Question

1. Consider the setting up of a p-chart with reference to the production of railway car side frames. Suppose that these frames are in continuous production in a foundry and that a random sample of 50 frames is taken from each day’s output and inspected. The results of 28 days of past operations are as follows:

Date                Number Rejected                               Date                            Number Rejected

Oct 1               4                                                          Oct 19                         4

Oct 2               9                                                          Oct 22                         3

Oct 3               10                                                        Oct 23                         11

Oct 4               11                                                        Oct 24                         8

Oct 5               13                                                        Oct 25                         14

Oct 8               30                                                        Oct 26                         21

Oct 9               26                                                        Oct 29                         25

Oct 10             13                                                        Oct 30                         18

Oct 11             8                                                          Oct 31                         10

Oct 12             23                                                        Nov 1                          8

Oct 15             34                                                        Nov 2                          18

Oct 16             25                                                        Nov 5                          19

Oct 17             18                                                        Nov 6                          4

Oct 18             12                                                        Nov 7                          8

Set up a control chart for controlling the fraction defective of railway car side frames. The control chart with its central line and upper and lower control limits should be shown, together with the past results plotted as fraction defective. State whether the process is in control or not? Discard out of control limit data points (assuming assignable causes have been found and corrected) and set up the modified control chart.                          

Answer 1

We will use following steps

Step One first calclulate p for every observation by following formula

p = no. of defective / no of observation = 4/50 for octobr 1 = 0.08 that is 8% similarly calculate for all observation

we will use Excel for doing this

Step 2

add all number of rejcted pieces in 28 days and devide by total number of samples to arrive at P bar

​ = total number of defect / total number of observation = 407/1400= 0.29

Now Upper control limit = =

0.29 + 3 * = 0.29 + 0.06421 = 0.3549

Similarly

LCL = 0.226496

Following is the table for the calculation

			p =
1	4	50	0.08
2	9	50	0.18
3	10	50	0.2
4	11	50	0.22
5	13	50	0.26
6	30	50	0.6
7	26	50	0.52
8	13	50	0.26
9	8	50	0.16
10	23	50	0.46
11	34	50	0.68
12	25	50	0.5
13	18	50	0.36
14	12	50	0.24
15	4	50	0.08
16	3	50	0.06
17	11	50	0.22
18	8	50	0.16
19	14	50	0.28
20	21	50	0.42
21	25	50	0.5
22	18	50	0.36
23	10	50	0.2
24	8	50	0.16
25	18	50	0.36
26	19	50	0.38
27	4	50	0.08
28	8	50	0.16
	407	1400	0.290714
			0.709286
			0.206199
			0.004124
			0.064218
			0.354933
			0.226496