【正文】 spected of units rejected. ? Compute the defective rate from the ith lot (i =1,2,...,k), pi = of units rejected / of units inspected ? Compute the average of the p’s, ? Compute the standard deviation of the p’s, ( ) S p p k 1 p i 2 i 1 k = ? ? = ? p p k i i 1 k = = ? 30 ? Compute the Control Limits: CL (p)= p UCL (p) = p + 3Sp LCL (p) = p 3Sp ? When LCL 0, put LCL = 0 or N/A ? Draw the control limits on p chart Note: 1. With varying sample sizes, the precision of our estimate of p is not constant. Because of this, the upper lower control limits are not constant need to be calculated separately for each point. 2. The above method describes how the control limits are calculated assuming equal (or nearequal) sample sizes. If the sample sizes vary by more than 50 % of each other, you should consult a statistician. Computing Control Limits for p Chart with 3 Std Dev Method 31 Notes : ? np Chart is applicable when all subgroups have constant sample sizes ? In terms of practicality, p Chart can/should be used when sample sizes are equal as p carry more meaning than of rejected units (np) ? The method described for puting attribute control limits requires that Sp be puted from a stable process. If the process is unstable, Sp is a poor estimate of the true process variation, hence the control limits will not be a realistic description of stable process fluctuation. Any outliers should be removed from the data before puting the control limits. Computing Control Limits for p Chart 32 Example of Computing Control Limits for p Chart 30 lots of product were visually inspected for defects. The defective rate, p, was recorded for each lot: (Maximum lot size = 1147, minimum lot size = 1024, difference = 12%) From this data, we pute the following: p = Sp = From which we can pute the centerline and control limits: CL (p) = p = UCL (p) = p + 3Sp = + 3() = LCL (p) = p 3 Sp = 3() = LotN u m b e rp LotS i z eLotN u m b e rp LotS i z eLotN u m b e rp LotS i z e1 0 . 0 6 5 1036 11 0 . 0 5 2 1072 21 0 . 0 4 8 11282 0 . 0 4 7 1120 12 0 . 0 8 0 1113 22 0 . 0 6 5 10443 0 . 0 8 1 1080 13 0 . 0 4 7 1084 23 0 . 0 6 0 11014 0 . 0 5 4 1056 14 0 . 0 5 3 1048 24 0 . 0 3 8 10685 0 . 0 6 4 1132 15 0 . 0 6 3 1024 25 0 . 0 6 9 10326 0 . 0 3 9 1147 16 0 . 0 3 3 1065 26 0 . 0 4 7 10897 0 . 0 7 2 1092 17 0 . 0 5 0 1025 27 0 . 0 4 1 10538 0 . 0 6 9 1029 18 0 . 0 7 0 1104 28 0 . 0 8 8 10379 0 . 0 9 6 1108 19 0 . 0 5 1 1041 29 0 . 0 6 0 107710 0 . 0 6 5 1060 20 0 . 0 8 1 1096 30 0 . 0 5 1 111633 Defect Rate 5 1 0 15 20 2 5 30 Lo t Num b er0 .0 00 .0 20 .0 40 .0 60 .0 80 .1 00 .1 2U C L = 0. 10 5L C L = 0 .0 15C L =0. 06 0Example of Computing Control Limits for p Chart Control Chart of Visual Inspection Data 34 Interpretation of p Chart Some special causes affecting the p Chart: ? Changes in variable data specifications ? Changes in inspection procedures ? Changes in MS skills, . new MSes ? Changes in pieceparts quality 35 Control Chart Trend Rules Goals ? Rapid detection to process or equipment problems (outofcontrol or unstable) ? Response by using Response Flow Checklist (RFC)/troubleshooting guide or other means to restore the process or equipment back to normal operating condition 36 How to Interpret a Control Chart? It is based on the Standard Normal Distribution. 0 . 1 3 5 % 2 . 1 4 5 % 1 3 . 5 9 0 % 3 4 . 1 3 0 % 3 4 . 1 3 0 % 1 3 . 5 9 0 % 2 . 1 4 5 % 0 . 1 3 5 %4 3 2 1 0 1 2 3 46 8 . 2 6 %9 5 . 4 4 %9 9 . 7 3 %37 SPC Trend Rules Rule 1: A single point beyond either control limit Uses: Detects very large/sudden shifts False alarm rate: % Example: UCL CL LCL 38 SPC Trend Rules Rule 2: 9 consecutive points on the same side of the centerline Uses: Detects small shifts or trends False alarm rate: % Example: UCL CL LCL 39 SPC Trend Rules Rule 3: 6 consecutive points steadily increasing or decreasing Uses: Detects strong trends Example: UCL CL LCL 40 SPC Trend Rules Rule 4: 2 out of 3 consecutive points at least 2 std dev beyond the centerline, on the same side Uses: Detects large changes False alarm rate: % Example: UCL CL LCL 41 Selection of Trend Rules ? Using a large of trend rules is unwise, since each trend rule has a false alarm rate the cumulative false alarm rate can be very large ? False alarm rate is the frequency of control chart signals when nothing at all is actually wrong with the process ? False alarms are undesirable: – They reduce productivity increase costs from unnecessarily shutting down the