Question

Problem 10-25

Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 10.13.

To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits.

SAMPLE NUMBER | READINGS (IN OHMS) | ||||

1 | 976 | 998 | 985 | 979 | |

2 | 1018 | 993 | 974 | 1025 | |

3 | 1027 | 1021 | 990 | 1019 | |

4 | 1015 | 1028 | 1027 | 1009 | |

5 | 1002 | 1016 | 992 | 972 | |

6 | 974 | 981 | 1009 | 1006 | |

7 | 976 | 1016 | 1027 | 1027 | |

8 | 999 | 1000 | 1015 | 992 | |

9 | 1024 | 997 | 986 | 979 | |

10 | 1009 | 996 | 987 | 1028 | |

11 | 994 | 974 | 994 | 1010 | |

12 | 977 | 990 | 1024 | 990 | |

13 | 993 | 1000 | 1006 | 1018 | |

14 | 1012 | 1015 | 1015 | 1004 | |

15 | 972 | 977 | 1018 | 1020 | |

**a.** Calculate the mean and range for the above
samples. **(Round "Mean" to 2 decimal places and "Range" to
the nearest whole number.)**

Sample Number | Mean | Range |

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | ||

7 | ||

8 | ||

9 | ||

10 | ||

11 | ||

12 | ||

13 | ||

14 | ||

15 | ||

**b.** Determine X=X= and R−R−. **(Round your
answers to 3 decimal places.)**

X=X= | |

R−R− | |

**c.** Determine the UCL and LCL for a X−X−chart.
**(Round your answers to 3 decimal places.)**

UCL | |

LCL | |

**d.** Determine the UCL and LCL for
*R*-chart. **(Leave no cells blank - be certain to
enter "0" wherever required. Round your answers to 3 decimal
places.)**

UCL | |

LCL | |

**e.** What comments can you make about the
process?

The process is in statistical control. | |

The process is out of statistical control. |

Answer #1

sample mean = Sum of observations in a sample / 4

Range = Max observation of a sample - Min observation

X-X = Average of all sample means = 1001.617

R-R = Average of all range = 35.667

Please see below images for part A & B

Formula

Part C)

For Sample size N = 4 , constants for X and R charts are

A2 = 0.729

D3 = 0.00

D4 = 2.282

UCL X-X chart = X-X + A2 * R-R = 1001.617 + 0.729 * 35.667 = 1027.618

LCL X-X chart = X-X - A2 * R-R = 1001.617 - 0.729 * 35.667 = 975.616

part d)

UCL R-R Chart = D4* R-R = 2.282*35.667 = 81.392

LCL -R-R Chart = D3 * R-R = 0.00 ( 35.667 = 0

part E) Process is in statistic control as all Sample means and Range are within the UCL and LCL range for X-chart and R-chart.

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