Optimal design of the double sampling chart with estimated parameters based on median run length
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- 作者：W.L. Teoh ; Michael B.C. Khoo ; Philippe Castagliola ; S. Chakraborti
- 关键词：Conditional run length ; Double sampling (DS) X¯ ; chart ; Optimal design ; Parameter estimation ; Statistical process control ; Unconditional run length
- 刊名：Computers and Industrial Engineering
- 出版年：January, 2014
- 年：2014
- 卷：67
- 期：Complete
- 页码：104-115
- 全文大小：1178 K
文摘
The double sampling (DS) chart when the process parameters are unknown and have to be estimated from a reference Phase-I dataset is studied. An expression for the run length distribution of the DS chart is derived, by conditioning and taking parameter estimation into account. Since the shape and the skewness of the run length distribution change with the magnitude of the mean shift, the number of Phase-I samples and sample sizes, it is shown that the traditional chart鈥檚 performance measure, i.e. the average run length, is confusing and not a good representation of a typical chart鈥檚 performance. To this end, because the run length distribution is highly right-skewed, especially when the shift is small, it is argued that the median run length (MRL) provides a more intuitive and credible interpretation. From this point of view, a new optimal design procedure for the DS chart with known and estimated parameters is developed to compute the chart鈥檚 optimal parameters for minimizing the out-of-control MRL, given that the values of the in-control MRL and average sample size are fixed. The optimal chart which provides the quickest out-of-control detection speed for a specified shift of interest is designed according to the number of Phase-I samples commonly used in practice. Tables are provided for the optimal chart parameters along with some empirical guidelines for practitioners to construct the optimal DS charts with estimated parameters. The optimal charts with estimated parameters are illustrated with a real application from a manufacturing company.