A Post Office hasinitiated Total Quality Management practices to measure the qua

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A Post Office hasinitiated Total Quality Management practices to measure the qualityof service and detecting whether the process is in control or notthrough statistical process control methods (SPC). The operationsmanager collected a random sample size of 3000 postal deliveriesand the number of defectives (wrong deliveries) was recorded. Thedata of 15 weeks are shown as under. Samplenumber                           No.ofdefectives            Sampleproportion 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 bethe central line on p-chart (p) i.e. total defectives/ samplesize*weeks
b. Find out sample proportion defective (p )i.e. no. of defectivesper week / Sample size
c. Calculate standard deviation of distribution of proportiondefective (p) using the formulappp=()/1 n.Where n= sample size.
d. Find out upper control limit (UCL) and lower control limit (LCL)using the formula (UCLpzLCLpzppp=+ p = and ).Use three sigma control limits(z=3)
e. On the basis of above data construct a p-chart taking samplenumbers on x-axis and sample proportion defective (p) ony-axis.
f. Which sample number is showing the highest proportion ofdefective? Is the process still in control? Analyze the trend inchart. A Post Office hasinitiated Total Quality Management practices to measure the qualityof service and detecting whether the process is in control or notthrough statistical process control methods (SPC). The operationsmanager collected a random sample size of 3000 postal deliveriesand the number of defectives (wrong deliveries) was recorded. Thedata of 15 weeks are shown as under. Samplenumber                           No.ofdefectives            Sampleproportion 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 bethe central line on p-chart (p) i.e. total defectives/ samplesize*weeks
b. Find out sample proportion defective (p )i.e. no. of defectivesper week / Sample size
c. Calculate standard deviation of distribution of proportiondefective (p) using the formulappp=()/1 n.Where n= sample size.
d. Find out upper control limit (UCL) and lower control limit (LCL)using the formula (UCLpzLCLpzppp=+ p = and ).Use three sigma control limits(z=3)
e. On the basis of above data construct a p-chart taking samplenumbers on x-axis and sample proportion defective (p) ony-axis.
f. Which sample number is showing the highest proportion ofdefective? Is the process still in control? Analyze the trend inchart.

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