# ISS (Statistical Services) Statistics Paper IV: Questions 6 - 8 of 92

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## Question number: 6

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Which control charts are used for continuous data? What is the chart we use to test the quality characteristics of a product such as diameter of a screw known as?

### Explanation

Variable data are measured on a continuous scale. Control chart for variables are applied to data with continuous distribution. And and R charts are two types of variable charts. Continuous data can take infinite number of values between whole numbers. For example: Age, time, weight, distance or temperature can be measured in fractions or

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## Question number: 7

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

1) When the characteristic representing the quality of a product is a discrete variable which chart can be used? Find 3- σ control limits on the chart.

2) Construct 3- σ control limits for and R charts for the following data, based on fuses, samples of 5 being taken every hour.

Sample No. | Observations | |||||

1 | 42 | 65 | 75 | 78 | 87 | 87 |

2 | 42 | 45 | 68 | 72 | 90 | 90 |

3 | 19 | 24 | 80 | 81 | 81 | 81 |

4 | 36 | 54 | 69 | 77 | 84 | 84 |

5 | 42 | 51 | 57 | 59 | 78 | 78 |

6 | 51 | 74 | 75 | 78 | 132 | 132 |

7 | 60 | 60 | 72 | 95 | 138 | 138 |

8 | 18 | 20 | 27 | 42 | 60 | 60 |

9 | 15 | 30 | 39 | 62 | 84 | 84 |

10 | 69 | 109 | 113 | 118 | 153 | 153 |

11 | 64 | 90 | 93 | 109 | 112 | 112 |

12 | 61 | 78 | 94 | 109 | 136 | 136 |

### Explanation

Discrete data is a data that can be counted and cannot have fractions or decimals. Control charts for attributes are used to measure quality characteristics that are counted rather than measured e. g. Number of broken eggs in a box, number of defective rivets in an aircraft wing.

3- σ control limits on the chart are given by .

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## Question number: 8

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Following is the data of 25 samples with 4 observations on the basis of volume of the bottles filled. Obtain the control limits for .

Sample No. | Observations | Sample No. | Observations | |||||||

1 | 15.85 | 16.02 | 15.83 | 15.93 | 13 | 15.85 | 15.76 | 15.74 | 15.98 | |

2 | 16.12 | 16.00 | 15.85 | 16.01 | 14 | 15.73 | 15.84 | 15.96 | 16.10 | |

3 | 16.00 | 15.91 | 15.94 | 15.83 | 15 | 16.20 | 16.01 | 16.10 | 15.89 | |

4 | 16.20 | 15.85 | 15.74 | 15.93 | 16 | 16.12 | 16.08 | 15.83 | 15.94 | |

5 | 15.74 | 15.86 | 16.21 | 16.10 | 17 | 16.01 | 15.93 | 15.81 | 15.68 | |

6 | 15.94 | 16.01 | 16.14 | 16.03 | 18 | 15.78 | 16.04 | 16.11 | 16.12 | |

7 | 15.75 | 16.21 | 16.01 | 15.86 | 19 | 15.84 | 15.92 | 16.05 | 16.12 | |

8 | 15.82 | 15.94 | 16.02 | 15.94 | 20 | 15.92 | 16.09 | 16.12 | 15.93 | |

9 | 16.04 | 15.98 | 15.83 | 15.98 | 21 | 16.11 | 16.02 | 16.00 | 15.88 | |

10 | 15.64 | 15.86 | 15.94 | 15.89 | 22 | 15.98 | 15.82 | 15.89 | 15.89 | |

11 | 16.11 | 16.00 | 16.01 | 15.82 | 23 | 16.05 | 15.73 | 15.73 | 15.93 | |

12 | 15.72 | 15.85 | 16.12 | 16.15 | 24 | 16.01 | 16.01 | 15.89 | 15.86 | |

25 | 16.08 | 15.78 | 15.92 | 15.98 |

### Explanation

**Control limits for R- chart:**

=0

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