xshewhartrunsrules.arl(spc)
xshewhartrunsrules.arl()所属R语言包：spc
Compute ARLs of Shewhart control charts with and without runs rules
休哈特控制图的运行规则和计算连串长度
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Computation of the (zero-state and steady-state) Average Run Length (ARL) for Shewhart control charts with and without runs rules
（零状态和稳定状态）的平均运行长度（ARL）和休哈特控制图的运行规则计算
用法----------Usage----------
xshewhartrunsrules.crit(L0, mu = 0, type = "12")
xshewhartrunsrules.ad(mu1, mu0 = 0, c = 1, type = "12")
参数----------Arguments----------
参数：mu
true mean.
真正的意思。
参数：L0
pre-defined in-control ARL, that is, determine c so that the mean number of observation until a false alarm is L0.
预先定义的控制ARL，也就是确定c“这样的平均数观察，直到一场虚惊L0。
参数：mu1, mu0
for the steady-state ARL two means are specified, mu0 is the in-control one and usually equal to 1, and mu1 must be given.
MU0稳态ARL两个指定装置，是在控制一个，通常等于1，MU1，必须给予。
参数：c
normalizing constant to ensure specific alarming behavior.
标准化常数，以确保特定的惊人行为。
参数：type
controls the type of Shewhart chart used, seed details section.
控制类型的休哈特图，种子细节部分。
Details
详细信息----------Details----------
xshewhartrunsrules.arl determines the zero-state Average Run Length (ARL) based on the Markov chain approach given in Champ and Woodall (1987). xshewhartrunsrules.matrix provides the corresponding transition matrix that is also used in xDshewhartrunsrules.arl (ARL for control charting drift). xshewhartrunsrules.crit allows to find the normalization constant c to attain a fixed in-control ARL. Typically this is needed to calibrate the chart. With xshewhartrunsrules.ad the steady-state ARL is calculated. With the argument type certain runs rules could be set. The following list gives an overview.
xshewhartrunsrules.arl确定的零状态的平均运行长度（ARL）的马尔可夫链方法在冠军和伍德尔（1987）。 xshewhartrunsrules.matrix提供相应的过渡矩阵，它也被用在xDshewhartrunsrules.arl（ARL控制图表漂移）。 xshewhartrunsrules.crit可以找到归一化常数c达到一个固定的控制ARL。通常，这是需要校准的图表。 xshewhartrunsrules.ad的稳态ARL的计算方法。参数type可以设置一定的运行规则。下面的列表给出了一个概述。
"1"The classical Shewhart chart with +/- 3 c sigma control limits (c is typically equal to 1 and can be changed by the argument c).
“1”经典的休哈特图+/- 3 c sigma控制界限（c是通常等于1，可以改变参数c）。
"12"The classic and the following runs rule: 2 of 3 are beyond +/- 2 c sigma on the same side of the chart.
“12”经典的和下面的运行规则：2 3超出+/- 2 c sigma在同一侧的图表。
"13"The classic and the following runs rule: 4 of 5 are beyond +/- 1 c sigma on the same side of the chart.
“13”经典的和下面的运行规则：4超出+/- 1 c sigma在同一侧的图表。
"14"The classic and the following runs rule: 8 of 8 are on the same side of the chart (referring to the center line).</ul>
“14”经典的和下面的运行规则：8 8（指的中心线）的同一侧上的图表。</微升>
值----------Value----------
Returns a single value which resembles the zero-state or steady-state ARL.
返回一个值，类似于零状态或稳态ARL。
（作者）----------Author(s)----------
Sven Knoth
参考文献----------References----------
C. W. Champ and W. H. Woodall (1987), Exact results for Shewhart control charts with supplementary runs rules, Technometrics 29, 393-399.
参见----------See Also----------
xDshewhartrunsrules.arl for zero-state ARL of Shewhart control charts with or without runs rules under drift.
xDshewhartrunsrules.arl休哈特控制图ARL的运行规则下的漂移带或不带零状态。
实例----------Examples----------
## Champ/Woodall (1987)[＃冠军/伍德尔（1987）]
## Table 1[＃1]
mus <- (0:15)/5
Mxshewhartrunsrules.arl <- Vectorize(xshewhartrunsrules.arl, "mu")
# standard (1 of 1 beyond 3 sigma) Shewhart chart without runs rules[没有运行规则的标准（超过3 1 1Σ）休哈特图]
C1 <- round(Mxshewhartrunsrules.arl(mus, type="1"), digits=2)
# standard + runs rule: 2 of 3 beyond 2 sigma on the same side[标准+运行规则：（3）超过2个标准差的同一侧]
C12 <- round(Mxshewhartrunsrules.arl(mus, type="12"), digits=2)
# standard + runs rule: 4 of 5 beyond 1 sigma on the same side[标准+运行规则：4超过1西格玛的同一侧]
C13 <- round(Mxshewhartrunsrules.arl(mus, type="13"), digits=2)
# standard + runs rule: 8 of 8 on the same side of the center line[标准+中心线的同一侧的运行规则：8 8]
C14 <- round(Mxshewhartrunsrules.arl(mus, type="14"), digits=2)
## original results are[＃原结果]
# mus C1 C12 C13 C14 [亩C1 C12 C13 C14]
# 0.0 370.40 225.44 166.05 152.73 [0.0 370.40 225.44 166.05 152.73]
# 0.2 308.43 177.56 120.70 110.52 [0.2 308.43 177.56 120.70 110.52]
# 0.4 200.08 104.46 63.88 59.76 [0.4 200.08 104.46 63.88 59.76]
# 0.6 119.67 57.92 33.99 33.64 [0.6 119.67 57.92 33.99 33.64]
# 0.8 71.55 33.12 19.78 21.07 [0.8 71.55 33.12 19.78 21.07]
# 1.0 43.89 20.01 12.66 14.58 [1.0 43.89 20.01 12.66 14.58]
# 1.2 27.82 12.81 8.84 10.90 [1.2 27.82 12.81 8.84 10.90]
# 1.4 18.25 8.69 6.62 8.60 [1.4 18.25 8.69 6.62 8.60]
# 1.6 12.38 6.21 5.24 7.03 [1.6 12.38 6.21 5.24 7.03]
# 1.8 8.69 4.66 4.33 5.85 [1.8 8.69 4.66 4.33 5.85]
# 2.0 6.30 3.65 3.68 4.89 [2.0 6.30 3.65 3.68 4.89]
# 2.2 4.72 2.96 3.18 4.08 [2.2 4.72 2.96 3.18 4.08]
# 2.4 3.65 2.48 2.78 3.38 [2.4 3.65 2.48 2.78 3.38]
# 2.6 2.90 2.13 2.43 2.81 [2.6 2.90 2.13 2.43 2.81]
# 2.8 2.38 1.87 2.14 2.35 [2.8 2.38 1.87 2.14 2.35]
# 3.0 2.00 1.68 1.89 1.99[3.0 2.00 1.68 1.89 1.99]
data.frame(mus, C1, C12, C13, C14)
## plus calibration, i. e. L0=250 (the maximal value for "14" is 255![＃加校准。 E。 L0 = 250（最大为“14”的值是255！]
L0 <- 250
c1 <- xshewhartrunsrules.crit(L0, type = "1")
c12 <- xshewhartrunsrules.crit(L0, type = "12")
c13 <- xshewhartrunsrules.crit(L0, type = "13")
c14 <- xshewhartrunsrules.crit(L0, type = "14")
C1 <- round(Mxshewhartrunsrules.arl(mus, c=c1, type="1"), digits=2)
C12 <- round(Mxshewhartrunsrules.arl(mus, c=c12, type="12"), digits=2)
C13 <- round(Mxshewhartrunsrules.arl(mus, c=c13, type="13"), digits=2)
C14 <- round(Mxshewhartrunsrules.arl(mus, c=c14, type="14"), digits=2)
data.frame(mus, C1, C12, C13, C14)
## and the steady-state ARL[＃和稳态ARL]
Mxshewhartrunsrules.ad <- Vectorize(xshewhartrunsrules.ad, "mu1")
C1 <- round(Mxshewhartrunsrules.ad(mus, c=c1, type="1"), digits=2)
C12 <- round(Mxshewhartrunsrules.ad(mus, c=c12, type="12"), digits=2)
C13 <- round(Mxshewhartrunsrules.ad(mus, c=c13, type="13"), digits=2)
C14 <- round(Mxshewhartrunsrules.ad(mus, c=c14, type="14"), digits=2)
data.frame(mus, C1, C12, C13, C14)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 14:34:19
