Question

The copper content of a plating bath is measured three times per day, and the results are reported in ppm. The and r values for 25 days are shown in the following table

Using all the data, find trial control limits for and R charts, construct the chart, and plot the data. Is the process in statistical control?

Day ?? r Day ?? r
1 5.45 1.21 14 7.01 1.45
2 5.39 0.95 15 5.83 1.37
3 6.85 1.43 16 6.35 1.04
4 6.74 1.29 17 6.05 0.83
5 5.83 1.35 18 7.11 1.35
6 7.22 0.88 19 7.32 1.09
7 6.39 0.92 20 5.9 1.22
8 6.5 1.13 21 5.5 0.98
9 7.15 1.25 22 6.32 1.21
10 5.92 1.05 23 6.55 0.76
11 6.45 0.98 24 5.9 1.2
12 5.38 1.36 25 5.95 1.19
13 6.03 0.83

Answer 1

The question pertains to creating α and R control charts for monitoring the copper content in a plating bath, calculating trial control limits using provided formulas, and analyzing the process stability.

Step-by-step explanation:

The question involves using statistical process control (SPC) techniques to analyze a data set of copper content measurements in a plating bath over 25 days. The data provided includes the average copper content (α, pronounced as 'x-bar') per day and the range (r) for three measurements each day. The goal is to calculate the trial control limits for the x-bar and R charts, plot the data on these charts, and determine if the process is in statistical control.

To find the trial control limits, we will use the following formulas:

• The average of the averages (α-bar): Sum of all α's divided by the number of days.
• The average range (R-bar): Sum of all r values divided by the number of days.
• Upper Control Limit (UCL) for α: α-bar + (A2 * R-bar).
• Lower Control Limit (LCL) for α: α-bar - (A2 * R-bar), where A2 is a constant that depends on the sample size.
• Upper Control Limit (UCL) for R: D4 * R-bar.
• Lower Control Limit (LCL) for R: D3 * R-bar, where D3 and D4 are constants based on the sample size.

After computing these values, we would plot the daily α and r values on their respective control charts. Each day's data should fall between its UCL and LCL. If any point lies outside these limits, or if there is a systematic pattern within the limits, the process may not be in statistical control. An in-control process would show a random pattern of points within the control limits.

Regarding the data provided, an analysis is required involving calculations based on the data table. However, as the A2, D3, and D4 constants are not provided and depend on group size (in this case, sample size of three per day), they would need to be obtained from an SPC control chart constants table before proceeding with the analysis.