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Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped.
6-8 Chapter 6: Process Performance and QualityWebster is concerned whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes are taken and each tube is weighed in ounces. Assuming that taking only 6 samples is sufficient, is the process in statistical control?Conclusion on process variability:708.0)38.0(864.14===RDUCLR052.0)38.0(136.03===RDLCLRSince the range is out of control, the xcalculation is moot.Consider dropping sample 6 because of an inoperative scale, causing inaccurate measures.What is the conclusion on process variability and process average?(29(29061.045.0136.0839.045.0864.134======RDLCLRDUCLRR(29(29832.745.0373.0034.8202.845.0373.0034.822=-=-==+=+=RAxLCLRAxUCLxxThe resulting control charts indicate that the process is actually in control. Tube NumberSample12345678AvgRange17.988.348.027.948.447.687.818.118.0400.7618.104.22.1688.418.318.187.998.068.1600.4337.897.777.918.048.007.897.938.097.9400.3248.248.187.838.057.908.167.978.078.0500.4157.878.137.927.998.107.818.147.887.9800.3322.214.171.124.126.96.36.199.148.1300.03Avgs8.0500.38Tube NumberSample12345678AvgRange17.988.348.027.948.447.687.818.118.0400.76188.8.131.528.418.318.187.998.068.1600.4337.897.777.918.048.007.897.938.097.9400.3248.248.187.838.057.908.167.978.078.0500.4157.878.137.927.998.107.818.147.887.9800.33Avgs8.0340.45
Chapter 6: Process Performance and Quality6-92.Control charts for attributes TEACHING TIPMention examples from banking and manufacturing. Emphasize that defects can be counted.a.p-chart — population proportion defective •Sampling for a p-chart involves a yes or no decision, based on the binomial distribution•Take a random sample of nunits.•Count the number of defectives.•Proportion defective = number of defectives ÷ sample size•Plot sample proportion defective on a chart. If it is outside the range between the upper and lower control limits, search for an assignable cause. If cause is found do not use these data to determine the control limits.UCLp=p +zσpLCLp=p –zσpwhereσp=p 1 –p (29n•Two things to note: ⇒The lower control limit cannot be negative ⇒When the number of defects is less than the LCL, then the system is out of control in a good way. We want to find the assignable cause. Find what was unique about this event that caused things to work out so well. •Use Application 6.2: p-Chart for Attributes for an example of a p-chart problem. The short answers are: p=0.025;UCLp=0.064;LCLp=0; INCONTROLA sticky scale brings Webster’s attention to whether caulking tubes are being properly capped. If a significant proportion of the tubes aren’t being sealed, Webster is placing their customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following number of leaking tubes are found:Sample Tubes Sample Tubes Sample Tubes138615525941603310917244112186521261926413520172141Total=72
6-10 Chapter 6: Process Performance and QualityCalculate the p