6 ms·

Draw an control chat with your data. Here is one for your initial example: http://beza1e1.tuxen.de/spc?data=1,2,3,4,5,6,7,8,9,10,100 http://beza1e1.tuxen.de/spc

by qznc 3y ago

Draw an control chat with your data. Here is one for your initial example: http://beza1e1.tuxen.de/spc?data=1,2,3,4,5,6,7,8,9,10,100 http://beza1e1.tuxen.de/spc?data=1,2,3,4,5,6,7,8,9,10,100 It is immediately obvious that it is not a stable process.

kqr 3y ago
I think GPs point is that there are software processes that are fundamentally stable but still generate values like that. I'm in the process of writing an article on that topic, because it annoys me I don't have a good answer.
fjkdlsjflkds 3y ago
Ok. So, let's try again... First, let's draw some data and show that the sample mean is not roughly close to the sample median: > data <- asinh(exp(rnorm(30))) > mean(data) [1] 1.227973 > median(data) [1] 1.059046 > sum(as.numeric(data > mean(data)))/length(data) [1] 0.4 Now you can take the dataset and make a control chart with it: > cat(paste0(data,collapse=",")) 0.397291781860484,1.01791591678607,2.29127398581896,0.317548192016798,0.825779972770721,0.978034869623426,1.45689922574378,0.722379000865545,2.68231132467641,0.786713029297768,1.20492120955161,1.7082762081373,0.632259821911453,0.346590855307735,2.48238023470879,0.0989934260605276,1.61233320755675,0.906918026775941,1.73743152912329,1.21715325934946,2.78776306537914,0.296838101056961,2.29303061152949,2.65277514999252,0.88486942904647,0.0860402641329708,1.255123685342,0.526097043743278,1.53307173756969,1.10017654868633 https://beza1e1.tuxen.de/spc?data=0.397291781860484,1.01791591678607,2.29127398581896,0.317548192016798,0.825779972770721,0.978034869623426,1.45689922574378,0.722379000865545,2.68231132467641,0.786713029297768,1.20492120955161,1.7082762081373,0.632259821911453,0.346590855307735,2.48238023470879,0.0989934260605276,1.61233320755675,0.906918026775941,1.73743152912329,1.21715325934946,2.78776306537914,0.296838101056961,2.29303061152949,2.65277514999252,0.88486942904647,0.0860402641329708,1.255123685342,0.526097043743278,1.53307173756969,1.10017654868633 https://beza1e1.tuxen.de/spc?data=0.397291781860484,1.017915... Looks like the data is "stable" (according to that website) and, yet, you get a 40/60 split, rather than a 50/50 split.
- qznc 3y ago
  I guess the next step in our discussion is if 40/60 is „roughly half“?
  - fjkdlsjflkds 3y ago
    Oh. I didn't understand that "roughly" was supposed to be doing all the work, in this context. I guess a 30/70 split is also "roughly" a 50/50 split, right? Example: > cat(paste0(data,collapse=",")) 0.194377163769996,0.0102070939265764,0.309119108211189,0.0120786780598317,1.45982220742052,0.00158028772404075,0.035004295275816,0.329022291919098,-0.00635736453948977,0.0158683345454085,1.19240981895862,-0.0127659220845804,-0.00650696353310367,0.00716707476017206,1.85868411217008,0.374960693228966,0.114533107998102,0.591872380192402,0.469305862127421,0.60161713700353,0.000421158731442352,0.265325485949535,-0.00279113302976559,0.0168217608051942,-0.00654584643918818,0.701343388607726,1.84387017506994,-0.00461644730360566,0.0781831777299275,1.05989990859088 https://beza1e1.tuxen.de/spc?data=0.194377163769996,0.0102070939265764,0.309119108211189,0.0120786780598317,1.45982220742052,0.00158028772404075,0.035004295275816,0.329022291919098,-0.00635736453948977,0.0158683345454085,1.19240981895862,-0.0127659220845804,-0.00650696353310367,0.00716707476017206,1.85868411217008,0.374960693228966,0.114533107998102,0.591872380192402,0.469305862127421,0.60161713700353,0.000421158731442352,0.265325485949535,-0.00279113302976559,0.0168217608051942,-0.00654584643918818,0.701343388607726,1.84387017506994,-0.00461644730360566,0.0781831777299275,1.05989990859088 https://beza1e1.tuxen.de/spc?data=0.194377163769996,0.010207... > sum(as.numeric(data > mean(data)))/length(data) [1] 0.3 > mean(data) [1] 0.3834637 > median(data) [1] 0.09635814 Would you say that the mean and the median are "roughly" the same, in this context? I'm curious...
    - kqr 3y ago
      Now this is getting interesting. I did not think there existed a data set with these properties! I don't have a computer at hand, but if you bootstrap from that population, in how many cases are the XmR limits violated? If it's more than, say, 15 %, I would not consider that distribution stable in the SPC sense, and thus not really a counter-example. Edit: I found a computer with R: > mean(replicate(5000, signal(sample(xx, length(xx), replace=T)))) [1] 0.514 This implies a false positive rate of 98 %, so I'd reconsider using XmR charts with this distribution.

by qznc 3y ago

kqr 3y ago

I think GPs point is that there are software processes that are fundamentally stable but still generate values like that. I'm in the process of writing an article on that topic, because it annoys me I don't have a good answer.

fjkdlsjflkds 3y ago

Ok. So, let's try again... First, let's draw some data and show that the sample mean is not roughly close to the sample median: > data <- asinh(exp(rnorm(30))) > mean(data) [1] 1.227973 > median(data) [1] 1.059046 > sum(as.numeric(data > mean(data)))/length(data) [1] 0.4 Now you can take the dataset and make a control chart with it: > cat(paste0(data,collapse=",")) 0.397291781860484,1.01791591678607,2.29127398581896,0.317548192016798,0.825779972770721,0.978034869623426,1.45689922574378,0.722379000865545,2.68231132467641,0.786713029297768,1.20492120955161,1.7082762081373,0.632259821911453,0.346590855307735,2.48238023470879,0.0989934260605276,1.61233320755675,0.906918026775941,1.73743152912329,1.21715325934946,2.78776306537914,0.296838101056961,2.29303061152949,2.65277514999252,0.88486942904647,0.0860402641329708,1.255123685342,0.526097043743278,1.53307173756969,1.10017654868633 https://beza1e1.tuxen.de/spc?data=0.397291781860484,1.01791591678607,2.29127398581896,0.317548192016798,0.825779972770721,0.978034869623426,1.45689922574378,0.722379000865545,2.68231132467641,0.786713029297768,1.20492120955161,1.7082762081373,0.632259821911453,0.346590855307735,2.48238023470879,0.0989934260605276,1.61233320755675,0.906918026775941,1.73743152912329,1.21715325934946,2.78776306537914,0.296838101056961,2.29303061152949,2.65277514999252,0.88486942904647,0.0860402641329708,1.255123685342,0.526097043743278,1.53307173756969,1.10017654868633 https://beza1e1.tuxen.de/spc?data=0.397291781860484,1.017915... Looks like the data is "stable" (according to that website) and, yet, you get a 40/60 split, rather than a 50/50 split.

qznc 3y ago
I guess the next step in our discussion is if 40/60 is „roughly half“?
- fjkdlsjflkds 3y ago
  Oh. I didn't understand that "roughly" was supposed to be doing all the work, in this context. I guess a 30/70 split is also "roughly" a 50/50 split, right? Example: > cat(paste0(data,collapse=",")) 0.194377163769996,0.0102070939265764,0.309119108211189,0.0120786780598317,1.45982220742052,0.00158028772404075,0.035004295275816,0.329022291919098,-0.00635736453948977,0.0158683345454085,1.19240981895862,-0.0127659220845804,-0.00650696353310367,0.00716707476017206,1.85868411217008,0.374960693228966,0.114533107998102,0.591872380192402,0.469305862127421,0.60161713700353,0.000421158731442352,0.265325485949535,-0.00279113302976559,0.0168217608051942,-0.00654584643918818,0.701343388607726,1.84387017506994,-0.00461644730360566,0.0781831777299275,1.05989990859088 https://beza1e1.tuxen.de/spc?data=0.194377163769996,0.0102070939265764,0.309119108211189,0.0120786780598317,1.45982220742052,0.00158028772404075,0.035004295275816,0.329022291919098,-0.00635736453948977,0.0158683345454085,1.19240981895862,-0.0127659220845804,-0.00650696353310367,0.00716707476017206,1.85868411217008,0.374960693228966,0.114533107998102,0.591872380192402,0.469305862127421,0.60161713700353,0.000421158731442352,0.265325485949535,-0.00279113302976559,0.0168217608051942,-0.00654584643918818,0.701343388607726,1.84387017506994,-0.00461644730360566,0.0781831777299275,1.05989990859088 https://beza1e1.tuxen.de/spc?data=0.194377163769996,0.010207... > sum(as.numeric(data > mean(data)))/length(data) [1] 0.3 > mean(data) [1] 0.3834637 > median(data) [1] 0.09635814 Would you say that the mean and the median are "roughly" the same, in this context? I'm curious...
  - kqr 3y ago
    Now this is getting interesting. I did not think there existed a data set with these properties! I don't have a computer at hand, but if you bootstrap from that population, in how many cases are the XmR limits violated? If it's more than, say, 15 %, I would not consider that distribution stable in the SPC sense, and thus not really a counter-example. Edit: I found a computer with R: > mean(replicate(5000, signal(sample(xx, length(xx), replace=T)))) [1] 0.514 This implies a false positive rate of 98 %, so I'd reconsider using XmR charts with this distribution.