Question

Question:

The time to make beds at a motel should fall into an agreed-on range of times. A sample of four maids was selected, and the time needed to make a bed was observed on three different occasions:

Maid | Sample 1 (sec) | Sample 2 (sec) | Sample 3 (sec) |
---|---|---|---|

Ann | 120 | 90 | 150 |

Linda | 130 | 110 | 140 |

Marie | 200 | 180 | 175 |

Michael | 165 | 155 | 140 |

a. Determine the upper and lower control limits for an X-bar chart and R-chart with a sample size of four.

b. After the control chart was established a sample of four observations has the following times in seconds: 180, 198, 193, and 218. Is corrective action needed?

Answer #1

Given

Sample size =4

Maid | Sample1(Sec) | Sample2(sec) | Sample3(Sec) | Mean=sum of 3 samples/3 | Range=(Max-Min) |

Ann | 120 | 90 | 150 | 120.00 | 60 |

Linda | 130 | 110 | 140 | 126.67 | 30 |

Marie | 200 | 180 | 175 | 185.00 | 25 |

Michael | 165 | 155 | 140 | 153.33 | 25 |

585.00 | 140.00 | ||||

Xbar = Sum of means/4= | 146.25 | ||||

Rbar= Sum of Ranges/4 = | 35 |

Xbar = 146.25

Rbar=35

A2 = 0.729 , D3 =0 ,D4=2.282 ( For sample size 4)

(a)

**For X-bar
chart**

UCL = Xbar + A2* Rbar = 146.25+0.729*35 =146.25 + 25.51 =171.76

LCL = Xbar - A2* Rbar = 146.25 - 0.729*35 =146.25 - 25.51 =120.74

**For R-bar
chart**

UCL=D4*Rbar =2.282*35 =79.87

LCL =D3*Rbar = 0*35 =0

(b)

Observations are 180,198,193, 218.

All the readings are above the upper control limit , hence corrective action is needed.

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