An np chart is to be used following an operation on an assembly line. A roving i

Question

An np chart is to be used following an operation on an assembly line. A roving inspector takes a sample of 100 pieces every hour and checks for nonconforming pieces. The inspector posts the results to the chart and has authority to shut down the line if a sample is out of control. The chart is based on a standard value of p_0 = 0.04. What are the centerline and control limits for the np chart? If the true process average fraction nonconforming it 0.12, what is the probability the inspector will shut down the line following his next inspection?

Explanation / Answer

Answer to part a)

n = 100

p = 0.04

Centreline = n*p = 100*0.04 = 4

Control limits = np - 3 sqrt(n * p *(1-p)) , np + 3 sqrt(n * p *(1-p))

Control limits : 4 - 3*sqrt(100*0.04*0.96) , 4+ 3*sqrt(100*0.04*0.96)

Control limits = -1.8788 , 9.8788

.

Answer to part b)

n = 100 , and fraction non-confroming = 0.12

Then np = 100*0.12 = 12

The probability can be calculated with the help of Poisson distribution formula

P(x >12) = 1 - (4)^12 * e^-4 / 12 ! = 1 - 0.999 = 0.0001

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