Question

The following data gives the number of defectives in 5 independent samples from a production process. The samples are of varying size. Draw appropriate chart and comment on the process

Sample number     Sample size     Number of defectives

1                              2000                   400

2                              1000                   150

3                              1000                   120

4                               600                     80

5                               400                     50

Answer 1

For our example we use np or do chart For this chart it is not necessary to calculate the problem of proportion of defectives to set up the control limits. we can construct the control chart for the actual number of defective we know that for a sample of size n having d defectives d = np. for our example specified value of p of p is unknown - In this situation we estimate the value of p by è as P = Epi total no. of defectives in k - sample total number of units in samplek For given example total no. of defective in five sample - 800 total no. of units in five sample = 5000x5= 25000 800 P = Sobox5 = 25000 0-032 25000 500 O X5 q= 1-7 = 1-0.032 = 0.968 and n=5000 so the control limits are LC - D - 3 VIP1 - (5ooo * 0 032 - 35oCo x 03210 968 = 160 - 3 V 154.88 CSScanned with CamScanner = 160 - (3 x 12.4450)

[LCLd = 122.665] Cld = npe 5000 x 0:032 = 160 [cLd=160 UCLI = np + 3 vno a = ( 5600 X 0.032) + 3 J5000X 0.03 2x0.968 = 160+ 3 V154-88 = 160 + (3 x12.4450) = 160 + 37.335 UCLA = 197.335 d-chart is observation table sample sample number 1 size Number of detectives UCL. CL LO 2000 400 197.335 160 122.665 looo 150 197.335 160 122.665 - d m en 1ooo 120 197.335 - 160 | 122.665 80 160 197.335 600 122-665 1 50 197.335 I 160 | 122.665 CSScanned with CamScanner

d-chart is scale on axis = 1cm= 1 on-y-axis = 50 detectives 250 Defectives 2.00 150 JUCL → CL LCL TO 0 1 2 3 4 5 sample number Conclusion :- There are three points in d-chart which are not lie in the control limits. Therefore the d-chart shows process is out of control. CSScanned with CamScanner