PROBLEM 1

As a part of an overall quality improvement programme, a textile manufacturer decides to monitor the defects in each bolt(large bundle of cloth). The number of defects for 10 inspected bolts are recorded in the following table:

Bolt Serial No. 1 2 3 4 5 6 7 8 9 10
Number of defects 10 9 5 9 4 8 7 12 6 4

Draw an appropriate control chart and comment on the state of statistical control.

b = 1:10; #bolt serial nos
d = c(10,9,5,9,4,8,7,12,6,4); #no of defects
n = length(b) #no of rational subgroups
est.lambda = mean(d) #estimated lambda
cl  = est.lambda #control line
lcl = max(0,cl-3*sqrt(est.lambda))
ucl = cl+3*sqrt(est.lambda)
plot(x=b,y=d,xlab="Rational Sub-Group No",ylab="No. of defects",main="Control Chart for No. of Defects",xlim=c(0,16),ylim=c(0,20))
abline(h=cl,col="black");
abline(h=lcl,col="red");
abline(h=ucl,col="red")

Problem 2

Following are the inspection results of 8 samples of magnets selected from a manufacturing process:

Weeks Serial No. 1 2 3 4 5 6 7 8
No. of magnets inspected 724 763 748 727 719 736 739 748
No. of defective magnets 58 63 70 56 67 52 50 57

Draw a suitable control chart and comment on the state of control.

n = 8 #rational sub-groups
n1 = c(724,763,748,727,719,736,739,748) #no of items inspected
d  = c(58,63,70,56,67,562,50,57) #no of defectives in the items inspected
p  = d/n1 #fraction defective
mean.p = mean(p) #mean of the fraction defectives
z = (p-mean.p)/sqrt(mean.p*(1-mean.p)/n) #z-score
plot(x=1:8,z,xlab="Rational Sub-Group",ylab="Z-score",main="Z-Chart",xlim=c(1,8),ylim=c(-3.5,5))
abline(h=0)
abline(h=3,col="red")
abline(h=-3,col="red")

Problem 3

In a single sampling inspection plan for attributes with n=52 and c=2, draw the OC curve and comment. It is known that the lot is large.

n = 52; #no of samples
c = 2;  #acceptable no of defectives
L = function(x) pbinom(2,n,x)
curve(L,main="OC Curve",xlab="p")