Consider a precision machining operation. An NC lathe makes rods whose diameter

Question

Consider a precision machining operation. An NC lathe makes rods whose diameter should follow a normal distribution with a mean of 2.80cm and a standard deviation of 0.60cm. Assume that we select nine rods at random every two hours and plot the average on a control chart with CL = 2.80cm, UCL = 3.25cm, LCL = 2.35cm. The only sensitizing rule applied is to signal when a point falls outside the control limits. Find the in-control ARL and ATS. If the process shifts to a mean of 2.70cm, find the out-of-control ARL and ATS. If the process shifts to a standard deviation of 1.00cm, find the out-of-control ARL and ATS. Repeat parts a)-c) for a chart with UCL = 3.40, LCL = 2.20, six rods per subgroup, sampled every three hours, same sensitizing rule

Explanation / Answer

Mean = 2.80 and std dev = 0.60

Std error for 9 samples = 0.60/rt 9 = 0.20

a) If within control means length of rods within 3 std dev from the mean

Hence within 2.20 and 3.40

b) If mean = 2.70

out of control would be either length < 2.70-0.6 or greater than2.70+0.6

i.e. length less than 2.10 or length > 3.30

c) If std dev = 1 then std error = 0.33 and mean 2.80 then

out of control would be either below 1.80

or greater than 3.80

d)

Std error = 0.6/rt 6 = 0.245

Hence either below 2.80-0.735 or above 2.80+0.735

< 2.065 or > 3.535

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