当前位置: X-MOL 学术Qual. Reliab. Eng. Int. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the design of nonparametric runs‐rules schemes using the Markov chain approach
Quality and Reliability Engineering International ( IF 2.3 ) Pub Date : 2020-03-26 , DOI: 10.1002/qre.2648
Sandile C. Shongwe 1
Affiliation  

The aim of this paper is to highlight some concerns about the partly inaccurate manner in which the currently available 2‐of‐2 and 2‐of‐3 simple and improved runs‐rules charts based on the sign and the signed‐rank statistics were designed using Markov chain matrix. Because of the memory‐less property of the Markov chains, the empirical average run‐length (ARL) values were not affected; but the design structure of the matrix makes it difficult to formulate the general expressions of the ARL explicitly. Also, the dimension (and consequently, the simplicity) of the transition probability matrices (TPMs) and the false alarm rates expressions were affected negatively. Thus, we present some zero‐ and steady‐state formulae that make it easier to construct some key elements of the run‐length distribution (including the TPMs) of the simple and improved 2‐of‐(H + 1) runs‐rules charts based on the sign and the signed‐rank statistics, for any positive integer value H > 0, not just H = 1 and 2, as currently available for these monitoring schemes, so that any interested reader may use these formulae to obtain the corresponding empirical study.

中文翻译:

关于使用马尔可夫链方法的非参数行程规则方案的设计

本文的目的是强调一些关于部分不准确的担忧,这些问题是基于符号和正负号统计设计当前可用的2之23之2简单和改进的运行规则图表而设计的使用马尔可夫链矩阵。由于马尔可夫链的无记忆特性,经验平均游程长度(ARL)值不受影响;但是矩阵的设计结构使其难以表达ARL的一般表达式明确地。此外,转换概率矩阵(TPM)的尺寸(以及因此的简单性)和错误警报率表达式也会受到负面影响。因此,我们提出了一些零和稳态公式,这些公式使构建简单且经过改进H + 1)游程规则图表2的游程长度分布(包括TPM)的一些关键元素变得更加容易根据符号和正负号统计,对于任何正整数值H > 0,不仅限于H = 1和2,如当前可用于这些监视方案的信息,以便任何感兴趣的读者都可以使用这些公式获得相应的经验值研究。
更新日期:2020-03-26
down
wechat
bug