show calculation for UCL and LCL

A quality inspector took five samples, each with four observations (n = 4), of the length of time for glue to dry. All values are in minutes. Use this information to obtain three-sigma (i.e., z = 3) control limits. Construct three sigma mean and range charts. Determine if corrective action is needed. SAMPLE 1 2 3 4 5 Observation 1 2 3 4 12.11 12.10 12.11 12.08 12.15 12.12 12.10 12.11 12.09 12.09 12.11 12.15 12.12 12.10 12.08 12.10 12.09 12.14 12.13 12.12 Steps for X bar and R Determine # of sample Periods/Times Determine how many observations per Sample Period. This # will be used in three sigma table Determine the mean (average) of the observations per Sample Period = X bar Average the means (x bar) of each sample period = X (double bar) or grand mean. Calculate the dispersion (high vs low) for each sample period = Range. Average the Ranges (dispersions) to get R bar. Go to Table and using # of observations get A2, D3, and D4. Graph UCL and LCL and plot X bar means and R dispersions to see if in control . Instructor Slides 10-18 Table - Three sigma control limits - 33 TABLE 10.3 Factors for three-sigma control limits for x and R charts FACTORS FOR CHARTS Number of Observations in Suhgroun, Factor for 7 Chart, Lower Control Limit D Upper Control Limit D. 2 3 1.B8 1.02 073 5 258 7 8 9 10 11 12 13 14 15 16 17 18 19 20 48 0.12 0.37 0.31 0.31 229 0.27 0.25 0.24 0.22 0.25 0.20 0.19 0.19 0.18 0 0 0 0 0 0.08 D.14 R18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 238 0.33 0.40 041 3.27 2.57 2.26 211 2.00 1.92 1.86 1.82 1.78 174 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.60 1.99 Instructor Slides Chapter 10 Glue Drying Problem - Answer Sheet X double bar R bar UCL x bar LCL x bar Show calculation: Show calculation: UCL R LCLR Show calculation: Show calculation: Using X bar, Is the process in control If not, what is the problem Using R, Is the process in control If not, what is the