# Evaluate 5.2 Problem 11

Jim Outfitters, Inc. makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results which are in the attached table.

a. Assuming that 10 observations are adequate for these purposes, determine the three sigma control limits for defects per shirt.

b. Suppose that the next shirt has 13 flaws. What can you say about the process now?

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# xxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxShirt | Defects | xxxx xxx | (xi-x bar)^2 | Shirt | Defects | xi-x bar | xxxxx bar)^2 |

1 | 8 | x | x | 1 | 8 | 1.3600000000000003 | xxxx |

x | x | -6 | xx | 2 | x | xxxxx | xxxxx |

3 | x | 1 | 1 | x | x | xxxxxxxxxxxxxxxxxxx | 0.13 |

4 | xx | 6 | 36 | 4 | xx | 5.36 | xxxxx |

5 | xx | x | 5 | -1.6399999999999997 | xxxx | ||

x | xx | x | 16 | x | 10 | 3.3600000000000003 | xxxxx |

x | x | xx | xx | x | 2 | -4.6399999999999997 | xxxxx |

8 | 4 | xx | x | x | x | xxxxxxxxxxxxxxxxxxx | xxxx |

x | 6 | x | x | 9 | 6 | xxxxxxxxxxxxxxxxxxxx | xxxx |

10 | 6 | x | x | 10 | x | xxxxxxxxxxxxxxxxxxxx | 0.41 |

60 | 114 | 11 | 13 | 6.36 | 40.45 | ||

73 | xxxxxx | ||||||

xxxxx xxxxx x 6 | mean= 73/11= 6.64 | ||||||

xxx sq rt 114/9= xxxx | sd= sq xx 158.55/10=3.98 | ||||||

x xxxxxx xxxxxx xxx xxxxx of xxxxxx xx xxx | x xxxxxx limits for means xx sample of xxx | ||||||

xxx = mean x xxxxxxxxxxx | 6 + xxxxxxxxxxxx x | xxxx x xxxxxxx | UCL x mean + xxxxxxxxxxx | xxxx +3(3.98/3.32)= xxxx x xxx = | xx defects | ||

xxxxxxx line = xxxx | 6 | xxxxxxx line = mean | xxxxx x xxxxxxx | ||||

xxxxxxxx xxxxxxxxxxxx | 6-3 =3 xxxxxxx | xxxxxxxx xxxxxxxxxxxx | 6.64-3.6= | x defects |

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