【正文】 ur site statistician for advice on this. ? As for CCC Chart, it is based on Geometric distribution works well with low dpm environment. Control Limits for Attribute Control Charts 26 p Chart Concept ? It plots proportion of defective units in a sample ? The proportion of defective units in a sample can be in terms of fraction, percent or dpm ? It allows us to chart production processes where sample size cannot be equal ? It can be successfully used for processes with 10,000 dpm and above 27 Binary Data Lot 1 2 3 4 5 * * * * * Distribution of Individual Lot Distribution of Lot Means Overall Distribution of Combined Lots Good = 0 Bad = 1 0 1 Lot Mean Variance Components Many products are manufactured in batches or lots. Due to random fluctuations, these lots will vary in quality even though the process is stable. 28 Variance Components ? The total variation can be separated into 2 variance ponents: s2Total = s2Lot + s2Within where s2Total = The total variation in the process s2Lot = The amount of variation between lots. Its is a measure of how different the lots are from each other. s2Within = The amount of variation within each lot. It is a measure of how different the parts within each lot are from each other. Note: Most conventional statistical analysis methods for Binary data ignore the existence of variance ponents, and assume that the population defective rate is constant does not vary from lot to lot. The result of this is a rather unrealistically low estimate of the true process variation. 29 Computing Control Limits for p Chart with 3 Std Dev Method ? Obtain at least k = 30 subgroups or lots. Data collected in of units inspected 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