Cumulative sum charts for monitoring the COM-Poisson processes
Cumulative sum charts for monitoring the COM-Poisson processes
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DOI：
10.1016/j.cie.2013.12.004
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发表时间：
2014-02
期刊：
影响因子：
--
通讯作者：
A. Saghir;Zhengyan Lin
中科院分区：
文献类型：
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作者：
A. Saghir;Zhengyan Lin
COM-泊松分布概括了标准泊松分布，允许欠离散或过度离散。它用于对制造过程中不合格产品过度或不足分散的缺陷计数进行建模。 COM-泊松分布有两个参数；速率参数 (μ) 和色散参数 (ν)。本研究提出了三种基于速率参数、离散参数或两者的累积和 (CUSUM) 控制图来检测偏移。两个控制图（即 μ-CUSUM 和 ν-CUSUM）分别检测两个参数之一的偏移，而单个 CUSUM 图（即 s-CUSUM）同时考虑两个参数的偏移。所提出的 μ-CUSUM 图对于过度分散或欠分散的数据非常灵活，并将伯努利图、泊松图和几何 CUSUM 图概括为其特殊情况。所提出的图表的性能已根据平均信号数 (ANOS) 进行了评估，并与 Sellers (2012) 图表进行了比较。性能比较表明，灵活且广义的 μ-CUSUM 图比 Sellers (2012) 图更好地检测泊松参数的小到中等变化。 ν-CUSUM 能够很好地检测色散参数中小到中等的变化。对CUSUM图的性能评估表明，当两个参数都增加（减少）时效果更好，但如果一个参数增加（减少）而其他参数减少（增加）则效果很差。给出了两个数值示例来演示所提出的图表在实际数据集上的应用。
The COM-Poisson distribution generalizes the standard Poisson distribution, allowing for under- or over-dispersion. It is used to model defect counts in manufacturing processes with over- or under-dispersed non-conforming products. The COM-Poisson distribution has two parameters; the rate parameter (μ) and dispersion parameter (ν). This study proposes three kinds of cumulative sum (CUSUM) control charts based on either the rate parameter, dispersion parameter, or both to detect shifts. Two control charts, namely,μ-CUSUM andν-CUSUM detect shift respectively on one of two parameters, while a single CUSUM chart, namely,s-CUSUM considers the shift in both parameters at once. The proposedμ-CUSUM chart is flexible for over- or under-dispersed data and generalizes the Bernoulli, the Poisson and the geometric CUSUM charts as its special cases. The performance of the proposed charts have been evaluated in terms of average number of signals (ANOS) and compared with the Sellers (2012) chart. The performance comparison shows that the flexible and generalizedμ-CUSUM chart is better to detect small to moderate shifts in thePoissonparameter than the Sellers (2012) chart. Theν-CUSUM performs very well to detect small to moderate shifts in thedispersionparameter. The performance evaluations of thes-CUSUM chart showed that, it works better when both of the parameter increases (decreases), but very poorly if one parameter increases (decreases) and other parameter decreases (increases). Two numerical examples are given to demonstrate the application of the proposed charts on practical data sets.