Question 20.4: MEASURING THE PROPORTION OF DEFECTIVE CHIPS AT SOUNDTECH Sou......
MEASURING THE PROPORTION OF DEFECTIVE CHIPS AT SOUNDTECH
SoundTech is a company that manufactures electronic chips for sound systems in personal computers. Each chip is classified as conforming or nonconforming. The nonconforming chips cannot be used and are discarded. Each hour 75 chips are tested for conformance. These 75 chips represent a random sample of all chips that are produced in a given hour. The file Chips1.xlsx lists the number of nonconforming chips (out of 75) for 25 consecutive hours (See Figure 20.21). Is the process currently in control? Is it behaving well?
Objective To use p charts to see whether the chip manufacturing process at SoundTech is in control and is producing a “small” number of nonconforming chips.
The mechanics of constructing a p chart with StatTools are very similar to those for \bar{X} and R charts. The main difference is that the data can be set up in several ways. First, the data can either list the numbers of nonconforming items or the fractions of nonconforming items. (Chips1.xlsx lists the former.) Second, a variable that lists the sample sizes, the n_i’s, can either be present or absent. (There is such a variable in the file.) If the sample size variable is absent, it is assumed that the sample sizes are constant, and you must supply this common value.
To create the p chart, select P Chart from the StatTools Quality Control group to obtain the dialog box in Figure 20.22. For this example it should be filled out as shown. (Alternatively, you could check the Use Common Size option, in which case the value 75 would be entered manually in a box that would appear.) Note that the procedure prompts for the “Val” variable that contains the numbers nonconforming and the “Siz” variable that contains the sample sizes. The variables Number Nonconforming and Sample Size should be selected for this example. The other options in the dialog box are analogous to those for X/R charts.
The p chart appears in Figure 20.23. You can see that the points, each of which indicates a proportion nonconforming, vary randomly around a centerline of \bar{p} = 0.255. The control limits are at 0.104 and 0.407, and no points are beyond the control limits. Therefore, the current process appears to be in control. But is it any good? We would argue that an average percent nonconforming of about 25% is not very good. As usual, an in-control process is predictable but not necessarily acceptable. SoundTech management should begin searching for improvements to its process. For example, they might select different suppliers of raw material, purchase new machinery, or institute better worker training. Then by charting future values, the company can see whether any improvements it employs have the desired effect.
For the sake of comparison, we illustrate a variation of this example where SoundTech samples a different number of chips each hour. For example, it might actually sample all chips produced, but production quantities might vary considerably from hour to hour. The file Chips2.xlsx contains the data. The only difference is that the Sample Size variable in this file is not constant. You have two options. You can fill out the dialog box in Figure 20.22 exactly as before, or you can check the Use Common Size box and enter an “average” sample size in the box that appears. If you select the former option, the resulting p chart appears in Figure 20.24. As you can see, the nonconstant sample sizes result in uneven control limits. Although we are still looking for points beyond the control limits, the bumpiness of these limits is somewhat distracting. Therefore, SoundTech might decide to base the chart on the average sample size (about 75). Fortunately, the practical difference between these two approaches is usually minor.
