Question

The thickness of support beams has specifications of USL =59.48 mm and LSL 42.04 mm. It is known that the process mean is μ=50.15 mm and the process standard deviation is σ=2.17 mm. Compute the Cpk index. (Round to 2 decimal places)

Answer 1

The Cpk index is a measure of process capability, calculated using the formula (USL - μ) / (3σ) and (μ - LSL) / (3σ). In this case, the Cpk index is 1.714.

Step-by-step explanation:

The Cpk index is a measure of process capability, specifically how well a process is able to stay within specification limits. It is calculated by taking the minimum of two values: (USL - μ) / (3σ) and (μ - LSL) / (3σ). In this case, the upper specification limit (USL) is 59.48 mm, the lower specification limit (LSL) is 42.04 mm, the process mean (μ) is 50.15 mm, and the process standard deviation (σ) is 2.17 mm.

Using the formula, we can calculate both values:

For (USL - μ) / (3σ): (59.48 - 50.15) / (3 * 2.17) = 1.714

For (μ - LSL) / (3σ): (50.15 - 42.04) / (3 * 2.17) = 1.898

The Cpk index is the minimum of these two values, so the Cpk index for this process is 1.714.