TitleMonitoring and interpreting multistage and multicategory processes
NameDuran Lopez, Rodrigo Ignacio (author), Albin, Susan (chair), Elsayed, Elsayed (internal member), Chaovalitwongse, Wanpracha (internal member), Lahr, Michael (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectIndustrial and Systems Engineering,
Process control--Mathematical models,
Manufacturing processes--Quality control
DescriptionConsider processes where a transaction moves through stages and falls within a category at each stage. For example, in a tax complaint process, the stages are the steps taxpayers follow to resolve a property tax dispute from initial complaint through final resolution. The primary motivation here is customer service, although the transactions could be related to manufacturing applications as well.
The main contribution here is a method to monitor the fractions and numbers of transactions within and across stages of multistage and multicategory processes, a problem that has not been formulated before in the literature. The proposed method not only signals an out-of-control situation, it identifies accurately and easily which stages and categories are causing the disturbance, providing interpretations within and across stages of the process.
The proposed methodology works as follows: If a multinomial distribution fits the number of transactions in each category at every stage, then the process is decomposed into single stages that are monitored separately, and finally into independent binary substages with two categories. Each binary substage is characterized by a conditional probability and monitored with an independent fraction, called a tree fraction. The number of tree fractions that are monitored depends on the number of final categories, i.e., those that do not split in any further categories, not on the number of stages.
Two other contributions, summarized next, address the single stage case. Each is useful by itself, and each contributes to the method for the multistage case as well.
The first is a new two-sided CUSUM Arcsine method to monitor a process with two categories. The second is the p-tree method that monitors a multinomial process. The p-tree method not only signals an out-of-control situation, it identifies accurately which categories are causing the problem, in contrast to the widely used method in Marcucci (1985).
Future research would cover monitoring other types of multistage processes in service. An application of using probability trees to test and interpret associations in contingency tables is envisioned.
NoteIncludes bibliographical references (p. 114-120)
Noteby Rodrigo Ignacio Duran Lopez
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work