Title page for ETD etd-03022010-020326


Type of Document Dissertation
Author Hsu, Margaretha Mei-Ing
URN etd-03022010-020326
Title Economically optimum design of cusum charts when there is a multiplicity of assignable causes.
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Reynolds, Marion R. Jr. Committee Chair
Hinkelmann, Klaus H. Committee Member
Kramer, Clyde Y. Committee Member
Myers, Raymond H. Committee Member
Schmidt, J. William Committee Member
Keywords
  • cost models
  • cumulative sum charts
Date of Defense 1978-10-05
Availability restricted
Abstract
This study is concerned with the design of cumulative sum charts based on a minimum cost criterion when there are multiple assignable causes occurring randomly, but with known effect. A cost model is developed that relates the design parameters (i.e. sampling interval, decision limit, reference value and sample size) of a cusum chart and the cost and risk factors of the process to the long run average loss cost per hour for the process. Optimum designs for various sets of cost and risk factors are found by minimizing the long run average loss-cost per hour of the process with respect to the design parameters of a cusum chart. Optimization is accomplished by use of Brown's method. A modified Brownian motion approximation is used for calculating ARLs in the cost model.

The nature of the loss-cost function is investigated numerically. The effects of changes in the design parameters and in the cost and risk factors are also studied. An investigation of the limiting behavior of the loss-cost function as the decision limit approaches infinity reveals that in some cases there exist some points that yield a lower loss-cost than that of the local minimum obtained by Brown's method. It is conjectured that if the model is extended to include more realistic assumption about the occurrence of assignable causes then only the local minimum solutions will remain.

This paper also shows that the multiple assignable cause model can be well approximated by a matched single cause model. Then in practice it may be sufficient to find the optimum design for the matched. single cause model.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
[VT] LD5655.V856_1978.H88.pdf 2.75 Mb 00:12:43 00:06:32 00:05:43 00:02:51 00:00:14
[BTD] next to an author's name indicates that all files or directories associated with their ETD are accessible from the Virginia Tech campus network only.

Browse All Available ETDs by ( Author | Department )

dla home
etds imagebase journals news ereserve special collections
virgnia tech home contact dla university libraries

If you have questions or technical problems, please Contact DLA.