Economic Design of x-Control Charts under Weibull Shock Models

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Advanced Statistical Process Monitoring Reliability and Maintenance Optimization Fault Detection and Control Systems

Abstract

In this article, a moditied version of Duncan's (1956) model for the economic design of -control charts is extended to deal with situations involving the Weibull shock model. In the traditional Duncan approach to Markovian shock models, the length of sampling intervals is kept constant. When the process-failure mechanism follows a Weibull model or some other model having an increasing hazard rate. however, it may be desirable to have the frequency of sampling increased with the age of the system. This study proposes a cost model that uses variable sampling intervals as opposed to sampling intervals of fixed length. The computational results indicate that the proposed model under variable sampling intervals provides a lower cost than those obtained by using the existing model developed by Hu (1984) for a Welbull shock model having sampling intervals of fixed length.

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References

1956The Economic Design of X Charts Used to Maintain Current Control of a Process 1986The Economic Design of Control Charts: A Unified Approach 1980The Economic Design of Control Charts: A Review and Literature Survey

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2000Effect of maintenance on the economic design of x-control chart 2004An integrated systems approach to process control and maintenance 1994JOINT DETERMINATION OF PRODUCTION QUANTITY, INSPECTION SCHEDULE, AND CONTROL CHART DESIGN 1993A generalized model for the economic design of ??control charts for production systems with increasing failure rate and early replacement 2000Combining preventive maintenance and statistical process control: a preliminary investigation 1992THE USE OF STATISTICAL PROCESS CONTROL AND DESIGN OF EXPERIMENTS IN PRODUCT AND PROCESS IMPROVEMENT 1999Integrated production maintenance and quality model for imperfect processes 1999Economic Design of a Variable Sampling Rate X Chart

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