MGT613 - Production / Operations Management Assignment # 2

A Post Office has initiated Total Quality Management practices to measure the quality of service and detecting whether the process is in control or not through statistical process control methods (SPC). The operations manager collected a random sample size of 3000 postal deliveries and the number of defectives (wrong deliveries) was recorded. The data of 15 weeks are shown as under.

Sample number No. of defectives Sample proportion defective (p)
1 16
2 13
3 20
4 3
5 18
6 6
7 26
8 9
9 8
10 24
11 14
12 5
13 12
14 19
15 18
a. Find out average population proportion defective which would be the central line on p-chart (p) i.e. total defectives/ sample size*weeks
b. Find out sample proportion defective (p )i.e. no. of defectives per week / Sample size
c. Calculate standard deviation of distribution of proportion defective (σp) using the formulaσppp=−()/1 n. Where n= sample size.
d. Find out upper control limit (UCL) and lower control limit (LCL) using the formula (UCLpzLCLpzppp=+ p =−σσ and ). Use three sigma control limits(z=3)
e. On the basis of above data construct a p-chart taking sample numbers on x-axis and sample proportion defective (p) on y-axis.
f. Which sample number is showing the highest proportion of defective? Is the process still in control? Analyze the trend in chart.