It may look bad, but it’s good
The X and R chart in Figure 1 shows depths. Each point on the X chart is the average of six measurements. Thischart’s upper control limit (UCL) and lower control limit (LCL) were calculated using the mean plus or minus the average range multiplied by the A2 factor (0.48 or 0.483) for subgroups of six. Each point on the R chart is the range of those six measurements.
This chart’s UCL was calculated using the average range multiplied by the D4 factor (2.00 or 2.004) for subgroups of six. These are typicalShewhart charts with three sigma control limits developed during a defined control period. Thus, if the control trends are maintained, it would be expected that 99.7% of the recorded points would be within the control limits.
The obvious stands out in Figure 1. What looks like cyclic behavior and loss of control can be seen. The operator and engineer monitoring this would be expected to adjust theprocess and look for attributable causes.
The X chart shows 19 points and two runs above the UCL indicating that the process is running too high and needs adjustment downward. It also shows four points below the LCL, indicating that the process average is too low and requires adjustment upward. Something has changed since these limits were developed and some attributable causes may need to becorrected. The process average seems to have shifted for extended periods of time.
The R chart shows points above the UCL indicating that there is more variation in the process than when the limits were developed. One could state that the process is often out of control. The R chart has many low points that indicate little or normal variation. This is good unless the measurements are in error and aremasking a problem.
From these observations, operators would be expected to make adjustments to the process. If this chart was designed correctly under conditions of control and normal process capability, then it is a useful chart showing out-of-control conditions that must be corrected.
Some observations include Type I and Type II errors. Type I errors are when it is stated that good things arebad. Type II errors are when it is stated that bad things are good. Type I and II errors obscure the truth. When it is stated that good things are good or bad things are bad, both cases are correct and the truth is known.
Even when stated, it is still not known if the product had to be scrapped or reworked. One cannot tell because the process capability is not shown on X and R charts. If this were acapable process, virtually no product would be out of specification, and conversely, if this were an incapable process, even in-control product may not be satisfactory.
It looks good, but is it very good?
Figure 2 shows what appears to be a functioning and useful X and R chart used in height control. The 30 points of subgroup size six appear to be normally distributed within the controllimits. More points are near the centerline and less are near the control limits. One point in the X chart is slightly above the UCL. There is an apparent cyclic behavior in the process average because of a typical method of operation. This was accepted during the chart control limit development run.
Having seen this functional chart, a customer, auditing a vendor’s SPC of some critical...