For a variable control chart, how to find the optimal sample size, control limits, and frequency?

2018-04-24 11:44:36

I need help to solve this question:

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 Rf hours and costs Cf.

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

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

nonconforming unit is Cn.

If the process is in statistical control,

Pr(the process stays in control during run time) = p0;

Note:(p0 + p1) = 1

Pr(mean shifts from µ0 to µ0 + kσ 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