# ISS (Statistical Services) Statistics Paper IV: Questions 15 - 17 of 92

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## Question number: 15

» Statistical Quality Control » Acceptance Sampling by Attributes

### Describe in Detail

a) What is the small percentage of defects that consumers are willing to accept?

b) What is upper limit of the percentage of defective items consumers are willing to tolerate?

c) What is probability that a lot will be accepted that contains a greater number of defects than the LTPD limit known as?

### Explanation

a) The small percentage of defects that consumers are willing to accept is known as Acceptance Quality level (AQL).

If is a lot with relatively small fraction defective, that we do not wish to reject then

P (rejecting a lot of quality ) = 0.05 Or P (Accepting a lot of quality ) = 0.95

Consumers are willing to accept this small percentag

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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 mean of 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 cars p

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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

From the tables, for n = 10, we have ,

**Control limits for R chart:**

= (0.223) (0.115) =0.0256

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