3. A pharmaceutical company manufactures tablets. The amount of active ingredient in the tablets is showing alarming variability and it is decided to set up a control chart to ensure process control. Eight tablets were sampled from each of twenty six batches. The FDA requires that the level of active ingredient must be within the specification limits 70.10mm. (a) Calculate the control limits for an X chart and R chart based on these data. (b) The data are plotted on the final page of the exam paper, which should be detached and included in your answer book. (NB! Please ensure to write your Student ID at the top of the page.) Check for process control using the limits calculated in (a). (c) Why is it important that the R chart is in control before examining the X chart? (d) Distinguish between "special-cause" and "random" variation. In the context of this example, what can be said about the presence of special-cause and/or random variation? (e) Briefly explain how a CUMSUM chart is constructed and used. What type of departures from the production target value is this type of chart useful for detecting? What is its primary advantage over X/R charts