上海交通大学：《现代机械工程图学》教学资源_教学课件_Lec10_Statistics

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

Reliability Reliability is the likelihood that an object will perform its function or a process will yield satisfactory results. Often,the reliability of system must be predicted from an estimate of the reliability of its components. Shanghai Jiao Tong University 6

Shanghai Jiao Tong University 6 Reliability n Reliability is the likelihood that an object will perform its function or a process will yield satisfactory results. n Often, the reliability of system must be predicted from an estimate of the reliability of its components

Statistical Process Control Statistical Process Control is used to monitor processes in a way such that normal variability of the operation is accounted for, but long term degradation is observed. The process is sampled at given intervals and the statistics of the samples compared.The cost of the inspection must be balanced versus the dangers of either missing a change in the process or misinterpreting a statistical fluctuation for a change in the process. Shanghai Jiao Tong University 7

Shanghai Jiao Tong University 7 Statistical Process Control n Statistical Process Control is used to monitor processes in a way such that normal variability of the operation is accounted for, but long term degradation is observed. n The process is sampled at given intervals and the statistics of the samples compared. The cost of the inspection must be balanced versus the dangers of either missing a change in the process or misinterpreting a statistical fluctuation for a change in the process

Regression Regression allows us to determine a relationship between two or more variables,even when there is uncertainly in the measurements and the relationship may not be immediately obvious. We will use regression to establish the Taylor's Tool Life Equation. Shanghai Jiao Tong University 8

Shanghai Jiao Tong University 8 Regression n Regression allows us to determine a relationship between two or more variables, even when there is uncertainly in the measurements and the relationship may not be immediately obvious. n We will use regression to establish the Taylor’s Tool Life Equation

Terminology If the parameters of a model of a system or a process are known,given,or established from past history,then we have a probability problem and we can deduce the behavior of the system from the model.However,if the parameters are unknown and have to be estimated from the available data,then we have a statistical problem. Shanghai Jiao Tong University 9

Shanghai Jiao Tong University 9 Terminology n If the parameters of a model of a system or a process are known, given, or established from past history, then we have a probability problem and we can deduce the behavior of the system from the model. However, if the parameters are unknown and have to be estimated from the available data, then we have a statistical problem

Representing Statistical Data ■Histogram Group the data into bins or intervals and show the size of each bin (interval)graphically. Cumulative distribution Show graphically how much of the data is below a given value Shanghai Jiao Tong University 10

Shanghai Jiao Tong University 10 Representing Statistical Data n Histogram Group n the data into bins or intervals and show the size of each bin (interval) graphically. n Cumulative distribution n Show graphically how much of the data is below a given value