Explore BrainMass
Share

Control Charts

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

A) A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each lot of tablets is measured in order to control the compression process. The process has been operating in control with mean at the target value = 11.5 kilograms (kg) and estimated standard deviation = 0.2 kg. The table below gives three sets of data, each representing x for 20 successive samples. One set remains in control at the target value. In a second set, the process mean shifts suddenly to a new value. In a third the process mean drifts gradually.
(1) What are the center line and control limits for an x chart for this process?
(2) Construct a separate x chart for each of the three data sets. Identify any points that are beyond the control limits.

Sample Data with N=20
Data Set A Data Set B Data Set C
1 11.602 11.627 11.495
2 11.547 11.613 11.475
3 11.312 11.493 11.465
4 11.449 11.602 11.497
5 11.401 11.360 11.573
6 11.608 11.374 11.563
7 11.471 11.592 11.321
8 11.453 11.458 11.533
9 11.446 11.552 11.486
10 11.522 11.463 11.502
11 11.664 11.383 11.534
12 11.823 11.715 11.624
13 11.629 11.485 11.629
14 11.602 11.509 11.575
15 11.756 11.429 11.730
16 11.707 11.477 11.680
17 11.612 11.570 11.729
18 11.628 11.623 11.704
19 11.603 11.472 12.052
20 11.816 11.531 11.905

© BrainMass Inc. brainmass.com October 25, 2018, 1:48 am ad1c9bdddf
https://brainmass.com/statistics/control-chart/control-charts-275163

Solution Summary

Prepares control charts and identifies control limits.

$2.19
See Also This Related BrainMass Solution

Performance: Control Chart for Process Mean

13-14
Boston-based Legal Seafoods prides itself on having instituted an advanced quality control system that includes the control of both food quality and service quality. The following are successive service times at one of the chain's restaurants on a Saturday night in May 2007 (time is stated in minutes from customer entry to appearance of waitperson)
5, 6, 5,5,5,7, 4, 12, 4, 4.5, 2, 5, 5, 5, 6, 6, 13, 2, 5, 4, 4.5, 6.5, 4, 1,
2 3, 5, 5, 4, 4, 8, 12 3, 4.5, 6.5, 6, 7, 10, 6, 6.5, 5, 3, 6.5 7,
Aggregate the data into groups of four, and construct a control chart for the process mean. Is the waiting time at the restaurant under control?

13-17
The following data are tensile strengths, in pounds, for a sample of string for industrial use made at a plant. Construct a control chart for the mean, using groups of 5 observations each. Test for statistical control of the process mean.
5, 6, 4, 6, 5, 7, 7, 7, 6, 5, 3, 5, 5, 5, 6, 5, 5, 6, 7, 7, 7, 7, 6, 7, 5,
5, 5, 6, 7, 7, 7, 7, 7, 5, 5, 6, 4 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 5, 7, 6,

13-23
Create R and s charts for problem 13-17. Is the process in control?

13-25

The capacity of the fuel tank of the 2007 Volvo S40 is designed to be 12.625 gallons. The actual capacity of tanks produced is controlled using a control chart. The data of 9 random samples of size 5 each collected on 9 different days are tabulated below. Draw X-bar, R, and s charts. Is the process in control? If it is not, remove the sample that is out of control, and redraw the charts.
1 2 3 4 5 6 7
12.667 12.600 12.599 12.607 12.738 12.557 12.646
12.598 12.711 12.583 12.524 12.605 12.745 12.647
12.685 12.653 12.515 12.718 12.640 12.626 12.651
12.700 12.703 12.653 12.615 12.653 12.694 12.607
12.722 12.579 12.599 12.554 12.507 12.574 12.589
8 9
12.710 12.529
12.627 12.725
12.605 12.306
12.648 12.551
12.545 12.600

13-29
BASF Inc. makes CDs for use in computers. A quality control engineer at the plant tests batches of 50 disks at a time and plots the proportions of defective disks on a control chart. The first 10 batches used to create the chart had the following numbers of defective disks: 8, 7, 6, 7, 8, 4, 3, 5, 5, 8. Construct the chart and interpret the results.

13-31

The following are the numbers of imperfections per yard of yarn produced in a mill in Pennsylvania in May 2007: 5, 3, 4, 8, 2, 3, 1, 2, 5, 9, 2, 2, 2, 3, 4, 2, 1. Is there evidence that the process is out of control?

13-32

The following are the numbers of blemishes in the coat of pain of new auto mobile made by Ford in June 2007: 12, 25, 13, 20, 5, 22, 8, 17, 31, 40, 9, 62, 14, 16, 9, 28. Is there evidence tat the painting process is out of control?

13-33

The following are the numbers of imperfection in rolls of wallpaper made by Laura Ashley: 5, 6, 3, 4, 5, 2, 7, 4, 5, 3, 5, 5, 3, 2, 0, 5, 5, 6, 7, 6, 9, 3, 3, 4, 2, 6. Construct a c chart for the process, and determine whether there is evidence that the process is out of control.

View Full Posting Details