A quality characteristic is monitored by a control chart designed so the probability that an out-of-control condition will be detected on the first sample following the shift is 1 – ß. Find the following: th (a) The probability that the out-of-control condition will be detected on the n' sample following the shift. (b) The expected number of samples analyzed until the shift is detected. (c) The probability that the first sample following the shift produces a statistic that plots inside the control limits. (d) The probability of detecting the shift after the nth sample following the shift, which means the shift is detected in the (n+1)th, or (n+2) th, .... sample (e) The probability that n consecutive samples produce statistics that plot outside of the control limits.