ME250:Statistics Probability ME 250:Design Manufacturing I School of Mechanical Engineering Shanghai Jiao Tong University 1
Shanghai Jiao Tong University 1 ME250: Statistics & Probability ME 250: Design & Manufacturing I School of Mechanical Engineering
Outline ■Introduction Tolerances ■Reliability Statistical Process Control ■Regression ■ Summary Shanghai Jiao Tong University 2
Shanghai Jiao Tong University 2 Outline n Introduction n Tolerances n Reliability n Statistical Process Control n Regression n Summary
Introduction Uncertainty in Design Manufacturing Learning Objectives Understand the elementary aspects of statistics and probability. How to represent data. Discrete and continuous distributions. The normal distribution and how to use tables of the cumulative distribution. Probability of single and multiple events. Obtaining trends from noisy data by regression. Applications in statistical process control and geometric dimensioning and tolerances. Taylor's tool life equation and how to use it. Shanghai Jiao Tong University 3
Shanghai Jiao Tong University 3 Introduction n Uncertainty in Design & Manufacturing n Learning Objectives n Understand the elementary aspects of statistics and probability. n How to represent data. n Discrete and continuous distributions. n The normal distribution and how to use tables of the cumulative distribution. n Probability of single and multiple events. n Obtaining trends from noisy data by regression. n Applications in statistical process control and geometric dimensioning and tolerances. n Taylor’s tool life equation and how to use it
Example 1 Suppose a company produces 1000 engines per year and 5 engines fail on average per year.The failures can be eliminated by a 100%inspection program.If it costs $10,000 to replace an engine but $100 to inspect each one,then the costs are: ■Inspect:1000*$100=$100,000 ■Replace:5*$10,000=$50,000 Obviously,it is cheaper not to inspect.If 10 or more engines fail, then the inspection program is cheaper. Therefore,it is very important for the company to maintain good statistical data on its manufacturing process. Shanghai Jiao Tong University 4
Shanghai Jiao Tong University 4 Example 1 n Suppose a company produces 1000 engines per year and 5 engines fail on average per year. The failures can be eliminated by a 100% inspection program. If it costs $10,000 to replace an engine but $100 to inspect each one, then the costs are: n Inspect: 1000 * $100 = $100,000 n Replace: 5 * $10,000 = $50,000 n Obviously, it is cheaper not to inspect. If 10 or more engines fail, then the inspection program is cheaper. n Therefore, it is very important for the company to maintain good statistical data on its manufacturing process
Tolerances Tolerances refer to how close a dimension or a surface finish of a manufactured part is to the desired or "nominal"dimension. The explicit specification of tolerances is critical for determining the manufacturing process(es)required to make a part and therefore its final cost. If the surface finish is not important,it may be possible to use cheaper or faster process than if the surface finish is critical. Shanghai Jiao Tong University 5
Shanghai Jiao Tong University 5 Tolerances n Tolerances refer to how close a dimension or a surface finish of a manufactured part is to the desired or “nominal” dimension. n The explicit specification of tolerances is critical for determining the manufacturing process(es) required to make a part and therefore its final cost. n If the surface finish is not important, it may be possible to use cheaper or faster process than if the surface finish is critical