# 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

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | Defects | xxxx bar | xxxxx xxxxxx | xxxxx | Defects | xxxx bar | (xi-x xxxxxx |

x | x | 2 | x | x | 8 | 1.3600000000000003 | 1.85 |

x | x | xx | xx | x | 0 | xxxxx | 44.09 |

x | x | x | x | x | 7 | 0.36000000000000032 | xxxx |

4 | 12 | x | 36 | x | xx | xxxx | 28.73 |

5 | xx | 1 | x | -1.6399999999999997 | xxxx | ||

6 | 10 | 4 | xx | x | 10 | 3.3600000000000003 | 11.29 |

x | 2 | xx | 16 | x | x | xxxxxxxxxxxxxxxxxxx | 21.53 |

8 | 4 | xx | 4 | x | 4 | xxxxxxxxxxxxxxxxxxx | 6.97 |

9 | 6 | x | x | 9 | 6 | -0.63999999999999968 | xxxx |

xx | x | 0 | x | xx | x | xxxxxxxxxxxxxxxxxxxx | xxxx |

60 | xxx | xx | xx | xxxx | 40.45 | ||

xx | xxxxxx | ||||||

xxxxx 60/10 x 6 | mean= 73/11= xxxx | ||||||

sd= xx xx xxxxxx 3.56 | sd= sq rt 158.55/10=3.98 | ||||||

3 -sigma limits xxx means xx xxxxxx xx xxx | 3 xxxxxx limits xxx xxxxx of sample of xxx | ||||||

UCL x mean x xxxxxxxxxxx | 6 x 3(3.56/3.16) x | xxxx x defects | xxx = xxxx x 3(SD/Sqrtn) | xxxx xxxxxxxxxxxxxx 6.64 + 3.6 x | 10 xxxxxxx | ||

central line = mean | 6 | central xxxx = mean | xxxxx 7 defects | ||||

LCL=mean -3(SD/Sqrtn) | xxx =3 xxxxxxx | xxxxxxxx -3(SD/Sqrtn) | 6.64-3.6= | x xxxxxxx |

# xxxxxx

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