Question

Problem 6.67: The waiting time for treatmening in a "minute-clinic" locaed in a drugstore is monitored using control charts for individuals and the moving range. Table 6E.24 contains 30 successive measurements. (a) Set up individual and moving range control charts using this data. (b) Plot these observations on the charts constructed in part (a). Interpret the results. Does the process seem to be in statistical control? (c) Plot the waiting time data on a normal probability plot. Is it reasonable to assume normality for these data? Wouldn't a variable like waiting time often tend to have a distribution with a long tail (skewed) to the right? Why?

5. The waiting time for treatment in a "minute-clinic" located in a drugstore is monitored using control charts for individuals and the moving range. Table contains 30 successive measurements on waiting time Clinic Waiting Time for Waiting Waiting 2.49 134 21 1.14 3.39 12 050 22 266 7.41 13 23 467 167 24 15 0.76 25 506 132 16 26 340 7.05 17 15.19 27 1.39 067 1.37 18 28 1.11 692 6.17 4.14 5.12 20 216 30 36 99 10 Set up individual and moving range control charts using this data. a. b. Plot these observations on the charts constructed in part (a). Interpret the results. Does the process seem to be in statistical control? Plot the waiting time data on a normal probability plot. Is it reasonable to assume normality c. for these data? Wouldn't a variable like waiting time often tend to have a distribution with a long tail (skewed) to the right? Why?

Answer 1

R Code for individual and moving control charts.

# Clinic waiting time Dataset

waiting_time <- c(2.49,3.39,7.41,2.88,0.76,1.32,7.05,1.37,6.17,5.12,1.34, 0.50,4.35,1.67,1.63,4.88,15.19,

0.67,4.14,2.16,1.14,2.66,4.67,1.54,5.06,3.40,1.39,1.11,6.92,36.99)

# Installing qcc package

install.packages("qcc")

# Loading qcc package

library(qcc)

# PART (a)

# ' Create the individuals chart and qcc object

wait.x <- qcc(waiting_time, type = "xbar.one", plot = TRUE)

#' Create the moving range chart and qcc object. qcc takes a two-column matrix

#' that is used to calculate the moving range.

wait.xmr.raw.r <- matrix(cbind(waiting_time[1:length(waiting_time)-1], waiting_time[2:length(waiting_time)]),

ncol=2)

my.xmr.mr <- qcc(wait.xmr.raw.r, type="R", plot = TRUE)

Code screen shot Clinic waiting time Dataset 2 waiting time c(2.49,3.39,7.41,2.88,0.76,1.32,7.05,1.37,6.17,5.12,1.34, 0.50,4.35,1.67,1.63,4.88,15.19, 0.67,4.14,2.16,1.14.2.66,4.67,1.54.5.06.3.40,1.39,1.11.6.92.36.99 Installing qcc package 5 install.packages ("qcc" 6 # Loading qcc package 7 library(qcc) 8 PART (a) . Create the individuals chart and qcc object 10 wait.xqcc (waiting time, type "xbar.one", plot -TRUE) #. Create the moving range chart and qcc object, qcc takes a two-column matrix 12 that is used to calculate the noving range 13 wait.xmr. raN.rmatrix(cbind (waiting time[1: length waiting time)-11, waiting time[2: length waiting time)), トcol-2) 15 myxmr.mr- qcc (wait.xmr.raw.r, type-"R", plotTRUE 16

Output-Indlvldual Chart xbar.one Chart for waiting_ time CL 1 3 5 7 911 14 17 20 23 26 29 Group Number of groups30 Center 4.645667 LCL--6.830856 Number beyond limits 1 UCL 16.12219 Number violating runs0 StdDev 3.825507

Output- Moving Range chart R Chart for wait.xmr.raw.r CL CL 1 3 5 7 9 11 14 1720 23 26 29 Group Number of groups 29 Center = 4 31 51 72 9 LCL 0 Number beyond limits 2 0 StdDev 3.825507 UCL = 14 09895 Number violating runs = 5 Interpretatlon- Most of the polnts are around the mean, showing the process Is In statlstical control, leavlng the two polnts showed In red.