2 Chemical Process Concentration

EXAMPLE 15-2 Chemical Process Concentration

  Table 15-3 shows 20 observations on concentration for the

  same time, the observed concentration reading will differ only

  output of a chemical process. The observations are taken at

  because of measurement error. Since the measurement error is

  one-hour intervals. If several observations are taken at the

  small, only one observation is taken each hour.

  Table 15-3 Chemical Process Concentration Measurements

  Concentration

  Moving Range

  20 101.0 3.8 x 99.1 mr 2.59

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  CHAPTER 15 STATISTICAL QUALITY CONTROL

  Moving range (2)

  Figure 15-11 Control charts for individuals and the moving range (from Minitab) for the chemical process concentration data.

  To set up the control chart for individuals, note that the

  99.1 UCL x 3

  mr

  d 99.1 3 1.128 2 105.99

  sample average of the 20 concentration readings is x

  and that the average of the moving ranges of two observations

  shown in the last column of Table 16-3 is mr 2.59. To set up

  CL x 99.1

  the moving-range chart, we note that D 3 0 and D 4 3.267

  d mr 99.1 3 1.128 92.21

  2. Therefore, the moving-range chart has center line

  0, and UCL D 4 mr 13.267212.592

  8.46. The control chart is shown as the lower control chart in Fig. 15-11. This control chart was constructed by Minitab.

  The control chart for individual concentration measure-

  Because no points exceed the upper control limit, we may now

  ments is shown as the upper control chart in Fig. 15-11. There

  set up the control chart for individual concentration measure-

  is no indication of an out-of-control condition.

  ments. If a moving range of n

  2 observations is used,

  Practical Interpretation: These calculated control limits

  d 2 1.128. For the data in Table 15-3 we have

  are used to monitor future production.

  The chart for individuals can be interpreted much like an ordinary X control chart. A shift

  in the process average will result in either a point (or points) outside the control limits, or a pattern consisting of a run on one side of the center line.

  Some care should be exercised in interpreting patterns on the moving-range chart. The moving ranges are correlated, and this correlation may often induce a pattern of runs or cycles on the chart. The individual measurements are assumed to be uncorrelated, however, and any apparent pattern on the individuals’ control chart should be carefully investigated.

  The control chart for individuals is not very sensitive to small shifts in the process mean. For example, if the size of the shift in the mean is one standard deviation, the average number of points to detect this shift is 43.9. This result is shown later in the chapter. While the per- formance of the control chart for individuals is much better for large shifts, in many situations the shift of interest is not large and more rapid shift detection is desirable. In these cases, we recommend time-weighted charts such as the cumulative sum control chart or an exponen-

  tially weighted moving-average chart (discussed in Section 15-8).

  Some individuals have suggested that limits narrower than 3-sigma be used on the chart for individuals to enhance its ability to detect small process shifts. This is a danger- ous suggestion, for narrower limits dramatically increase false alarms and the charts may

  be ignored and become useless. If you are interested in detecting small shifts, consider the

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  15-4 CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS