Original sample lesson · allow approximately 10–15 minutes
By the end of this lesson
Separate process behavior from customer requirements using an original capability example.
Control limits and specification limits answer different questions. Control limits describe the observed behavior of a process over time. Specification limits describe what is acceptable to the customer or design. A stable process can consistently produce unacceptable output, and a good-looking capability number can be misleading if the process is unstable.
For a stable, approximately normal process using an appropriate estimate of within-process variation, Cp compares the specification width with six standard deviations: Cp = (USL − LSL)/(6σ). Cpk also accounts for where the process mean sits: it is the smaller of (USL − μ)/(3σ) and (μ − LSL)/(3σ). Check the assumptions before interpreting either number.
An original example has LSL = 9.5 mm, USL = 10.5 mm, μ = 10.2 mm and σ = 0.10 mm. Cp is 1.0/0.60 = 1.67. The upper-side index is 0.30/0.30 = 1.00; the lower-side index is 0.70/0.30 = 2.33. Therefore Cpk is 1.00. The gap between Cp and Cpk tells you that centering matters here.
Check 1: A second characteristic on the same stable process has LSL = 40.0 mm, USL = 40.9 mm, μ = 40.7 mm and σ = 0.10 mm. What are Cp and Cpk?
The next action depends on evidence. If the process is stable and the measurement system is suitable, moving the mean toward the center could improve the limiting side without changing the inherent spread. If special causes are present, first understand and address those causes; a capability calculation cannot make the instability disappear.
Check 2: In the worked example, Cp is 1.67 but Cpk is only 1.00. Why?
After the questions, write two sentences: what does this process do, and what does the customer require? Keeping those questions separate helps prevent a common exam error and a costly workplace decision.
Check 3: Before relying on these indices, what should you verify?
Take it into your study session
Write a one-sentence explanation of the principle, then describe a situation where the wrong answer would create a problem. Revisit the questions tomorrow without looking at the explanations first.
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