CONTROL CHARTS FOR ATTRIBUTES P-charts and C-charts are charts will used for attributes. This chart shows the quality characteristics rather than measurements. -CHART A p-chart is a commonly used control chart for attributes, whereby the quality characteristic is counted, rather than measured, and the entire item or service can be declared good or defective The standard deviation of the proportion defective, p. is: 0,= P(1-5), where n = sample size, and n = average of several past p values and central line on the chart. Using the normal approximation to the binomial distribution, which is the actual distribution of p. UCL, = 5 + Z0, and LCLP = 1-Zo, where is the normal deviate number of standard deviations from the average). ILLUSTRATIONS ON X BAR CHART AND R BAR CHART (i) Standard Deviation of the Process, Unknown Several samples of size = 8 have been taken from today's production of fence posts. The average post was 3 yards in length and the average sample range was 0.015 yard. Find the 99.73% upper and lower control limits. X = 3 yds R = 0.015 yds A = 0.37 from Statistical Table UCL = + A R = 3 +0.37(0.015) = 3.006 yds LCL = K - A R = 3 -0.37(0.015) = 2.996 yds ILLUSTRATION 2 (Problem on i and R Chart): The results of inspection of 10 samples with its average and range are tabulated in the following table. Compute the control limit for the X and R-chart and draw the control chart for the data. x9 X (Mean) R (Range) Sample No. (Sample Size 5) 1 2 3 7.0 2 75 3 8,0 2 4 10.0 2 S 3 6 6 9.5 11.0 115 4 3 7 8 4.0 2 9 3 3.5 4.0 10 2 X EX= 76 UR = 26