A process has only one assignable cause. The process will run for 20,000 hr continuously The...

A process has only one assignable cause. The process will run for 20,000 hr continuously The process generates N units/hour. To take a sample, there is a fixed cost a₁ and cost for each observation a₂

In case of false alarm, process investigation takes t_f hours and costs c_f.

In case of assignable cause, it takes t_a hours(including repair) and costs c_a.

Units produced under the presence of the assignable cause are assumed nonconforming. Cost of a nonconforming unit is c_n.

If the process is in statistical control,

Pr(the process stays in control during run time) = p₀ (p₀ + p₁) = 1

Pr(mean shifts from µ₀ to µ₀ + k? after exactly 8,000 hr) = p₁ If the process is repaired it may fail again with same probabilities.

Find the optimal sample size n, control limits L, and sampling frequency T

Given that:
N=150 || a1=130 || a2=11 || tf=10 || cf=1200 || ta=7 || ca=59 || cn=4600 || p0=0.89 || k=1

Expert Solution

Manojponduru answered 2 years ago

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