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Determination of the Optimum Process Mean and Optimization Design of the Control Charts Based on Non-normal Distribution

Author: ZhangBin
Tutor: HanZhiJun
School: Nanjing University of Technology and Engineering
Course: Management Science and Engineering
Keywords: process mean loss function quality investment sensitivity analysis G/G/S system control chart
CLC: F224
Type: PhD thesis
Year: 2008
Downloads: 293
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In modern quality management systems,the objective of the quality improvement is to have a zero-defect product,and to make the process mean closing to its target,the variance closing to zero.However,we may face the problem in production that the process is in control but is not capable of meeting the specifications in a short term.There are two methods to solve this problem:one is to set the optimum process mean;the other is to reduce the variance of the process.Selecting the optimum process target affects the process defective rate,material cost, scrap or rework cost,and a loss to the customer due to product performance deviation from an ideal target value.The right process mean is critically important to the advance of the productivity and the improvement of the quality.It can realize the object of quality improvement with no investment or little investment.The selection of the optimum process mean is of major interest in a wide variety of industrial processes.Optimal resetting for the process mean is usually set at the beginning of the production cycle and remains unchanged throughout the production period.However,the process mean needs to be reset frequently due to the random shock.On the other hand, reduce the process variance often need quality investment.The optimal investment problem is focused on the balancing of investment sunk cost and future financial return.The competition of modem product is the competition of product’s quality.High quality products need not only high level design but also high quality management.One of the key methods in on-line management is the control chart technique.The major function of control charting is to detect the occurrence of assignable causes so that the necessary corrective action may be taken before a large quantity of non-conforming product is manufactured.The designing of traditional control charts supposes that the pdf of the quality characteristic has to be normal.If the quality characteristics are not normally distributed,the traditional way for designing the control chart may reduce the ability of the control chart.Meanwhile,the traditional way does not consider the economic of the control chart.Thus,the study to the optimum process mean and the control charts for the non-normal distribution has an important value not only on theory but also on application.This paper is organized as follows:In chapter 1,a brief overview of the approach about determining the optimum process mean and designing control charts is provided.In chapter 2,the determination of the optimal process mean of truncated normal distribution under the asymmetric piecewise linear loss function and the asymmetric Taguchi’s loss function is studied.The loss of neglecting truncated distribution is examined. At last,a multivariate quality loss function and the optimization scheme to determine the optimal process target levels for multiple quality characteristics are introduced.In chapter 3,we consider a Beta distribution and use the asymmetric quadratic quality loss function to determine the optimum process mean.An inspection strategy is developed.If complete inspection is chosen,we propose an optimization model to determine the optimal process mean and specification limits.Numerical example and associated sensitivity analysis are given to illustrate the proposed models.Aiming at the question that the process mean often shift due to occurrences of some random shocks,we consider the problem of selecting an optimal setting of the process mean and the length of the production run in chapter 4.The number of shocks is assumed to follow a Poisson process and the drift of the process mean is assumed to follow an exponential distribution.An asymmetric loss function is utilized for developing the economic model.In chapter 5,the relation of the optimal investment problem with the process mean is developed.In chapter 6,we use the Burr distribution as the appropriate of various non-normal distributions to determine the control limits and the sampling plan based on Taguchi’s loss function.In chapter 7,we propose the design methods of the acceptance control charts for non-normal data.In chapter 8,we provide an approach for the design of the optimal control charts about G/G/S system.On the basis of the first risk and combined the costs of the shortage and redundance of the workpieces,the loss function of the control charts is presented and the control limits can be ascertained.Compared with other methods,this approach is verified to be effective and feasible.This paper is marked by its in-depth analysis on determining the process mean and designing the control charts for non-normal distribution.The innovation of this paper embodies at the following aspects:(1)Using the principle of minimizing the expected total cost,this dissertation presents the methods of determination the optimum process mean and the relation of the process quality improvement and the quality investment. (2)Assuming that the quality characteristic obeys Beta distribution,a general optimization model is formulated to determine whether 100%inspection or no inspection is to be performed.If complete inspection is chosen then the optimal process mean and specification limits can be determined at the same time.(3).Considering that the process mean is subject to gradual shifts due to occurrences of random shocks,an economic model is constructed to select the optimal setting of the process mean and the optimal production run for a continuous production process.(4)Using the control chart technique for control the workpieces on the production line,an economic-statistical model for measuring the loss of the control chart is developed.

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CLC: > Economic > Economic planning and management > Economic calculation, economic and mathematical methods > Economic and mathematical methods
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