## Selecting a Control Chart:

Data Type | Measurement Type | Subgroup Size | Control Chart |
---|---|---|---|

Variable | Individual | 1 | Individual & MR (Moving Range) |

Variable | Continuous | 2-9 (small) | X-bar & R |

Variable | Continuous | 10+ (large) | X-bar & S |

Attribute | Defective | Constant | p Chart |

Attribute | Defective | Variable | np Chart |

Attribute | Defect | Constant | c Chart |

Attribute | Defect | Variable | u Chart |

## Control Chart Limits (UCL, LCL and Mean)

Control Chart | Center Line | Upper Control Limit (UCL) | Lower Control Limit (LCL) |
---|---|---|---|

X-bar Chart | $$\bar{X}$$ | $$\bar{X} + A_2 \bar{R}$$ | $$\bar{X} - A_2 \bar{R}$$ |

R Chart | $$\bar{R}$$ | $$D_4 \bar{R}$$ | $$D_3 \bar{R}$$ |

S Chart | $$\bar{S}$$ | $$B_4 \bar{S}$$ | $$B_3 \bar{S}$$ |

p Chart | $$\bar{p}$$ | $$\bar{p} + 3\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$ | $$\bar{p} - 3\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$ |

np Chart | $$n\bar{p}$$ | $$n\bar{p} + 3\sqrt{n\bar{p}(1-\bar{p})}$$ | $$n\bar{p} - 3\sqrt{n\bar{p}(1-\bar{p})}$$ |

c Chart | $$\bar{c}$$ | $$\bar{c} + 3\sqrt{\bar{c}}$$ | $$\bar{c} - 3\sqrt{\bar{c}}$$ |

u Chart | $$\bar{u}$$ | $$\bar{u} + 3\sqrt{\frac{\bar{u}}{n}}$$ | $$\bar{u} - 3\sqrt{\frac{\bar{u}}{n}}$$ |

## Table of Control Chart Constants:

Sample Size (n) | D3 | D4 | B3 | B4 | d2 | A2 |
---|---|---|---|---|---|---|

2 | 0 | 3.267 | 0 | 2.606 | 1.128 | 1.880 |

3 | 0 | 2.574 | 0 | 1.880 | 1.693 | 1.023 |

4 | 0 | 2.282 | 0.030 | 1.604 | 2.059 | 0.729 |

5 | 0 | 2.114 | 0.118 | 1.427 | 2.326 | 0.577 |

6 | 0.030 | 2.004 | 0.185 | 1.287 | 2.534 | 0.483 |

7 | 0.118 | 1.924 | 0.235 | 1.182 | 2.704 | 0.419 |

8 | 0.185 | 1.864 | 0.270 | 1.099 | 2.847 | 0.373 |

9 | 0.235 | 1.816 | 0.296 | 1.032 | 2.970 | 0.337 |

10 | 0.270 | 1.777 | 0.315 | 0.975 | 3.078 | 0.308 |

11 | 0.296 | 1.744 | 0.330 | 0.927 | 3.173 | 0.285 |

12 | 0.315 | 1.717 | 0.342 | 0.886 | 3.258 | 0.266 |

13 | 0.330 | 1.693 | 0.352 | 0.850 | 3.336 | 0.249 |

14 | 0.342 | 1.672 | 0.361 | 0.817 | 3.407 | 0.235 |

15 | 0.352 | 1.653 | 0.369 | 0.789 | 3.472 | 0.223 |

25 | 0.435 | 1.541 | 0.447 | 0.668 | 4.459 | 0.153 |

50 | 0.576 | 1.427 | 0.550 | 0.560 | 6.864 | 0.114 |

100 | 0.704 | 1.341 | 0.620 | 0.481 | 10.577 | 0.080 |