Average run length is the average number of number of quality charactristics point must be plotted beween the control climits before any point lie outside the limit>

ARL theoritcal defined as 1 divded be the prob(any point lie out side control limits)

I agree...but it's important to take into account the difference between ARL in control (ARLi) and ARL out of control (ARLo). On the one hand the ARLi should be as big as possible because you want the minimum number of false alarms (for a Shewhart type control chart ARLi=370). And on the other hand the ARLo should be as small as possible because you want to detect the process goes out of control as soon as possible.

If you are a beginner practitioner read this:

Montgomery, D. C. (2009). Introduction to Statistical Quality Control. John Wiley & Sons Incorporated.

And for the advanced ones:

Klein, M. (2000). Two alternatives to the Shewhart (X)over-bar control chart. Journal of Quality Technology, 32(4), 427–431.

I agree with you, Sancho. In addition, the optimum levels of ARL0 and ARL1 should be determined by taking into account the cost function of the product.

If you are a beginner practitioner read this:

Douglas C. Montgomery (1980) The Economic Design of Control Charts: A Review and Literature Survey,Journal of Quality Technology, 12:2, 75-87, DOI: 10.1080/00224065.1980.11980940

And for the advanced ones:

Bakir, M.A., Altunkaynak, B. The optimization with the genetic algorithm approach of the multi-objective, joint economical design of the x̄ and R control charts

(2004) Journal of Applied Statistics, 31 (7), pp. 753-772.