Question

The Precision Machining Company makes​ hand-held tools on an assembly line that produces one product every minute. On one of the​ products, the critical quality dimension is the diameter​ (measured in thousandths of an​ inch) of a hole bored in one of the assemblies. Management wants to detect any shift in the process average diameter from 0.015 in. Management considers the variance in the process to be in control.​ Historically, the average range has been 0.002 in., regardless of the process average. Design an X Bar chart to contol this process, with a center line at 0.015 in. and the control limits set at three sigmas from the center line.

Management provided the results of 80 minutes of output from the production line, as shown in the table below. During these 80 minutes, this process average changed once. All measurements are in thousandths of an inch.
--- Set up an x bar chart with n=4. The frequency should be sample 4 and then skip 4. Thus, your first sample would be for minutes 1-4, the second would be for minute 9-12 and so on. When would you stop the process to check for a change in the process average?

Answer 1

An X Bar chart for the Precision Machining Company would be set up with a control limit centered at 0.015 inches and the upper and lower control limits calculated to be three sigmas away from the center line, using the historical average range and a sample size of 4.

Step-by-step explanation:

Designing an X Bar Chart for the Precision Machining Company

To design an X Bar chart for controlling the process of drilling holes with a critical quality dimension of 0.015 inches in diameter, we need to calculate the control limits based on the given variance and the average range. The company considers a process range change of 0.002 inches to be acceptable. Using a sample size of 4 (n=4), we'll use the frequency of sampling every 8 minutes (sample 4, skip 4), starting with minutes 1-4.

The control limits are three standard deviations (three sigmas) from the center line. Using the historical average range, we can calculate the standard deviation for individual measurements (because we know that the range is approximately the average range times a d2 factor, which is a statistical constant based on sample size). In this case, for n=4, d2 is typically about 2.059.

To find the control limits, we multiply the standard deviation by three (for the three-sigma limits) and add and subtract this value from the center line average:

• Upper Control Limit (UCL): 0.015 + (3 x (0.002 / d2))
• Lower Control Limit (LCL): 0.015 - (3 x (0.002 / d2))

When calculating these limits, you'll determine when the process is going out of control and needs to be stopped for a check.