Number of nonconformities in a process detected by inspection of sample size 50 are: 3, 2,...

Number of nonconformities in a process detected by inspection of sample size 50 are: 3, 2, 3, 1, 4, 0, 2, 3, 4, and 5. For sigma = 3:

a. Construct a control chart for the fraction of nonconformities.

b. Construct a control chart for the number of nonconformities.

c. Can you conclude that this process is in statistical control? Why?

Solutions

Expert Solution

a) Control Chart for the fraction of nonconformities:

Computations for C.C. for fraction defective

S.No.	d	p = d/50
1	3	0.06
2	2	0.04
3	3	0.06
4	1	0.02
5	4	0.08
6	0	0
7	2	0.04
8	3	0.06
9	4	0.08
10	5	0.1
Total	27	0.54

Control Limits for p-chart are given by :

UCL_p =0.054+0.0956 = 0.1499

LCL_p = 0.054-0.0956 = negative value

CL_p = 0.054

2) A Control Chart for the number of nonconformities

c) Yes we can conclude that this process is in statistical control because, all the sample points are within the control limits for both control chart for the fraction of nonconformities and control chart for the number of nonconformities.

orchestra answered 1 year ago

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