Question: Quality (March 2009) presented a problem that actually occurred at a plant that produces a high volume, blow-molded container with multiple layers. One of the

Quality (March 2009) presented a problem that actually occurred at a plant that produces a high volume, blow-molded container with multiple layers. One of the layers is very expensive to manufacture. The quality manager at the plant desires to lower the average thickness for the expensive layer of material and still meet specifications. To estimate the actual thickness for this layer, the manager measured the thickness for one container from each of two cavities every 2 hours for 2 consecutive days. The data (in millimeters) are shown in the following tables.

a. Construct an R-chart for the data.

b. Construct an x-chart for the data.

c. Based on the control charts in parts a and b, comment on the current behavior of the manufacturing process. As part of your answer, give an estimate of the true average thickness of the expensive layer.

Day 1 Time 7 А.М. 9 А.М. 11 А.М. 1 р.м. 3 р.М. 5 Р.М. 7 Р.М. 9 Р.М. Thickness .167 (mm) Average Range .2

Day 1 Time 7 .. 9 .. 11 .. 1 .. 3 .. 5 .. 7 .. 9 .. Thickness .167 (mm) Average Range .241 .232 203 .204 221 .255 .224 .216 .235 .214 .190 .207 .238 .210 .210 .1995 .2220 .2090 .2055 .2310 .2310 .2310 .2225 .065 .038 .010 .031 .048 .014 .006 .025 Day 2 Time 7 .. 9 .. 11 .. 1 .. 3 .. 5 .. 7 .. 9 .. Thickness 223 .202 .258 .216 .215 .243 .248 .192 .208 .223 .221 .252 221 .245 .224 .2195 .2085 .2430 .2320 .2500 .2065 .2265 .2235 .022 .004 .029 .037 .001 (mm) Average Range .228 .007 .013 .030

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