be applied simultaneously to a control chart to determine whether the process is out of control.

• when one (or more) point falls beyond the control limits

  • basic criterion

• when the plotted points exhibit some nonrandom pattern (even inside the control limits).

  • When some consecutive points increase/decrease in magnitude => run/shift/drift

  • In these cases, we have a monotonic drift/shift of the process mean

  • Supplementary criteria are often used to increase the sensitivity of the control charts to process shifts

Suggestion rules for detection nonrandom patterns in control charts

• One observation falls beyond the m ± 3∙s control rule

• Two out of three consecutive observations fall beyond the m ± 2∙s limits warning limits

• Four out of five consecutive observations fall beyond the m ± 1∙s limits

• Eight observations in a row fall on one side with respect to the m value

• Snapshot approach

  • each sample consists of units that were ideally produced at the same time (actually consecutive units of production)

  • This approach gives a “snapshot” of the process at each point in time where a sample is collected.

  • this method is used to detect (even small) changes in the process mean

  • Is perferred

• Continous approach

  • each sample consists of units that are representative of all units that have been produced since the last sample (selection is distributed in the time)

  • If the process mean drifts between several levels (during the interval between samples) the variability within the sample can be relatively large.

  • this method can be used when the control chart is employed to make decisions about the acceptance of all units produced since the last sample.

• samples (or subgroups) should be selected so that if assignable causes are present:

  • The chance for differences between samples will be maximized,

  • While the chance for differences within a sample will be minimized

• → Snapshot approach is preferred

• By moving the control limits farther from the center line, we decrease the risk of a type I error (a) => FALSE ALARMS

• But widening the control limits will also increase the risk of a type II error (b) => Not detecting a defective

  
  

It is used to monitor the central tendency of the process

It is used to monitor the dispersion of the process.

• Determine the sample size (n)

• Determine the frequency of sampling (or sampling period: h)

• Determine the width of the control limits (LCL and UCL)

• Statistical criteria

• Economic criteria