Some Special Process Control Procedures. and s charts Warning limits Control charts for moving averages chart with a linear trend. and s Chart. Why s chart instead of R chart?
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Note: This can also be written as
where, is the sample standard deviation and is as obtained from Appendix 3
Where, the values of are as obtained from Appendix 3
Problem 10.1: A certain company manufactures electronic components for television sets. One particular component is made to a critical length of 0.450 in. On the basis of past production experiences, the standard deviation of this dimension is 0.010 in. Because of the critical nature of the dimension, the quality control group maintains warning limits on control chart as well as the normal 3-sigma control limits. The chart is based on subgroups of four samples, and warning limits are maintained at two standard deviations from the mean. Compute the warning limits and the control limits for the chart.
(a) What is the probability that a subgroup average will exceed the UWL but not exceed the UCL when the process is correctly centered?
(b) Supervisor should be notified if (i) 2 successive subgroup averages exceed one of the warning limits or (ii) if one subgroup average exceeds either of the control limits. What is the probability that, when there has been no change in the process, the supervisor will have to be notified because of (i) or (ii)?
(c) If the process suddenly shifts to 0.460 with no change in the standard deviation, what is the probability that 2 successive points will exceed the upper warning limit but not exceed the upper control limit?