#######################################################
# Name: Rahul Sachan
#
# Roll No: MA14C035
#
# Subject : Applied Statistics
#Assignment on Quality Control
#
#*******************Assignment**************************************
library(qcc)
## Warning: package 'qcc' was built under R version 3.3.3
## Package 'qcc', version 2.6
## Type 'citation("qcc")' for citing this R package in publications.
rm(list = ls())
##we will use data from given file
d1= read.csv("D:/R/AssignmentCSV.csv")
d2= read.csv("D:/R/AssignmentCSV2.csv")
d3= read.csv("D:/R/AssignmentCSV3.csv")
#Question -1
d1.df=data.frame(d1)
A=matrix(0,90,1)
A=data.frame(A)
for(i in 1:30){
for(j in 1:3){
A[3*i-3+j,1]=d1.df[i,j]
}
}
batch=rep(1:30,each=3)
E=data.frame(A,batch)
dim(E)
## [1] 90 2
d1data=qcc.groups(E$A,E$batch)
d1data
## [,1] [,2] [,3]
## 1 64.010 63.989 63.990
## 2 64.015 64.008 63.993
## 3 63.982 63.984 63.995
## 4 63.988 64.024 64.021
## 5 64.002 63.996 63.993
## 6 63.992 64.007 64.015
## 7 64.009 63.994 63.997
## 8 63.995 64.006 63.994
## 9 63.985 64.003 63.993
## 10 64.008 63.995 64.009
## 11 63.998 74.000 63.990
## 12 63.994 63.998 63.994
## 13 64.004 64.000 64.007
## 14 63.983 64.002 63.998
## 15 64.030 64.002 64.019
## 16 63.995 63.992 64.001
## 17 64.006 63.967 63.994
## 18 64.012 64.014 63.998
## 19 64.000 63.984 64.005
## 20 63.994 64.012 63.986
## 21 64.006 64.010 64.018
## 22 63.984 64.002 64.003
## 23 64.000 64.010 64.013
## 24 63.988 64.001 64.009
## 25 64.004 63.999 63.990
## 26 63.998 58.000 63.990
## 27 63.994 63.998 63.994
## 28 64.004 64.000 64.007
## 29 63.983 64.002 63.998
## 30 64.030 64.002 64.019
#part-A
# Calculate the control limits for Xbar and R charts
obj1=qcc(d1data,type ="xbar")
summary(obj1)
##
## Call:
## qcc(data = d1data, type = "xbar")
##
## xbar chart for d1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 62.00 64.00 64.00 64.04 64.01 67.33
##
## Group sample size: 3
## Number of groups: 30
## Center of group statistics: 64.04474
## Standard deviation: 0.324808
##
## Control limits:
## LCL UCL
## 63.48216 64.60733
obj2<-qcc(d1data,type ="R")
summary(obj2)
##
## Call:
## qcc(data = d1data, type = "R")
##
## R chart for d1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00400 0.01225 0.01850 0.54990 0.02275 10.01000
##
## Group sample size: 3
## Number of groups: 30
## Center of group statistics: 0.5499
## Standard deviation: 0.324808
##
## Control limits:
## LCL UCL
## 0 1.415549
# part-B
##Determine the control limits for Xbar and S charts and draw the charts.
obj3 <-qcc(d1data,type ="S")
summary(obj3)
##
## Call:
## qcc(data = d1data, type = "S")
##
## S chart for d1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.002309 0.006695 0.009518 0.316500 0.011800 5.777000
##
## Group sample size: 3
## Number of groups: 30
## Center of group statistics: 0.3164702
## Standard deviation: 0.3570984
##
## Control limits:
## LCL UCL
## 0 0.8127492
#part- C
##No, the process is not under the control.
newdata=E[-c(11,26),]
d1newdata=qcc.groups(newdata$A,newdata$batch)
obj4=qcc(d1newdata,type = "xbar")
summary(obj4)
##
## Call:
## qcc(data = d1newdata, type = "xbar")
##
## xbar chart for d1newdata
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 62.00 64.00 64.00 64.04 64.00 67.33
##
## Summary of group sample sizes:
## sizes 2 3
## counts 2 28
##
## Number of groups: 30
## Center of group statistics: 64.04545
## Standard deviation: 0.3249564
##
## Control limits:
## LCL UCL
## 63.48261 64.6083
## 63.48261 64.6083
## ...
## 63.48261 64.6083
obj5<-qcc(d1newdata,type ="R")
summary(obj5)
##
## Call:
## qcc(data = d1newdata, type = "R")
##
## R chart for d1newdata
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00400 0.01200 0.01750 0.54950 0.02275 10.01000
##
## Summary of group sample sizes:
## sizes 2 3
## counts 2 28
##
## Number of groups: 30
## Center of group statistics: 0.5614886
## Standard deviation: 0.3249564
##
## Control limits:
## LCL UCL
## 0 1.427533
## 0 1.427533
## ...
## 0 1.427533
obj6 <-qcc(d1newdata,type ="S")
summary(obj6)
##
## Call:
## qcc(data = d1newdata, type = "S")
##
## S chart for d1newdata
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.002309 0.006247 0.009367 0.316500 0.011800 5.777000
##
## Summary of group sample sizes:
## sizes 2 3
## counts 2 28
##
## Number of groups: 30
## Center of group statistics: 0.3233332
## Standard deviation: 0.357219
##
## Control limits:
## LCL UCL
## 0 0.8197798
## 0 0.8197798
## ...
## 0 0.8197798
# part-D
# hence Avg = 64.04545 and Std Dev : 0.3249564
# part-E
process.capability(obj4,spec.limits=c(63.98,64.02))
##
## Process Capability Analysis
##
## Call:
## process.capability(object = obj4, spec.limits = c(63.98, 64.02))
##
## Number of obs = 88 Target = 64
## Center = 64.05 LSL = 63.98
## StdDev = 0.325 USL = 64.02
##
## Capability indices:
##
## Value 2.5% 97.5%
## Cp 0.02052 0.017470 0.02356
## Cp_l 0.06714 0.008098 0.12619
## Cp_u -0.02611 0.032427 -0.08465
## Cp_k -0.02611 0.043642 -0.09586
## Cpm 0.02032 0.017291 0.02334
##
## Exp<LSL 42% Obs<LSL 2.3%
## Exp>USL 53% Obs>USL 4.5%
#*******************************************************************************
#Question-2
# part-A.
##Artibute chart we will use. Use C chart as well
#part-B
## control limits and plot the chart.
obj7=qcc(d2,sizes = 500,type = "c")
#part-c
# remove 17
d2=d2[-c(17),]
obj8=qcc(d2,sizes = 500,type = "c")
##***************************************************************************
#Question- 3
## create three control charts with this data to monitor each machine.
d3=data.frame(d3)
m1data=qcc.groups(d3$Machine.1,d3$Subgroup.ID)
m2data=qcc.groups(d3$Machine.2,d3$Subgroup.ID)
m3data=qcc.groups(d3$Machine.3,d3$Subgroup.ID)
obj9=qcc(m1data,type = "xbar")
summary(obj9)
##
## Call:
## qcc(data = m1data, type = "xbar")
##
## xbar chart for m1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 598.2 599.5 600.0 600.1 600.6 601.4
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 600.072
## Standard deviation: 1.16939
##
## Control limits:
## LCL UCL
## 598.5031 601.6409
obj10=qcc(m2data,type = "xbar")
summary(obj10)
##
## Call:
## qcc(data = m2data, type = "xbar")
##
## xbar chart for m2data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 599.0 599.3 599.5 599.5 599.7 600.2
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 599.548
## Standard deviation: 0.5846948
##
## Control limits:
## LCL UCL
## 598.7635 600.3325
obj11=qcc(m3data,type = "xbar")
summary(obj11)
##
## Call:
## qcc(data = m3data, type = "xbar")
##
## xbar chart for m3data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 598.1 599.5 600.1 600.2 600.8 603.0
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 600.23
## Standard deviation: 1.599312
##
## Control limits:
## LCL UCL
## 598.0843 602.3757
obj12=qcc(m1data,type = "R")
summary(obj12)
##
## Call:
## qcc(data = m1data, type = "R")
##
## R chart for m1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.20 2.60 2.80 2.72 3.30 4.00
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 2.72
## Standard deviation: 1.16939
##
## Control limits:
## LCL UCL
## 0 5.751358
obj13=qcc(m2data,type = "R")
summary(obj13)
##
## Call:
## qcc(data = m2data, type = "R")
##
## R chart for m2data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.60 1.00 1.20 1.36 1.65 2.60
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 1.36
## Standard deviation: 0.5846948
##
## Control limits:
## LCL UCL
## 0 2.875679
obj14=qcc(m3data,type = "R")
summary(obj14)
##
## Call:
## qcc(data = m3data, type = "R")
##
## R chart for m3data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.80 2.20 3.50 3.72 4.85 7.40
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 3.72
## Standard deviation: 1.599312
##
## Control limits:
## LCL UCL
## 0 7.865827
obj15=qcc(m1data,type = "S")
summary(obj15)
##
## Call:
## qcc(data = m1data, type = "S")
##
## S chart for m1data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1095 1.0620 1.1810 1.1480 1.4810 1.6150
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 1.147503
## Standard deviation: 1.220767
##
## Control limits:
## LCL UCL
## 0 2.397131
obj16=qcc(m2data,type = "S")
summary(obj16)
##
## Call:
## qcc(data = m2data, type = "S")
##
## S chart for m2data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3033 0.4117 0.5099 0.5440 0.6697 1.0060
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 0.5440291
## Standard deviation: 0.5787632
##
## Control limits:
## LCL UCL
## 0 1.136476
obj17=qcc(m3data,type = "S")
summary(obj17)
##
## Call:
## qcc(data = m3data, type = "S")
##
## S chart for m3data
##
## Summary of group statistics:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.7266 0.9583 1.4830 1.5370 2.0090 2.6590
##
## Group sample size: 5
## Number of groups: 20
## Center of group statistics: 1.537047
## Standard deviation: 1.635181
##
## Control limits:
## LCL UCL
## 0 3.210888