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# Control charts tool

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### Control charts tool

1. 1. FICCI CE Control charts - P charts The p charts are used to control the overall number of defective units in a process. The proportion of non conforming items are plotted on this chart which gives us the graphical display of variability of the data.
2. 2. FICCI CE Example -construction of P charts Day Rejects Tested Proportion 1 14 286 0.049 2 22 281 0.078 3 9 310 0.029 4 19 313 0.061 5 21 293 0.072 6 18 305 0.059 7 16 322 0.050 8 16 316 0.051 9 21 293 0.072 10 14 287 0.049 11 15 307 0.049 12 16 328 0.049 13 21 296 0.071 14 9 296 0.030 15 25 317 0.079 16 15 297 0.051 17 14 283 0.049 18 13 321 0.040 19 10 317 0.032 20 21 307 0.068 21 19 317 0.060 22 23 323 0.071 23 15 304 0.049 24 12 304 0.039 25 19 324 0.059 26 17 289 0.059 27 15 299 0.050 28 13 318 0.041 29 19 313 0.061 30 12 289 0.042 Total 493 9155
3. 3. FICCI CE Construction of P charts Number of defective units Data points P= Number of units in the sample Total defective units Process Average P= = 0.053 Total units observed Upper control Limit ( UCL ) = P+3 P ( 1-P ) = 0.0926 n = P-3 P ( 1-P ) Lower control Limit =0.1508 n n=Average sample size= 305* * Since the data size do not vary much around the mean value, P chart is simplified by taking the average sample size to calculate he control limits.
4. 4. FICCI CE Construction of P charts The construction of control charts is very simple. Simply select the range of data points ( “proportion” column in the excel sheet ) and click the graph button. Select “Line graph” and the p chart is automatically calculated. The average, UCL and LCL can be manually displayed by drawing three additional lines on the graph. Please refer the next slide for the graph.
5. 5. FICCI CE P chart 0.1 0.09 UCL 0.0926 0.08 0.07Proportion 0.06 CL 0.05 0.053 0.04 0.03 0.02 LCL 0.01 0.015 0 5 Days 15 25
6. 6. FICCI CE NP charts The NP chart is used for plotting number of defectives instead of proportion defectives. This is another version of P chart and its applicability depends upon the interest of the end user.
7. 7. FICCI CE Example -construction of np charts Day Rejects Sample size 1 10 100 2 12 100 3 10 100 4 11 100 5 6 100 6 7 100 7 12 100 8 10 100 9 6 100 10 11 100 11 9 100 12 14 100 13 16 100 14 21 100 15 20 100 16 12 100 17 11 100 18 6 100 19 10 100 20 10 100 21 11 100 22 11 100 23 11 100 24 6 100 25 9 100 Total 272 2500
8. 8. FICCI CE Example -construction of np charts p = X1 + X2 + X3 +…..Xk 275 = = 0.1088 kn 25*100 np = 0.1088*100 =10.88 UCL = np + 3 np ( 1-p ) =20.22 =1.54 LCL = np - 3 np ( 1-p ) n = subgroup sample size = 100
9. 9. FICCI CE Example -construction of np charts 25 20 UCL 20.22 15Rejects Np 10 10.88 5 LCL 1.54 0 5 15 25 Days
10. 10. FICCI CE