A production line assembly electric clocks The average numbe

A production line assembly electric clocks. The average number of non-conformities is estimated to be 0.75. establish a c chart for this operation using an unit of 6 clocks, and then Find the three-sigma limits for this chart.

Solution

If the inspection units are the same, c chart is also practical.

Recall that c = u/n, the problem states u-bar 0.75.

Therefore, c-bar for this problem is (0.75)(6) = 4.5, then you can work on this problem based on c-chart formulation

There are 2 formulas for ARL

1/alpha for in control process ==> Karndee: tell you when you will see the false alarm

1/ (1- beta ) for out of control process ==> Karndee: tell you when you will detect the shift in the process. When there is shifting in the process mean, it implies that the process is out of control.

ARL_0 is generic when you choose the type of control limits, either to be 3-sigma, or 2-sigma. Each type of control limits associates with certain value of alpha. For example, for 3-sigma limits, alpha would be 0.0027. Then, in this case, ARL_0 will be a certain number of 1/0.0027.

On the other hand, ARL_1 is calculated when process is out of control or when there is some shifting in the mean. If you can find the magnitude of mean shifting, you can find ARL_1. Normally, the practical question usually asks if the process is shifted by such and such, what will be the chance or how long it will take to detect the shift.