RUN-LENGTH DISTRIBUTION FOR SHEWHART CONTROL CHART WITH RUNS RULES USING FINITE MARKOV CHAIN IMBEDDING
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Shewhart developed a control chart to statistically control the production process in 1924. The classic Shewhart chart is e ective for large shifts and can be easily implemented in the real production pro- cess. However, it is not e ective for detecting small shifts. To compensate for this, a control chart with the addition of runs rules was proposed by Western Electric Company (1956). And Champ and Woodall (1987) in- troduced how to calculate the average run-length in runs rules using a method called Markov chain. We have combined runs rules to compen- sate for the shortcomings of the traditional control chart, and suggest the nite Markov chain imbedding method to get the run-length distri- bution. The Shewhart control chart with supplementary runs rules can sensitively detect small shifts in means and variances in the production process, and calculate run-length probability distribution accurately and quickly.
Abstract
Shewhart developed a control chart to statistically control the production process in 1924. The classic Shewhart chart is e ective for large shifts and can be easily implemented in the real production pro- cess. However, it is not e ective for detecting small shifts. To compensate for this, a control chart with the addition of runs rules was proposed by Western Electric Company (1956). And Champ and Woodall (1987) in- troduced how to calculate the average run-length in runs rules using a method called Markov chain. We have combined runs rules to compen- sate for the shortcomings of the traditional control chart, and suggest the nite Markov chain imbedding method to get the run-length distri- bution. The Shewhart control chart with supplementary runs rules can sensitively detect small shifts in means and variances in the production process, and calculate run-length probability distribution accurately and quickly.
참고문헌 (18)
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