14-1 Control Charts for Variation and Mean 703 Interpreting Run Charts A run chart with no obvious pattern suggests that the data are from a process that is statistically stable, and the data can be treated as if they came from a population with a constant mean, standard deviation, distribution, and other characteristics. Figure 14-1 shows a pattern of increasing values, and that is one of several criteria for determining that a process is not statistically stable (or out of statistical control). Violating one or more of the following criteria indicates that a process is not statistically stable or out of statistical control. Treating the 140 global Earth temperatures from Table 14-1 as a string of consecutive measurements, construct a run chart using the vertical axis for the temperatures and the horizontal axis to identify the chronological order of the temperatures. CP YOUR TURN. Do Exercise 6 “Pepsi Cans: Run Chart.” EXAMPLE 2 Run Chart of Earth Temperatures SOLUTION Figure 14-1 is the Minitab-generated run chart for the data in Table 14-1. In Figure 14-1, the horizontal scale identifies the sample number, so the number 1 corresponds to the first temperature measurement in 1880, the number 2 corresponds to the second temperature measurement in 1881, and so on. The vertical scale represents the mean global temperatures 1°C2. FIGURE 14-1 Run Chart of Earth Temperatures INTERPRETATION Examine Figure 14-1 and try to identify any patterns. From Figure 14-1 we see that as time progresses from left to right, the points appear to be rising. If this pattern continues, rising temperatures will cause melting of large ice formations, widespread flooding, and many other climatic changes. Figure 14-1 is evidence of global warming, which threatens us in many different ways. DEFINITION A process is statistically stable (or within statistical control) if it has only natural variation, with no patterns, cycles, or unusual points. Flynn Effect: Upward Trend of IQ Scores An IQ (Intelligence Quotient) is measured from standard tests of intelligence. A run chart or control chart of IQ scores would reveal that they exhibit an upward trend, because IQ scores have been steadily increasing from about 1930. The trend is worldwide, and it is the same for different types of IQ tests, even those that rely heavily on abstract and nonverbal reasoning with minimal cultural influence. This upward trend has been named the Flynn effect, because political scientist James R. Flynn discovered it in his studies of U.S. military recruits. The amount of the increase is quite substantial: Based on a current mean IQ score of 100, it is estimated that the mean IQ in 1920 would be about 77. The typical student of today is therefore brilliant when compared to his or her great-grandparents. It is not yet clear whether the upward trend in IQ scores indicates an increasingly intelligent population or whether there are problems with the methods used for IQ testing.
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