A process has only one assignablecause. The process will run for 20,000 hr continuously The processgenerates N units/hour. To take a sample, there is a fixedcost a1 and cost for each observationa2
In case of false alarm, processinvestigation takes tf hours and costscf.
In case of assignable cause, ittakes ta hours(including repair) and costsca.
Units produced under the presenceof the assignable cause are assumed nonconforming. Cost of anonconforming unit is cn.
If the process is in statisticalcontrol,
Pr(the process stays in controlduring run time) =p0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (p0 + p1) = 1
Pr(mean shifts from µ0to µ0 + k? after exactly 8,000 hr) = p1 Ifthe process is repaired it may fail again with sameprobabilities.
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