28. Consider the following table: Part Test 1 Test 2 Test 3 X-bar 1 383.75 373.75 446.25 401.25 7...
Part Test 1 Test 2 Test 3 X-bar R 1 383.75 373.75 446.25 401.25 72.5 2 406.25 531.25 435 457.5 125 3 368.75 270 398.75 345.8333 128.75 Averages 401.5278 108.75 1. If the specifications are set at 435 ± 45, and the process output is normally distributed, estimate the fraction nonconforming. 2. If the process mean shifts to 415 and the standard deviation simultaneously shifts to 10. Find the probability of detecting this shift on the X-bar chart on the...
Control charts for bar x chart and S have been maintained on a process and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows: Estimate the mean and standard deviation of the process. Assume that the process output is well modeled by a normal distribution. If specifications are 703 and 709, estimate the fraction nonconforming. Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of...
2. A process has a X-bar control chart with UCL=17.4, LCL=12.79 using a 3- sigma limit. The subgroup sample size is 3. (a) Estimate the standard deviation of the process, sigma hat. (6 pts) (b) Suppose that the process mean shifts to 13. Find the probability that this shift will be detected on the next sample. (8 pts) (c) Calculate the average run length (ARL) before detecting the shift. (6 pts)