8.8 Tools: Process Capability Analysis for CTQ(s)

In evaluating your process as part of the mapping procedure, you need to ask whether the process can provide what you and your customer needs. To answer this question, you perform a process capability analysis. Process capabilityProcess capability: The ability of a process to meet the specifications for a product or service. is the ability of a process to meet the specifications for a product or service. Simply put, a process capability analysis allows you to verify that the process is capable of consistently producing products within the specifications set.

Process capability compares the distribution of a process’s outputs (often called Voice of the Process) with the customer’s specification limits for the outcomes (the Voice of the Customer). The underlying logic here is that your process needs to be stable. You can consider your process stable if only chance variation exists. If your process shows any systematic variation beyond a certain degree, then you can conclude that your process is unstable. The specification limits define the range of acceptable deviation from the target level.

Assessing Process Capability

To assess a process’s capability, you need to collect real data on the process by performing a trial run or pilot test. During the pilot test, you want to make sure that the process replicates as closely as possible the actual, day-to-day operating environment. Simply put, you want to know how the process is going to work in real life. You want to use the same inputs, the same equipment, the same workers, and the same procedures. You can then measure the output against your quality standard using a precise statistical analysis called the process capability ratio (C_p)process capability ratio (C_p): It compares acceptable tolerances (set by your engineers) with the process’s actual variation so you can assess the process’s ability to achieve required quality levels.. The process capability ratio compares acceptable tolerances (set by your engineers) with the process’s actual variation so you can assess the process’s ability to achieve required quality levels. If you model real variation as a normal distribution, you can depict C_p as follows:

$\text{Process Capability} (C_{p}) = \frac{\text{Acceptable Tolerance}}{\text{Actual Process Variation}}$

Now, let's translate the process capability ratio (C_p) into statistical notation. C_p indicates the short-term level of performance that your process can potentially achieve. It does not consider the center of the process. C_p is the tolerance width (distance between the specification limits) divided by the short-term spread of the process (six times the short-term standard deviation).

$\text{Process Capability} (C_{p}) = \frac{|USL - LSL|}{6\sigma}$

Where:

USL = Upper Specification Limit

LSL = Lower Specification Limit

σ = Standard Deviation

You calculate the process standard deviation (σ) using actual output from the pilot test. You use a multiplier of six to establish a high degree of confidence that the process’s output will fall within the upper and lower limits. That is, 6σ captures almost 100% (99.74% actually) of the process variability. If your upper and lower specification limits are more significant than the process variability, you are pretty confident that the process can achieve your desired quality level. The higher the C_p value, the better the process.

If C_p < 1, the process output exceeds specifications; the process is incapable.
If C_p = 1, the process barely meets specifications.
If C_p > 1, the process output falls within specifications, but can be defective if the process is not centered.

As you consider a process's capability, you need to recognize that most processes do not yield a process mean (μ) that is precisely equal to your target mean (T). In other words, the process mean (μ) will be above or below your target (T). This reality shifts the process’s normal probability distribution to the right or the left. The farther off-center the process is operating, the more likely it is to produce unacceptable (i.e., defective) parts. You need to introduce an adjustment factor k that measures how far your process mean (μ) is from the design target (T). You calculate the adjusted capability ratio (C_pk) as follows:

C_pk = C_p(1 - k)

Where

$k = \frac{|T - \mu|}{\frac{\text{USL - LSL}}{2}}$

As a rule of thumb, a C_pk of 1.5 or higher indicates that your process can meet your desired quality levels. Now, let's work through a sample problem.

Suppose that the design engineering team set the specifications for the length of a stamped sheet-metal part at 10 inches (T) with acceptable tolerances of ± .05 inches (USL and LSL). The average length of the actual stamping process’s products is 9.99 inches (μ) with a standard deviation of .015 inches (σ). The calculations for the C_p and C_pk are as follows:

$(C_{p}) = \frac{|10.05 - 9.95|}{6(0.15)} = 1.11$

Now, since the process is producing off center (i.e., μ = 9.99 instead of the target 10), you need to adjust (or center) by calculating your C_pk:

$k = \frac{|10 - 9.99|}{\frac{10.05 - 9.95}{2}} = .20$

C_pk = 1.11(1 − 0.20) = 0.88

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