gen-define-process-capability-index-cpk-and-give-one-short-worke-c4e5

Define process capability index (Cpk) and give one short worked example.

# Process Capability Index (Cpk) ## Definition **Cpk** is a statistical measure that indicates how well a process can meet specification limits, accounting for process centering. It represents the capability of a process to produce output within customer specifications. **Formula:** Cpk = min[(USL - μ)/3σ, (μ - LSL)/3σ] Where: - USL = Upper Specification Limit - LSL = Lower Specification Limit - μ = Process Mean - σ = Process Standard Deviation ## Interpretation - **Cpk ≥ 1.33**: Process is capable - **Cpk < 1.0**: Process is not capable (defects likely) ## Worked Example A bottling company fills bottles with a target of 500 ml. **Given:** - LSL = 495 ml - USL = 505 ml - Process mean (μ) = 501 ml - Process std. dev. (σ) = 1.5 ml **Calculation:** Upper capability = (505 - 501)/(3 × 1.5) = 4/4.5 = **0.89** Lower capability = (501 - 495)/(3 × 1.5) = 6/4.5 = **1.33** **Cpk = min(0.89, 1.33) = 0.89** **Conclusion:** The process is **not capable** (Cpk < 1.0). The process mean is too close to the upper limit, causing potential overfills. The process needs centering or variation reduction.