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| 研究生： |
蔡瑋倫 Tsai, Wei Lun |
|---|---|
| 論文名稱： |
韋柏分配下規格下限與X-bar 管制圖之經濟設計 Economic design of specification limit and X-bar control chart under Weibull distribution |
| 指導教授： | 楊素芬 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 英文 |
| 論文頁數： | 80 |
| 中文關鍵詞： | 經濟設計 、X-bar 管制圖 、規格界限 、韋柏分配 |
| 外文關鍵詞： | Economic design, X-bar control chart, Specification limit, Weibull distribution |
| 相關次數： | 點閱：142 下載：13 |
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To determine the economic design of control charts and the specification limits with minimum cost are two separate issues in previous research areas. In this study, we proposed a method to determine the optimal design parameters of X control charts and the specification limits simultaneously from an economic viewpoint. We also consider two types of X control charts: one is the economic X control chart and the other is the economic statistical X control chart. We obtain the optimal results by minimizing the expected cost per unit time for the-larger-the-better quality characteristic with a Weibull distribution. We
consider the asymmetric control limits because of the asymmetric feature of theWeibull distribution. Also, we are considering the difference between monitoring the process by
using an economic statistical X control chart and conducting a complete inspection plan.
Which way is better, process control or inspection plan?
In our data analysis of the two types of X control chart, we find that the optimal expected cost per unit time with complete inspection is lower than without complete
inspection. This is because the coefficient of Taguchi’s quadratic loss function we set is too small. And the analysis shows us the significant parameters for the optimal expected cost per unit time and design parameters.
At last, in our numerical examples for two different types of X control chart, we find that the performance of the economic X control chart is as good as the economic statistical one. However, we suggest the producer use the economic statistical X control chart with a complete inspection plan to obtain a lower expected cost per unit time and larger power of the control chart.
CHAPTER 1. INTRODUCTION.............................................. 1
1.1 Research Motivation................................... 1
1.2 Literature Review..................................... 2
1.3 Research Method ...................................... 4
CHAPTER 2. ECONOMIC DESIGN OF A X CONTROL CHART FOR A
PROCESS WITH WEIBULL DATA................................. 6
2.1 Approximated In-Control Sampling Distribution of the X under Weibull Distribution.................................6
2.2 Approximated Out-of-Control Sampling Distribution of X under Weibull Distribution................................ 9
2.3 Construction of Economic X Probability Chart Based on X Sampling Distribution9
2.4 The Calculation of alpha and beta ................... 10
2.5 Derivation of Expected Cycle Time ................... 10
2.6 Derivation of the Expected Cycle Cost ............... 12
2.7 Determination of the Optimum Sampling Interval of the Economic X Control Chart.................................14
2.8 Data Analysis and Resulting Comparison to Different Out-of-Control Distributions ............................15
CHAPTER 3. DESIGN OF ECONOMIC X CHART AND INSPECTION
SPECIFICATION LIMIT FOR A PROCESS WITH WEIBULL DATA.......20
3.1 Derivation of the Expected Cycle Cost ................20
3.2 Determination of the Optimum Specification Limit and Design Parameters of the Economic X Control Chart ....... 22
3.3 Data Analysis and the Result Comparisons with and without the Inspection Plan ............................. 22
3.4 An Example .......................................... 28
3.4.1 Data .............................................. 28
3.4.2 Estimating the in-control parameters of the Weibull distribution ............................................ 29
3.4.3 Simulation Data for Out-of-control Distribution ......................................................... 30
3.4.4 Constructing the economic X control chart and inspection plan ......................................... 31
CHAPTER 4. ECONOMIC STATISTICAL DESIGN OF THE X CHART FOR
THE PROCESS USING WEIBULL DATA........................... 33
4.1 Construction of the Economic Statistical X Chart Based on the X Sampling Distribution and Determination of the Optimum Design Parameters of the Economic Statistical X Control Chart............................................ 33
4.2 Data Analysis and Result Comparisons for the Different Out-of-control Distributions ............................ 34
CHAPTER 5. DETERMINATION OF THE INSPECTION SPECIFICATION AND
ECONOMIC STATISTICAL X CHART FOR A PROCESS WITH
WEIBULL DATA ............................................ 40
5.1 Determination of the Optimum Specification Limit and Design Parameters of the Economic Statistical X Control Chart ................................................... 40
5.2 Data Analysis and Result Comparisons with and without the Inspection Plan ..................................... 40
5.3 An Example .......................................... 47
5.3.1 Obtaining the range of the UCL and LCL............. 47
5.3.2 Constructing the economic statistical X control chart and inspection plan ..................................... 47
5.3.3 Comparison of the economic X control chart with inspection plan and the economic statistical X control chart with inspection plan............................... 49
CHAPTER 6. COSTS COMPARISON OF THE PROCESS QUALITY CONTROL
AND PRODUCT INSPECTION................................... 51
6.1 Derivation of The Expected Cycle Cost ............... 51
6.1.1 The cost for process control in the observing time OT....................................................... 51
6.1.2 The total cost for product inspection in observing time OT ................................................. 52
6.2 Data Analysis and Comparing the Results with Different In-control Weibull Distributions ........................ 53
6.2.1 Cost for process control........................... 53
6.2.2 Cost for production inspection .................... 59
6.3 Analysis for the Cost Difference..................... 64
CHAPTER 7. CONCLUSION AND RECOMMENDATIONS FOR FUTURE STUDY76
REFERENCES .............................................. 78
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