Day 1: Fundamentals, Worst Cost, and Root Sum Square Approaches
Tolerance Analysis Fundamentals. The nature of dimensioning and tolerancing. Tolerance analysis purposes. Tolerance analysis history. How tolerances are typically assigned. Tolerance analysis concepts. Worst case tolerance analysis and worst case tolerance analysis shortfalls. Statistical tolerance analysis and statistical tolerance analysis shortfalls. Differences between worst case tolerance analysis and statistical tolerance analysis. Suggested tolerance analysis approach selection criteria.
Basic Statistical Considerations. The nature of variability. The normal distribution. Means and standard deviations. Manufacturing process variability. Process capability, Cp, and Cpk. Tolerances and nominal dimensions versus process capability. Coefficient incorporation to address differences in design nominal and process nominal dimensions. Exercises.
Statistical Tolerance Analysis Concepts. Statistical tolerance analysis purposes. Statistical tolerance analysis assumptions. The realism of statistical tolerance analysis. Maximum possible versus maximum probable dimensional variation. Why statistical tolerance analyses predict less variation. The economics of worst case tolerance analysis versus statistical tolerance analysis.
Root Sum Square Statistical Tolerance Analysis. Dimension chains, positive versus negative directions, and converting to equal-bilateral format. Finding the root sum square of all tolerances. Knowing the manufacturing process and assembly shift, and incorporating adjustment coefficients. Applying statistical tolerance analysis findings for dimensional predictions. Using statistical tolerance analysis for relaxing component tolerances. Using Excel. Exercises.
Day 2: Monte Carlo and Advanced Concepts
Monte Carlo Tolerance Analysis. The Monte Carlo approach. Differences in Monte Carlo simulation approaches. Applying uniform versus normal distributions in the simulation. Randomness and normal statistical variation. Monte Carlo simulations with Excel and VBA for Excel. Statistical tolerance analysis versus Monte Carlo tolerance analysis considerations. Exercises.
Tolerance Allocation Approaches. Typical tolerance assignment approaches. Tolerance allocation based on worst case, root sum square, and Monte Carlo tolerance analysis. Tolerance allocation incorporating the tolerance analysis approach and component size, process capability, cost, and mean shift. Using Excel for tolerance allocation. Exercises.
Assessing Statistical Tolerance Analysis Applicability. Number of tolerances. Production quantities. Process controls and process capability. Centered processes versus nominal dimensions. Design sensitivity. Interchangeability. Independent variables. Suggested guidelines.
Quality and Economics Considerations. Costs and benefits associated with statistical tolerance analysis. Costs associated with tighter versus looser tolerances. Rejections as a result of statistical tolerance analysis approaches. Using statistical tolerance analysis to predict assembly rejection rates. Targeting tolerance relaxation candidates.
Other Considerations. Non-normal distributions. Factor weighting by individual tolerance. Risks and risk management.
Course Wrap-Up. Course review. Questions and answers. Plans for future actions. Course critique.
