Tolerancing
Exercise
• Ten blocks are stacked on top of each other
• The Specification for the stack is 100 +/- 10
• What is the specification for an individual block?
• Simulate the results assuming• Normal distribution with Cpk of 1.33
• What specification is required if a Cpk of 1.33 is desired?• What could cause this to be incorrect?
Exercise – Strain Energy in a Solid Shaft
• Units
• U = Strain energy due to torsion
• T = torque
• L = length
• G = shear modulus
• r = radius
• Inputs
• T = normal, mean = 2000
• L = normal, mean = 100
• G = normal, mean = 994718.4
• r = normal, mean = 4
• Question
• 0.46 < U < 0.54
• Process s for T is 11
• Process s for L is 0.53
• Determine specifications for each input
• Allocate variance equally given no process information
• Compare to worst case tolerance
4
2
rG
LTU
=
Useful Practices for Input Variation
• Inputs from production variation
• Estimate variation statistically
• Identify the shape of the distribution from process knowledge
• Assume that long-term, there will be more variation than what is typically measured in a short-term data collection
• Inputs representing a range of usage
• Assume the worst case can happen
• Analyse at the extremes of the conditions
• Treat it as a mean shift and not as a random variable
• Inputs representing aging or deterioration
• Assume the worst case can happen
• Analyse at the extremes of the conditions
• Treat it as a mean shift and not as a random variable
Useful Practices for Input Variation – Examples
• Example production variation
• A device dispenses a coating material,
• The volume of material is affected by its heater temperature,
• The temperature is centered by computer control,
• Average temperature is 35°C, standard deviation is 1°C,
• Analyse with temperature as a normal distribution.
• Example range of usage
• A car radio is expected to work from -20°C to 120°C
• Analyze the radio performance twice, once at each temperature extreme
• Don’t treat temperature as a random variable with a uniform distribution
• This would assume you are designing for an “average” environment, with occasional excursions to the extremes,
• In fact, you are covering the full range of expected usage conditions.
Useful Practices for Input Variation – Examples• Example aging or deterioration
• The performance of a capacitor will degrade over time,
• Supplier expects 13% loss in capacitance over the life,
• The manufacturing tolerance is ±5%,
• Supplier’s capability is Ppk=2.0, s=5%/6 = 0.83%
• Do statistical analysis twice, at the extremes of capacitance:
• Statistical tolerance for new parts at nominal capacitance ands = 0.83%
• Statistical tolerance for aged parts at deteriorated capacitance ands = 0.83%
