The tensile strength of nonferrous pipes is of importance. Samples of size 5 are selected from the process output, and their tensile strength values are found. After 30 such samples, the process mean strength is estimated to be 3000 kg with a standard deviation of 50 kg.
(a) Find the 1σ and 2σ control limits. For the 1σ limits, what is the probability of concluding that the process is out of control when it is really in control?
(b) Find the 3σ limits.
(c) If Rules 1 and 2 are used simultaneously to detect out-of-control conditions, assuming independence, what is the overall probability of a type I error if 3σ control limits are used?