Q: What are typical target values for Cp and Cpk?

Cp = (USL − LSL) / (6σ) measures the spread of the process relative to the spec width. Cpk = min((USL − μ)/(3σ), (μ − LSL)/(3σ)) accounts for mean shift. Typical targets: Cpk ≥ 1.00 (minimum acceptable), Cpk ≥ 1.33 (stable production), Cpk ≥ 1.67 (high-quality or safety-critical parts). Automotive and aerospace suppliers are often required to achieve Cpk ≥ 1.67. When Cp > Cpk, the process spread is acceptable but the mean is off-centre, so a process adjustment (rather than a tolerance change) is the most efficient fix.

Question 1

What is the difference between the RSS method and the worst-case method for tolerance stackup?

Accepted Answer

The worst-case method computes T_WC = Σ|aᵢtᵢ|, assuming all parts are simultaneously at their maximum tolerance in the worst direction. This guarantees a 100% yield but produces overly tight tolerances for assemblies with many parts. The RSS (Root Sum of Squares) method assumes each part dimension is independently and normally distributed, giving T_RSS = k√(Σ(aᵢtᵢ)²) where k is the sigma level (k = 3 covers 99.73%). RSS yields more relaxed tolerances suitable for volume manufacturing.

Question 2

How does Monte Carlo tolerance analysis work?

Accepted Answer

Each part dimension xᵢ is sampled from a normal distribution N(μᵢ, σᵢ²) where σᵢ = tᵢ/k. The assembly gap Y = Σaᵢxᵢ is computed for a large number of trials (up to 50,000 in this tool). The resulting distribution yields mean μ, standard deviation σ, defect rate P(Y < target), and the minimum gap. Monte Carlo handles asymmetric tolerances and non-normal distributions, and can model complex stackup chains that RSS cannot.

Question 3

What are typical target values for Cp and Cpk?

Accepted Answer

Cp = (USL − LSL) / (6σ) measures the spread of the process relative to the spec width. Cpk = min((USL − μ)/(3σ), (μ − LSL)/(3σ)) accounts for mean shift. Typical targets: Cpk ≥ 1.00 (minimum acceptable), Cpk ≥ 1.33 (stable production), Cpk ≥ 1.67 (high-quality or safety-critical parts). Automotive and aerospace suppliers are often required to achieve Cpk ≥ 1.67. When Cp > Cpk, the process spread is acceptable but the mean is off-centre, so a process adjustment (rather than a tolerance change) is the most efficient fix.

Question 4

What is the sensitivity coefficient aᵢ and how should it be set?

Accepted Answer

The sensitivity coefficient aᵢ defines the direction in which part i contributes to the assembly gap Y. aᵢ = +1 means an increase in that part's dimension increases Y (e.g., housing bore diameter). aᵢ = −1 means an increase decreases Y (e.g., shaft outer diameter). For a clearance fit, the gap = bore − shaft, so bore gets a = +1 and shaft gets a = −1. Correctly assigning sensitivity coefficients is essential for accurate stackup analysis of multi-component assemblies.

Tolerance Stackup Analysis (RSS, Worst-Case, Monte Carlo)

Worst-Case Method (WC)

RSS Method (Statistical Tolerance)

Monte Carlo Method

Process Capability Index