Answer

B. Control Charts: X (bar) Chart

Construct an X (bar) chart and determine if the process is in control.

Given:

Sample size n=5

Number of Samples (m) =10

a. Determine the sample average for the 10 periods

Sample # | Hour | Observation | Observation | Observation | Observation | Observation | Average |

m | | 1 | 2 | 3 | 4 | 5 | Row |

1 | 8am | 45 | 60 | 55 | 49 | 63 | 54.4 |

2 | 9 | 31 | 37 | 44 | 37 | 51 | 40 |

3 | 10 | 43 | 47 | 56 | 41 | 43 | 46 |

4 | 11 | 37 | 61 | 31 | 28 | 47 | 40.8 |

5 | 12 | 65 | 52 | 28 | 27 | 37 | 41.8 |

6 | 1pm | 29 | 20 | 27 | 34 | 31 | 28.2 |

7 | 2 | 15 | 36 | 52 | 38 | 27 | 33.6 |

8 | 3 | 62 | 40 | 45 | 39 | 29 | 43 |

9 | 4 | 55 | 29 | 36 | 27 | 31 | 35.6 |

10 | 5 | 42 | 37 | 39 | 19 | 40 | 35.4 |

The table above shows the waiting time (in seconds) for a random sample of 5 customers calling a telephone service center during each hour. The sample data were collected for 10 hours.

b. Determine the mean of sample averages X (bar-bar)

X (bar-bar) = mean1+mean2+mean3…+mean1010

Sample # | Hour | Observation | Observation | Observation | Observation | Observation | Average |

m | | 1 | 2 | 3 | 4 | 5 | Row |

1 | 8am | 45 | 60 | 55 | 49 | 63 | 54.4 |

2 | 9 | 31 | 37 | 44 | 37 | 51 | 40 |

3 | 10 | 43 | 47 | 56 | 41 | 43 | 46 |

4 | 11 | 37 | 61 | 31 | 28 | 47 | 40.8 |

5 | 12 | 65 | 52 | 28 | 27 | 37 | 41.8 |

6 | 1pm | 29 | 20 | 27 | 34 | 31 | 28.2 |

7 | 2 | 15 | 36 | 52 | 38 | 27 | 33.6 |

8 | 3 | 62 | 40 | 45 | 39 | 29 | 43 |

9 | 4 | 55 | 29 | 36 | 27 | 31 | 35.6 |

10 | 5 | 42 | 37 | 39 | 19 | 40 | 35.4 |

Total | | | | | | | 39.9 |

X (bar-bar) = 39.9

c. Calculate the standard deviation σ = Σ ( x-39.9)2n*m-1

Hour | Observation | Observation | Observation | Observation | Observation | Total |

| 1 | 2 | 3 | 4 | 5 | |

8am | 26.0100 | 404.0100 | 228.0100 | 82.8100 | 533.6100 | 1274.4500 |

9 | 79.2100 | 8.4100 | 16.8100 | 8.4100 | 123.2100 | 236.0500 |

10 |...