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# Evaluate 5.2 Problem 5

Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inches) from the last six samples are in the attached file.

Assume that only these six samples are sufficient, and use the data to determine control limits for an R and an X chart.

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# Sheet1

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | x | x | 3 | 4 | total xxxxxxxx | Av, xxxxxxxx | xxxxx |

x | 0.59399999999999997 | 0.622 | 0.59799999999999998 | xxxx | xxxxxxxxxxxxxxxxxx | 0.601 | xxxxxxxxxxxxxxxxxxxxx |

2 | 0.58699999999999997 | 0.61099999999999999 | 0.59699999999999998 | 0.61299999999999999 | xxxxxxxxxxxxxxxxxx | 0.602 | xxxxxxxxxxxxxxxxxxxxx |

x | xxxxxxxxxxxxxxxxxxx | xxxxxxxxxxxxxxxxxxx | 0.59499999999999997 | 0.60199999999999998 | xxxxxxxxxxxxxxxxxx | 0.587 | 3.1000000000000028E-2 |

4 | xxxx | xxxxxxxxxxxxxxxxxxx | 0.58499999999999996 | 0.57799999999999996 | 2.3879999999999999 | 0.597 | 3.7000000000000033E-2 |

x | xxxxxxxxxxxxxxxxxxx | 0.624 | xxxxxxxxxxxxxxxxxxx | xxxxxxxxxxxxxxxxxxx | xxxxxxxxxxxxxxxxxx | 0.609 | 4.4000000000000039E-2 |

x | 0.58499999999999996 | xxxxxxxxxxxxxxxxxxx | 0.60699999999999998 | 0.56899999999999995 | 2.3540000000000001 | xxxxx | 3.8000000000000034E-2 |

total | 3.584 | 0.20800000000000018 | |||||

mean of the xxxxxx mean | 0.597 | ||||||

mean xx the xxxxxx range | 0.035 | ||||||

U.C.L.= | |||||||

A2 xxx N=6 xx 0.483 | |||||||

xxxx xxxxxx xxxxx x 0.035= 0.614 | |||||||

LCL= 0.597- xxxxx X 0.035= 0.580 |

# Sheet2

# xxxxxx

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