7QC Tools: Basis of Western Electric Rules of Control Charts

    Amrendra Roy

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    We all are aware of these famous rule, for beginners let’s understand the basis of these rule. All rules are applied to one half of the control chart. The probability of getting a reaction to the test is ~0.01.



    1. A single point outside 3σ control limits or beyond zone A.
      • Probability of finding a point in this region = 0.00135 if caused by the normal process. Anything in this region is a case of assignable cause.
    2. Two out of three consecutive points in zone A (beyond 2σ).
      • Probability of getting 2 consecutive points in zone A = 0.0227*0.0227 = 0.00052
      • Probability of 2 out of 3 points in zone A = 0.0227*0.0227*0.9773*3 = 0.0015
    3. Four out of 5 consecutive points in zone B (beyond 1σ)
      • Probability of getting one points in zone B = 0.1587
      • Probability of 4 points in zone B and 1 point in other part of the control chart = 0.1587*0.1587*0.1587*0.1587*0.8413*5 = 0.0027
    4. Eight consecutive points on one side of the central line.
      • Probability of getting one points in beyond central line = 0.5
      • Probability of 8 points in in succession on one side of the central line = 8*0.5 = 0.0039

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