# Control chart guidelines, out of control conditions, and corrective action procedures and examples

Figures 3.2 and 3.3 are examples of X and R charts showing the solder paste height deposition process for a surface mount technology (SMT) process. Several observations can be made from examining these charts:

1. In Figures 3.2 and 3.3, the two charts, X and R, are measuring process average and process variability, respectively. Although one might be out of control, the other one is not, or vice versa. This is due to the independence of the two attribute of the process.

2. The two charts are related mathematically, since the distance from the X to one of the control limits is equal to 3 s or A2 * R. The R number in the chart (1.25 in Figure 3.3) can be multiplied by 0.73

(the factor for n = 4 from Table 3.1), resulting in 0.9125. This is the approximate distance from the X (sometimes called the center- line or CL) to one of the control limits in the X chart.

3. The frequency of taking samples for control charts is left up to the manufacturing process quality status controller. For high-quality processes, a daily sample for each shift is adequate to ensure conformance. For production lines with frequent quality problems, more sampling might be required, depending on the number of parts being produced or the number of hours since the last sample. This is necessary if reworking out-of-control parts is required. In this case, material or parts produced since the last good sample plot on the chart has to be reworked. In addition, The problem has to be investigated by production engineers and possible causes recorded on the chart. The production engineer may require that more frequent samples be taken until the process is more stable. Figure 3.4 is an example of such a condition for a bonding process for plastic parts.

4.The control limits should not be recalculated unless there is a change in the manufacturing process. Examples could be new materials, machinery, operators, or process improvement projects. When a chart shows an out-of-control condition, the process should be investigated and the reason for the problem identified on the chart. Figure 3.5 shows a typical scenario of plotting a parameter (in this case the surface cleanliness measurements on PCBs), which was necessitated by a defective laminate lot. Note that the new lot has significantly increased the resistance value, which would necessitate recalculating the control limits.

5. In the X chart, the upper and lower control limits are usually symmetrical around the X or the centerline, as shown in Figure 3.3. In the case of a maximum specification, only one control limit is sufficient. In the R chart, symmetry is not necessary when the sample size is less than 7, since D3 (the control factor for the lower limit) is equal to zero.

6. In many six sigma manufacturing plants，manufacturing has added additional information such as the specification limits, and then calculated the Cp or Cpk on the control charts. This can easily be done, as shown in examples earlier in this chapter, by deriving cr either from the R or s calculation in step 2, using the formulasσ = s • orσ = R/d2.

7. The most common indicator of out-of-control condition is that one sample average is plotted outside the X chart control limits, or one sample range is outside the R chart control limits. If these observations are confined to one portion of the chart, then many other indicators of out-of-control conditions can be used as well. These indicators have a probability approaching that of the one X point outside the control limits, whose probability is equal to 0.00135. Each half of the X chart can be divided into three segments, being onr standard deviation (s) wide. The probability of an X point occurring outside the 2 s limit or beyond is f{-2) = 0.0228, and the probability of X point occurring outside the 1 s limit is /(-l) = 0.1587 from the standard normal distribution or z table (Table 2.3).

The probability of multiple X points occurring in succession might equal that of the one point outside the 3 s limits. For example, two successive points in the zone beyond 2 s (the outer one-third zone in the upper half of the chart) is 0.0228 • 0.0228 or 0.00052. A combination of points inside and outside the zones can be used. For this zone, two out three X points can be used. The probability of the third point is 1 - 0.0228 = 0.9772. Since this point can occur anywhere within the sequence, the total probability has to be multiplied by 3 or 0.0228 • 0.0228 • 0.9772 * 3 = 0.00152, which is comparable with the 0.00135 probability of a single point outside the control limit. Table 3.3 shows the out-of-control conditions for several successions of points in one- half of the X, R control charts.