STAT 496, Spring 2004Homework Assignment #11. A company produces plastic sheeting to be used in the manufacture of credit cards. Thetarget value for the thickness of the sheeting is 0.055 mm with specification limits of0.0525 mm and 0.0575 mm. The stability and capability of the process that producesthe sheets is to be investigated by randomly selecting sample rolls of sheeting fromskids. The thickness values for 25 subgroups of size n=4 are given below. The data isalso available on the course web page www.public.iastate.edu/∼wrstephe/stat496.htmlSubgroup X1X2X3X41 0.0574 0.0543 0.0554 0.05762 0.0568 0.0572 0.0576 0.05543 0.0555 0.0570 0.0551 0.05504 0.0556 0.0559 0.0557 0.05305 0.0542 0.0554 0.0565 0.05666 0.0555 0.0570 0.0573 0.05547 0.0561 0.0570 0.0585 0.05508 0.0580 0.0570 0.0580 0.05609 0.0560 0.0570 0.0566 0.055210 0.0552 0.0548 0.0550 0.055411 0.0535 0.0550 0.0560 0.056012 0.0560 0.0560 0.0580 0.056513 0.0573 0.0569 0.0565 0.055614 0.0555 0.0570 0.0560 0.059015 0.0570 0.0580 0.0560 0.055816 0.0556 0.0545 0.0545 0.054017 0.0548 0.0525 0.0560 0.055018 0.0550 0.0570 0.0570 0.055619 0.0566 0.0581 0.0587 0.055820 0.0551 0.0551 0.0580 0.057021 0.0580 0.0580 0.0580 0.055022 0.0550 0.0547 0.0551 0.055023 0.0538 0.0556 0.0546 0.054324 0.0570 0.0560 0.0560 0.057025 0.0559 0.0576 0.0570 0.05751(a) Construct X and R charts for these data.(b) Are there any points outside the control limits on the R chart? What does thissay about the stability of the process?(c) Using Nelson’s eight rules are there any out-of-control signals given by the Xchart? If so, where? What does this say about the stability of the process?(d) Construct a histogram for the data and comment on how many measurements areoutside the specification limits.(e) What else can be said about the capability of the process now, and in the future?2. One of the variables that affects customers’ perception of the quality of an automobileis the flushness of the top flange of a car door with the side surround of the body.Specifications call for a target flushness of 0 with limits of ±1.5 mm.(a) Initially, 50 consecutive automobiles are measured for fitness. The data are sum-marized using JMP, control charts and capability analysis: Flushness 1. Commenton the stability and capability of the process. Use the alarm rule of one pointoutside control limits.(b) A design change, installation of a rubber piece on the lower inside flange, isimplemented and another 50 consecutive automobiles are measured. Refer tothe JMP output that has control charts and capability analysis: Flushness 2.Comment on the stability and capability of the process. Again, use the alarmrule of one point outside control limits.(c) Has the design change improved the process? Be sure to comment on both themean and the variation. Back up your answer with summary measures.(d) Is there more room for improvement? Discuss
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