Process Capability Analysis

Before quality can be built into a product, it is necessary to verify that the selected production process is capable of performing at the desired quality level. This process proving involves some form of trial run or pilot test. As the trial run takes place, managers must replicate as closely as possible the actual operating environment. Deviations from a realistic operating environment invalidate results. Therefore, the same equipment, the same procedures, the same workers, and the same suppliers should all be used in the test run. The output of the process should then be measured against the standard using rigorous statistical analysis to assess the overall process capability.

The process capability ratio helps assess the process ability to achieve required quality levels. By comparing acceptable tolerances (set by engineering) with the process variation, this ratio indicates whether the process can consistently produce good quality parts. The ratio is calculated as follows:

C_p = | USL-LSL| where: USL= upper specification limit

6sLSL = lower specification limit

s = standard deviation (process variability)

The process standard deviation is calculated using actual output from the trial run. A multiplier of six is used to establish the degree of confidence that the process output will fall within the upper and lower limits. That is, using a standard normal distribution, 6ssets a standard of close to 100 percent confidence that the process can achieve the desired quality level. Since most processes do not yield a process mean that is exactly equal to the target mean, a correction factor kthat reflects the difference between the actual process mean (m) and the design target (D) must be introduced. The adjusted capability ratio is calculated using the following equations:

C_pk= C_p (1 - k) where: k= | D - m|

(USL-LSL)/2

A C_pkof 1.5 or higher suggests that the process can meet the desired or target quality levels.

Problem:

Suppose that the design engineering team set the specifications for length of a stamped sheet-metal part at 10 inches (D) with acceptable tolerances of .05 inches (USL and LSL). The average length of the products produced by the actual stamping process is 9.99 inches (m) with a standard deviation of .015 inches (s). The calculations for the Cp and Cpk are as follows:

C_p= (10.05-9.95)/6(.015) = .10/.09 = 1.11

k= (10 9.99)/((10.05-9.95)/2) = .01/.05 = .20

C_pk= 1.11 (1-.20) = 1.11(.8) = .88

Your Answers

Is the process capable of consistently producing high-quality parts (i.e., within specs)?

What can or should be done?

If an process engineering team makes adjustments that change the mean to 9.995

Inches and the standard deviation to, .005 inches, what is the new C_pk?

Summary: When working with new suppliers, new parts, or new processes, purchasers must take the time to verify that the process is capable of producing within acceptable tolerances. Because design engineers often lack confidence in the suppliers manufacturing capability and the purchasers ability to verify supplier process capabilities, they sometimes set the product specifications at levels that are much tighter than they really need to be in order to design in quality. Unfortunately, such guardbanding almost always increases production costs and lengthens lead times while failing to improve quality.