# ISS (Statistical Services) Statistics Paper IV: Questions 16 - 19 of 79

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## Question number: 16

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

a) What are control charts for Attributes?

b) A quality control inspector at the Pepsi soft drink company has taken twenty-five samples with four observations each of the volume of bottles filled. If the average range for the twenty-five samples is. 29 ounces and the average meanof the observations is 15.95 ounces, obtain 3- σ control limits for ?

### Explanation

a) To measure the quality characteristics, Control charts for attributes are used, that are counted rather than measured. P-charts and C-charts are common types of control charts used to measure the attributes.

P-charts measure the proportion of items in a sample that are defective. For example, proportion of broken eggs and the proportion of car

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## Question number: 17

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Following data gives the diameter of the rings manufactured by a company. Obtain the control limits for R Chart?

Sample No. | Observations | ||||

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 |

4 | 5.03 | 4.91 | 5.01 | 4.98 | 4.89 |

5 | 4.95 | 4.92 | 5.03 | 5.05 | 5.01 |

6 | 4.97 | 5.06 | 5.06 | 4.96 | 5.03 |

7 | 5.05 | 5.01 | 5.10 | 4.96 | 4.99 |

8 | 5.09 | 5.10 | 5.00 | 4.99 | 5.08 |

9 | 5.14 | 5.10 | 4.99 | 5.08 | 5.09 |

10 | 5.01 | 4.98 | 5.08 | 5.07 | 4.99 |

### Explanation

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

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 | 0.08 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 | 0.12 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 | 0.08 |

4 | 5.03 | 4.91 | 5.01 | 4.98 | 4.89 | 0.14 |

5 | 4.95 | 4.92 | 5.03 | 5.05 | 5.01 | 0.13 |

6 | 4.97 | 5.06 | 5.06 | 4.96 | 5.03 | 0.10 |

7 | 5.05 | 5.01 | 5.10 | 4.96 | 4.99 | 0.14 |

8 | 5.09 | 5.10 | 5.00 | 4.99 | 5.08 | 0.11 |

9 | 5.14 | 5.10 | 4.99 | 5.08 | 5.09 | 0.15 |

10 | 5.01 | 4.98 | 5.08 | 5.07 | 4.99 | 0.10 |

Total | 1.15 |

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## Question number: 18

» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games

Appeared in Year: 2015

### Describe in Detail

Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.

### Explanation

First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note

Summing the m constraints of eq (1), we get

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## Question number: 19

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

What are control charts for variables? Find 3- σ control limits on the chart. If we are given that μ=15.95 σ = 0.14 and n = 4 construct control limits for ?

### Explanation

Control chart for variables are used to monitor characteristics that can be measured, e. g. length, weight, diameter, time etc. When a record is made of an actual measured quality characteristic like dimension expressed as hundredths of a millimeter, the quality is expressed by variables. For quality control of such data, two types of control char

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