Please read the case study given below and answer questions given at the end.
A manufacturing plant make wind mill assemblies & can produce 50 units in a month in two period of 15 days each ; following is the data for number of defects arising per month.
Month
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
DEC
Number of Defects per period
43
3 2
1 0
4 5
6 7
7 7
96
5 4
2 3
0 2
2 3
4 3
Question I: Which control chart should be used for the above data and why?
Make the appropriate control chart on a graph paper.
Interpret the chart and give your recommendation. Whether the process is in control or not?
Answers
Answer 1: For the given data, we shall us a C-Chart. A c-chart is an attributes control chart used with data collected in subgroups that are the same size. C-charts show how the process, measured by the number of nonconformities (defects) per item or group of items, changes over time. Note: U charts can also be used to depict the changes in defects per unit. However, we choose to use C-Charts.
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Answer 2: In the given data, 2 data points have been taken in each month. Hence, the total number of data points in the year are 2*12 = 24 (2 per month). They are tabulated below: S No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Month JAN JAN FEB FEB MAR MAR APR APR MAY MAY JUN JUN JUL JUL AUG AUG SEP SEP OCT OCT NOV NOV DEC DEC Number of defects per period 4 3 3 2 1 0 4 5 6 7 7 7 9 6 5 4 2 3 0 2 2 3 4 3 Based on the data, following is the C-Chart: The control limits are calculated as follows: C - bar = Mean of all the data points = 3.83 UCL = (C-bar) + 3 * sqrt (C-bar) = 9.707 LCL = (C-bar) - 3 * sqrt (C-bar) = -2.403 However, number of defects cannot be negative. Hence, the LCL is taken as zero. LCL = 0 3
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Answer 3: Based on the C-Chart, we see that all the points lie within the control limits.