Question

13.9 The table below gives data on moisture content for specimens of a certain type of fabric. Copy the data into R to construct an x-bar chart. #Sample No. Moisture-Content Observations subsampl=c( 12.1, 12.1, 13.3, 13.0 , 13.0 ) subsamp2=c( 12.4, 13.3, 12.7, 12.6 , 12.9 ) subsamp3=CC 12.9, 12.7, 14.3, 12.5 , 12.9) subsamp4=( 13.2 , 13.0 , 13.0 , 12.6, 13.7 ) subsamp5=c 12.8 , 12.3, 12.1, 13.3, 12.0) subsamp6=( 13.4, 13.1, 12.4, 13.2 ) subsamp7=c( 12.2, 14.4, 12.4, 12.4, 12.5 ) subsamp8=( 12.6 , 12.8, 13.5, 13.9, 13.1 ) subsamp9=c 14.6, 13.4, 12.2, 13.7, 12.5 ) subsamp10=c( 12.8 , 12.3, 12.6 , 13.2, 12.8 ) subsamp11=c( 12.6, 13.1 , 12.7, 13.2, 12.3 ) subsamp12=c( 13.5, 12.5, 12.8 , 13.1 , 12.9) subsamp13=c( 13.4, 13.3, 12.0, 12.9, 13.1 ) subsamp14=c( 13.5, 12.4, 13.0 , 13.6 , 13.4 ) subsamp15=c( 12.3, 12.8, 13.0 , 12.8 , 13.5) subsamp16=c( 12.6 , 13.4, 12.1 , 13.2, 13.5) subsamp17=c( 12.1, 12.7, 13.4, 13.0 , 13.9) subsamp18=c( 13.0 , 12.8, 13.0 , 13.3, 13.1 ) subsamp19=C( 12.4, 13.2 , 13.0 , 14.0 , 13.1 ) subsamp20=c( 12.7, 12.4, 12.4, 13.9, 12.8) subsamp21=c( 12.6 , 12.8 , 12.7, 13.4, 13.0) subsamp22=c( 12.7, 13.4, 12.1 , 13.2, 13.3 ) # Combine the rows of sub samples into a data frame. # This structures data appropriately for control chart functions. moisture_content = data.frame(rbind(subsamp1, subsamp2, subsamp3,subsamp4,subsamp5,subsamp6, subsamp7, subsamp8,subsamp9, subsamp10, subsamp11, subsamp12, subsamp13, subsamp14, subsamp15, subsamp16, subsamp17, subsamp18, subsamp19, subsamp20, subsamp21, subsamp22)) # Check out the data frame moisture_content # Check subgroup means rowMeans(moisture_content) # If you have not already, install the qcc package in R. Skip this line otherwise. install.packages("acc") # Open the library of commands from the qcc package. library("acc") # Create x-bar - s chart qcc(moisture_content, type "xbar")

Answer 1

On R.H.S. is R code and on L.H.S. is R-output.

> moisture_content = data.frame (rbind (subsampl, subsamp2, subsamp3, + subsamp4, subsamp5, subsamp6, subsamp7, subsamp8, subsamp9, subsamplo, + subsampli, subsampl2, subsampl3, subsampl4, subsamp15, + subsampl6, subsamp17, subsamp18, subsamp19, subsamp20, subsamp21, subsamp22)) > # Check subgroup means > rowMeans (moisture_content) subsampl subsamp2 subsamp3 subsamp4 subsamp5 subsamp 6 subsamp7 subsamp8 12.66 12.86 13.06 13.14 12.50 13.20 12.78 13.18 subsamp9 subsampl0 subsampll subsamp12 subsamp13 subsamp14 subsamp15 subsampl6 13.22 12.74 12.78 12.94 12.94 13.18 12.88 12.88 subsampl7 subsamp18 subsamp19 subsamp20 subsamp21 subsamp22 13.02 13.04 13.14 12.84 12.90 12.98 > library (gcc) qcc (moisture_content, type = "xbar") List of 11 $ call :language acc (data = moisture_content, type = "xbar") $ type chr "xbar" $ data.name : chr "moisture_content" $ data num [1:22, 1:5] 12.1 12.6 12.9 13.2 12.8 13.9 12.2 12.6 14.6 12.$ ..- attr(", "dimnames")=List of 2 $ statistics: Named num [1:22] 12.7 12.9 13.1 13.1 12.5 ..- attr(", "names")= chr [1:22] "subsampl" "subsamp2" "subsamp3" "subsamp 4" $ $ sizes : Named int [1:22] 5 5 5 5 5 5 5 5 5 5 ... ..- attr(*, "names")= chr [1:22] "subsampl" "subsamp2" "subsamp3" "subsamp4" $ $ center num 12.9 $ std.dev num 0.569 $ nsigmas num 3 $ limits num [1, 1:2) 12.2 13.7 ..- attr(*, "dimnames")=List of 2 $ violations: List of 2 - attr(", "class")= chr "acc" R Untitled - R Editor subsampl=c(12.1, 12.1, 13.1, 13.0, 13.0) subsamp2=c( 12.6, 13.3, 12.9, 12.6, 12.9) subsamp3=c(12.9, 12.7, 14.3, 12.5, 12.9) subsamp4=c( 13.2, 13.0, 13.0, 12.6, 13.9) subsamp5=c( 12.8, 12.3, 12.1, 13.3, 12.0) subsamp6=c( 13.9, 13.4, 13.1, 12.4, 13.2) subsamp 7=c( 12.2, 14.4, 12.4, 12.4, 12.5) subsamp8=c( 12.6, 12.8, 13.5, 13.9, 13.1) subsamp9=c( 14.6, 13.4, 12.2, 13.7, 12.2 ) subsamp10=c( 12.8, 12.3, 12.6, 13.2, 12.8) subsampll=c( 12.6, 13.1, 12.7, 13.2, 12.3) subsampl2=c( 13.5, 12.4, 12.8, 13.1, 12.9) subsamp13=c( 13.4, 13.3, 12.0, 12.9, 13.1) subsampl4=c( 13.5, 12.4, 13.0, 13.6, 13.4) subsamp15=c( 12.3, 12.8, 13.0, 12.8, 13.5) subsamp16=c( 12.6, 13.4, 12.1, 13.2, 13.1) subsamp17=c( 12.1, 12.7, 13.4, 13.0, 13.9) subsampl8=c( 13.0, 12.8, 13.0, 13.3, 13.1) subsamp19=C( 12.4, 13.2, 13.0, 14.0, 13.1) subsamp20=c( 12.7, 12.4, 12.4, 13.9, 12.8) subsamp2l=c( 12.6, 12.8, 12.7, 13.4, 13.0) subsamp22=c( 12.7, 13.4, 12.1, 13.2, 13.5) moisture content = data.frame (rbind (subsampl, subsamp2, subsamp3, subsamp4, subsamp5, subsamp6, subsamp7, subsamp8, subsamp9, subsamplo, subsampli, subsamp12, subsamp13, subsampl4, subsamp15, subsamp16, subsamp17, subsamp|18, subsamp19, subsamp20, subsamp21, subsamp22 # Check subgroup means rowMeans (moisture_content) library (cc) qcc (moisture_content, type = "xbar") .. : : . >

RR Graphics: Device 2 (ACTIVE) xbar Chart for moisture_content HUCL 13.5 Group summary statistics 13.0 CL MA 12.5 LCL subsampl subsamp5 subsamp9 subsamp13 subsamp17 subsamp21 Group Number of groups = 22 Center = 12.94818 StdDev = 0.5686704 LCL = 12.18523 UCL = 13.71113 Number beyond limits = 0 Number violating runs = 0

We have

1)

T = 12.94818 LCL = 12.18523 UCL= 13.71113

The control chart is given above. Hence option (c) is correct.

All the points are between the control limits, so the process appears to be in control.