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• 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






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%

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