# Statistical Quality Control-Control Charts (ISS (Statistical Services) Statistics Paper IV): Questions 17 - 20 of 31

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## Question number: 17

» 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 we have,

**Control limits **

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## Question number: 18

» 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 | 410 | 1600 | 400 | 20 |

370 | 420 | 460 | 410 | 1660 | 415 | 90 |

390 | 400 | 390 | 400 | 1580 | 395 | 10 |

Total | 2515 | 400 |

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## Question number: 19

» Statistical Quality Control » Control Charts » Attributes

### Describe in Detail

The following are the figures of defectives in 22 lots each containing 2,000 bulbs. Ind control limit for p-Chart.

425 | 430 | 216 | 341 | 225 | 322 | 280 | 306 | 337 | 305 | 356 |

402 | 216 | 264 | 126 | 409 | 193 | 326 | 280 | 389 | 451 | 420 |

### Explanation

**We have n = 2000**

S. No. | d | |

1 | 425 | 0.2125 |

2 | 430 | 0.215 |

3 | 216 | 0.108 |

4 | 341 | 0.1705 |

5 | 225 | 0.1125 |

6 | 322 | 0.161 |

7 | 280 | 0.14 |

8 | 306 | 0.153 |

9 | 337 | 0.1685 |

10 | 305 | 0.1525 |

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## Question number: 20

» Statistical Quality Control » Control Charts » Attributes

### Describe in Detail

Each day a sample of 1500 items from a production process was examined. The number of defectives found in each sample was as follows. With a suitable control chart, check out for control 4,6, 6,2, 15,4, 4

### Explanation

We have n = 30

S. No. | d | |

1 | 4 | 0.00267 |

2 | 6 | 0.00400 |

3 | 6 | 0.00400 |

4 | 2 | 0.00133 |

5 | 15 | 0.01000 |

6 | 4 | 0.00267 |

7 | 4 | 0.00267 |

Total | 41 | 0.02733 |

**Cont**

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