Question

A component used as a part of a power transmission unit is manufactured using a lathe. Twenty samples, each of five components, are taken at half-hourly intervals. Within the flow of the day a number of (non-)technical incidents appear. These include taking a lunch break, and adjusting or resetting the machine. For the most critical dimension, the process mean (xˉ) is found to be 3.500 cm, with a normal distribution of the results about the mean, and a mean sample range (Rˉ) of 0.0007 cm. With the above scenario in mind, and considering the data in the table below, complete the following tasks. Use this information to set up suitable control charts.

Answer 1

Control charts are used to monitor a process over time and detect any unusual variations or patterns that may indicate a problem with the process. X-Bar chart monitors the process mean, while the R chart monitors the process range. By plotting the sample means and ranges on these control charts, we can monitor the process and determine if any corrective action is needed.

Step-by-step explanation:

In this scenario, we are dealing with control charts. Control charts are used to monitor a process over time and detect any unusual variations or patterns that may indicate a problem with the process. Control charts are particularly useful in manufacturing processes to ensure that products are consistently produced within specified limits.

Based on the given information, we can set up two types of control charts: X-Bar chart and R chart. The X-Bar chart monitors the process mean, while the R chart monitors the process range.

To set up these control charts, we need to calculate the control limits using the formulas:

UCL = X-Bar + A2*Rˉ

LCL = X-Bar - A2*Rˉ

Where A2 is a constant depending on the sample size (in this case, 5), and Rˉ is the mean sample range (0.0007 cm).

By plotting the sample means and ranges on these control charts, we can monitor the process and determine if any corrective action is needed.