Refer to Exercise 16.16 and the hourly data collected by BPI consulting.

a. Construct an R-chart for the data. Is the process variation in control?

b. Round each measurement in the data set to a whole number, like in Exercise 16.16b. Form an R-chart for the rounded data. What do you observe?

Data from Exercise 16.6

BPI Consulting, a leading provider of statistical process control software and training in the United States, recently alerted its clients to problems with “chunky” data. In an April 2007 report, BPI Consulting identified “chunky” data as data that result when the range between possible values of the variable of interest becomes too large. This typically occurs when the data are rounded. For example, a company monitoring the time it takes shipments to arrive from a given supplier rounded off the data to the nearest day. To show the effect of chunky data on a control chart, BPI Consulting considered a process with a quality characteristic that averages about 100. Data on the quality characteristic for a random sample of three observations collected each hour for 40 consecutive hours are given in the accompanying table.

Transcribed Image Text:

Sample Quality Levels sample Quality Levels 1 99.69 99.73 99.81 21 99.43 99.63 100.08 2 98.67 99.47 100.20 22 100.04 99.71 100.40 3 99.93 99.97 100.22 23 101.08 99.84 99.93 4 100.58 99.40 101.08 24 99.98 99.50 100.25 5 99.28 99.48 99.10 25 101.18 100.79 99.56 6 99.06 99.61 99.85 26 99.24 99.90 100.03 7 99.81 99.78 99.53 27 99.41 99.18 99.39 8 99.78 100.10 99.27 28 100.84 100.47 100.48 9 99.76 100.83 101.02 29 99.31 100.15 101.08 10 100.20 100.24 99.85 30 99.65 100.05 100.12 99.12 99.74 100.04 101.58 100.54 100.53 101.51 100.52 100.50 11 31 100.24 101.01 100.71 12 32 99.08 99.73 99.61 13 33 100.30 100.02 99.31 14 100.27 100.77 100.48 34 100.38 100.76 100.37 15 100.43 100.67 100.53 35 100.48 99.96 99.72 16 101.08 100.54 99.89 36 99.98 100.30 99.07 17 99.63 100.77 99.86 37 100.25 99.58 101.27 18 99.29 99.49 99.37 38 100.49 100.16 100.86 19 99.89 100.75 100.73 39 100.44 100.53 99.84 20 100.54 101.51 100.54 40 99.45 99.41 99.27