The quality engineer in charge of a salt packaging process is concerned about the moisture content in packages of salt. The primary concern is that variation in the ambient humidity in the plant may be causing variation in the mean moisture content in the packages over time. It is decided that packages in each sample will be produced as close to each other in time as possible. In this way, the ambient humidity will be nearly the same for each package in the sample so that the within-group variation will not be affected by this special cause. Five packages of salt are sampled every 15 minutes for 5 hours and the moisture content in each package is measured as a percentage of total weight. The data is found below. Sample Sample Values
1 2.53 2.66 1.88 2.21 2.26
2 2.69 2.38 2.34 2.47 2.61
3 2.67 2.23 2.10 2.43 2.54
4 2.10 2.26 2.51 2.58 2.28
5 2.64 2.42 2.56 2.51 2.36
6 2.64 1.63 2.95 2.12 2.67
7 2.58 2.69 3.01 3.01 2.23
8 2.31 2.39 2.60 2.40 2.46
9 3.03 2.68 2.27 2.54 2.63
10 2.86 3.22 2.72 3.09 2.48
11 2.71 2.80 3.09 2.60 3.39
12 2.95 3.54 2.59 3.31 2.87
13 3.14 2.84 3.77 2.27 3.22
14 2.85 3.29 3.25 3.35 3.59
15 2.82 3.71 3.36 2.95 3.37
16 3.17 3.07 3.14 3.63 3.70
17 2.81 3.21 2.95 3.04 2.85
18 2.99 2.65 2.79 2.80 2.95
19 3.11 2.74 2.59 3.01 3.03
20 2.83 2.74 3.03 2.68 2.49
The quality engineer is trying to establish the control limits for an X bar and R chart. Using the data, compute the centerline and control limits for an R chart. Plot the points. Is the process in statistical control?
If the chart is out-of-control, assume that the assignable cause is found and corrected. Eliminate the out-of-control point(s), recompute the limits and redraw the R chart. Does the process appear to be in control now? If the chart is in control, skip to part (c).
Compute the centerline and limits for and draw the X bar chart (Note: do not include any eliminated points from part (b)). Does the process mean appear to be in control?
Outline the remaining steps in this process to establish the control limits (do not carry them out).
Assume the process is in control with the following values: For the X bar chart, the centerline = 2.704 with UCL=3.060 and LCL=2.348. For the R chart, the centerline = 0.6164 with UCL = 1.33 and LCL = 0. Estimate the mean and standard deviation for this process.
If the specifications for moisture content are [1.80, 3.70], estimate the fraction nonconforming packages of salt (in ppm).
Estimate Cp and Cpk. Comment on their results.