# Statistical Quality Control (ISS (Statistical Services) Statistics Paper IV): Questions 18 - 20 of 34

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## Question number: 18

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

A machine is manufacturing mica discs. Samples of size 5 are drawn every hour and their thickness in units are recorded as follows. On the basis of chart, Check whether the production is under control?

Sample No. | Observations | ||||

1 | 8 | 9 | 15 | 4 | 11 |

2 | 7 | 10 | 7 | 6 | 8 |

3 | 11 | 12 | 10 | 9 | 10 |

4 | 12 | 8 | 6 | 9 | 12 |

5 | 11 | 10 | 6 | 14 | 11 |

6 | 7 | 7 | 10 | 4 | 11 |

7 | 10 | 7 | 4 | 10 | 10 |

8 | 8 | 11 | 11 | 7 | 7 |

9 | 8 | 11 | 8 | 14 | 12 |

10 | 12 | 9 | 12 | 17 | 11 |

11 | 7 | 7 | 9 | 17 | 13 |

12 | 9 | 9 | 4 | 4 | 11 |

13 | 10 | 12 | 12 | 12 | 12 |

14 | 8 | 11 | 9 | 6 | 8 |

15 | 10 | 13 | 9 | 4 | 9 |

16 | 9 | 11 | 8 | 5 | 11 |

### Explanation

Sample No. | Observations | Total | Sample Mean | Sample Range | ||||

1 | 8 | 9 | 15 | 4 | 11 | 47 | 9.4 | 11 |

2 | 7 | 10 | 7 | 6 | 8 | 38 | 7.6 | 4 |

3 | 11 |

## Question number: 19

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

a) If the average range for the 4 samples is 0.2 millimeters and the average mean of the observations is 12.5 millimeters, obtain the three-sigma control limits for the sample mean.

b) 5 observations have been taken from the10 samples in order to test the volume in the bags. The average sample range is 0.5 ounces. Obtain the 3-σ limits for the sample range.

### Explanation

a) It is given that n = 5 and

For n = 5, The value of

Control limits for :

And

b) We are given that, number of observations, n = 5,

For n = 5, from the tables

## Question number: 20

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

A new oven has been installed in a bakery and to test the efficiency of this, the oven temperature readings have been taken at four different places inside the oven every 30 min. The following table gives readings. Determine the control limits for the mean temperature.

Time | Readings | |||

8: 00 | 400 | 500 | 550 | 390 |

8: 30 | 440 | 420 | 380 | 380 |

9: 00 | 410 | 450 | 470 | 430 |

9: 30 | 390 | 390 | 410 | 410 |

10: 00 | 370 | 420 | 460 | 410 |

10: 30 | 390 | 400 | 390 | 400 |

### Explanation

Readings | Total | Sample mean | Sample Range | |||

400 | 500 | 550 | 390 | 1840 | 460 | 160 |

440 | 420 | 380 | 380 | 1620 | 405 | 60 |

410 | 450 | 470 | 430 | 1760 | 440 | 60 |

390 | 390 | 410 |