# Control charts:X bar and R charts

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These questions go along with the attached excel worksheets

Thirty samples of size 3 were taken from a Wilmer Machine Shop machining process over a 15 hr period. Prob 7-1 in the attached worksheet

a. compute the mean and standard deviation of the data

b. Compute the mean and range of each sample and plot them on control charts. Does the process appear to be in statistical control? Why or why not?

Electrical resistance measure values for 50 samples of size 5 were taken from Babbage Chips, Inc.'s computer making process over a 25 hr period. prob 7-2 in the attached worksheet.

a. compute the mean and standard deviation of the data

b. calculate the control limits and construct the x prime and R charts, using the first 30 samples. Is the process under control at this point?

c. After calculating the control limits, the last 20 samples were collected. When plotted using the control limits calculated earlier, does the process appear to be in statistical control? Why or why not? What should be done if it is not under control?

Electronics, Inc. has been having difficulties with circuit boards purchased from and outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Thirty samples of four boards each were taken from shipments sent by the supplier as shown in the data listed in this excel worksheet. prob 7-3 in the attached worksheet.

a. construct x prime and R charts for these data

b. if the suppliers plant quality manager admitted that they were experiencing quality problems for shipments 18, 19, and 21 how would that affect your control chart? Show revised x prime and R charts for these data.

c. Ten more observations were taken, as shown in the second table of this excel worksheet. Using the revised x prime and R charts from part b, comment on what the chart shows after extending it with the new data.

Consider the data for the time required to begin loading the home page in an internet browser for a website. Fifteen samples of size 5 are shown in this excel worksheet. Specifications are 0.076+ or - 0.009. Prob. 7-6 in the attached worksheet

a. compute control limits for and x chart (for individuals) using the statistic R prime/ d sub 2 as an estimate for the data. Why might they be different?

b. Construct the x and r charts and an x chart for individuals using the data. Interpret the results

c. Estimate the process capability by using the estimated sample standard deviation in the second attached spreadsheet

The fraction defective for a folding process in a Quality Printing plant is given in the attached excel worksheet for 25 samples. Fifty units are inspected each shift. Prob. 7-7 in the attached worksheet

a. construct a p chart and interpret the results

b. after the process was determined to be under control, process monitoring began, using the established control limits. The results of 25 more samples are shown in the second part of the worksheet. Is there a problem with the process? If so, when could the process have been stopped, and the steps taken to correct it?

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