Process Capability (Cpk ) and Real-Time SPC Software

SPC practitioners applying control charts to processes with high Cpk (>2.00) are typically burdened with very narrow control limits relative to specification limits. This promotes senselessly tight control limits, especially in cases where slight shifts in the process mean occur when an input parameter has been changed such as raw materials, setups, lots and so forth. X-bar charts on processes with small within-subgroup variability are very sensitive to shifts in the mean. Although these mean shifts are expected and do not jeopardize the process’ ability to produce conforming product, they do create plot point patterns that trigger statistical alarm rules.

The chart in Figure 1 has a Cp ratio of 3.13, yet, using traditional control limits, almost every plot point is in violation of one or more statistical alarm.


Figure 1 Control chart exhibiting out-of-control patterns on the X-bar chart yet all data points (see tier lines on each subgroup) are well within specification limits.

 

A New Solution - Economic Control Limits

Let's face it, there is more pay back to be gained working on in-control processes with low Cpk's than statistically out-of-control processes with very high Cpk's. Rather than continue to remain frustrated with this classic dilemma, lets look at the problem a little differently. Lets say that your company wants all processes to exhibit Cpk values of 1.33 or better. Given this goal, processes with Cpk's greater than 1.33 should not need much attention. Therefore, for these processes, let's set up control limits so that alarms are triggered only when the Cpk drops below the goal of 1.33. These modified control limits are called "Economic Control Limits."

Using InfinityQS, all the user needs to do is set the Target Cp to 1.33 and change a chart option to process the data with Economic Control Limits. After making these two easy changes, the control limits are modified (widened) so that the process mean is allowed to shift and drift so long as a plot point does not violate the control limits based on the Target Cp.

Figure 2 shows the same data, but with Economic Control Limits based on a Target Cp of 1.33.


Figure 2 Control chart with Economic Control Limits based on a Target Cp of 1.33. Economic Control Limits only apply to the X-bar chart.

 

Economic Control Limit Formulas

For processes with bilateral tolerances



Where:

USL, is the Upper Specification Limit
LSL, is the Lower Specification Limit
σ, is the process sigma
Cp, is the target process capability index
Size, is the subgroup size

For processes with unilateral tolerances





Where:

Mean, is the Process Mean
SL, is the Specification Limit
TT, is the Total Tolerance
σ, is the process sigma
Cp, is the target process capability index
Size, is the subgroup size

Economic Control Limits should be used if and only if the actual Cpk is higher than the target Cpk.

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