Cumulative Quantity Control Chart and Maintenance Strategies for Industrial Processes

This dissertation, "Cumulative Quantity Control Chart and Maintenance Strategies for Industrial Processes" by Jintao, Ouyang, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis titled Cumulative Quantity Control Chart and Maintenance Strategies for Industrial Processes submitted by Ouyang Jintao for the degree of Master of Philosophy at the University of Hong Kong in December 2004 It is well-known that the commonly used c-chart and u-chart are unsatis- factory for monitoring high-yield processes with low nonconforming rate. To overcome this difficulty, one may use statistical process control methods de- veloped based on the quantity of product inspected until r nonconformities are observed. The cumulative quantity control chart (CQC chart) is an ex- ample. A CQC chart with a small value of r requires to inspect less quantity of product in order to obtain an out-of-control signal, but is less sensitive in detecting shifts of nonconforming rate than a CQC chart with a large value of r. Most control charts available in the literature are one-stage control proce- dures in which a decision is made when an out-of-control signal appears. In the present thesis, inspired by the concept of double sampling procedures in acceptance sampling, a 2-stage CQC chart is proposed to gain the advantages of the one-stage CQC charts with r =1;2. In contrary to the usual approach ofnumericalverificationintheliterature, acontributionofthisthesisistopro- iivide an analytic proof of a theoretical result that compares the discrimination power of three types of CQC charts to detect shift in the process nonconform- ing rate. Economic design of the CQC charts is also considered. Numerical examples are given to illustrate that under different circumstances, the high- est economic gain can be achieved by using different CQC charts or not using statistical process control at all. In the literature, statistical control chart and maintenance of production systems have been considered separately as two topics. Combining the ratio- nales of statistical process control and maintenance will provide an effective approach for control and improvement of the production processes. In Part Two of this thesis, the economic design of cumulative control chart is applied to the maintenance strategies on a continuous production system. It is as- sumedthesystemhasthreedifferentstates: normalstate, slightlydeteriorated state and seriously deteriorated state. Two kinds of maintenance actions are available: minor maintenance and major maintenance. In this model, the sys- tem can stochastically change from one state to another instantly, where the time to occurrence of state transition follows exponential distribution. The plotting zone of the cumulative quantity control chart is divided into three different zones to give different types of signals for indicating different states of the system. Investigation errors are also considered in this thesis. Under such assumption, special cases can be covered, such as the case where only major maintenance is available and the case where slight deterioration can only be detected by major investigation. Finally, the economic plan of this iiimaintenance model is made by minimizing the average cost per unit quantity of product produced taking into account four kinds of costs. A numerical ex- ample is given to indicate how to select the appropriate control limits for cost minimization. iv DOI: 10.5353/th_b3112118 Subjects: Process control - Statistical methodsProduction management - Statistical methods