Question

A manufacturing company produces cylindrical tubes for engines that are specified to be 1.20 centimeters thick. As part of the company’s statistical quality-control effort, random samples of four tubes are taken each hour. The tubes are measured to determine whether they are within thickness tolerances. Shown here are the thickness data in centimeters for nine samples of tubes. Use these data to develop an x¯ chart and an R chart.

Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9

1.22 1.20 1.21 1.16 1.24 1.19 1.24 1.17 1.22 1.19 1.20 1.18 1.17 1.20 1.21 1.17 1.23 1.17 1.20 1.22 1.17 1.20 1.21 1.21 1.18 1.22 1.16 1.23 1.20 1.20 1.16 1.18 1.20 1.19 1.16 1.19

Create an  x¯ chart.

Answer 1

1. Find mean and range of the given nine samples of tubes

Formula Reference:

Table of constants for control chart:

A2, D# and D$ values for sample 4

X-bar and R-chart:

Formula Reference:

Chart:

X-bar : The process is out of control

Range: The process is "in-control"