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Statistical Process Control (SPC) Definitions Overview Data Characteristics Nature or Shape of the Distribution Representative Value - Mean Measure of Variation - Standard Deviation Pattern of Change with respect to Time Process Data Chronologically arranged data. Statistically Stable ( Within Statistical Control ) Only random variation, no patterns or cycles. Variation Random Variation - Due to chance, inherent in any process. Assignable Variation - Results from identifiable causes. Quality Control Consistency (limited variation from unit to unit) 1 Concept of Statistical Quality Control 2 SPC - Data Charts Run Chart Sequential plot of individual data values over time. Only when a process is statistically stable can the data be treated as if it came from a single population. Control Charts (Quantitative & Qualitative) Sequential plot of average values over time. Control values indicate central tendency and the limits of acceptable excursions. Upper Control Limit ( UCL ) Center Line Lower Control Limit ( LCL ) Quantitative ( R, X, s ) Qualitative ( p, c ) One method of maintaining quality is to reduce the amount of assignable variation. Minimum Assignable Variation implies a stable process; a stable process is indicative of a quality product or service. Data charts are useful tools for monitoring the stability of a process, and hence help maintain quality. 3 Control Charts 4 Out-of-Control Criteria Quantitative Control Charts R Charts - Monitor Variation (Range) Obviously apparent non-random pattern, trend, or cycle. s Charts - Monitor Variation ( Standard Deviation) Outlying point beyond upper or lower control limit. X Charts - Monitor Means (Averages) Run-of-#-Points Rule Eight consecutive points above or below the centerline. Qualitative Control Charts p Charts - Monitor Proportions of Characteristic Value Six consecutive points all increasing or all decreasing. c Charts - Monitor Number of Characteristic Values Note: p Charts & c Charts are often used to track the proportion or number of defective items per lot. Fourteen consecutive points alternating above and below the center line. 5 6 R Charts (Range) s Charts (Standard Deviations) R Charts are used to monitor variation (plots of sample ranges, not individual values) s Charts are used to monitor variation (plots of sample standard deviations) Notation n = size of each sample R = mean of sample ranges Notation n = size of each sample s = mean of sample standard deviations Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = D4R Upper Control Limit (UCL) = B4s Center Line Center Line =R Lower Control Limit (LCL) = D3R =s Lower Control Limit (LCL) = B3s 7 8 X Charts (Means) X Charts (Means) X Charts are used to monitor sample means (plots of sample means, based on ranges) X Charts are used to monitor sample means (plots of sample means, based on standard deviations) Notation n = size of each sample X = mean of sample means = mean of all samples Notation n = size of each sample X = mean of sample means = mean of all samples Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = X + A2R Upper Control Limit (UCL) = X + A3s Center Line Center Line =X Lower Control Limit (LCL) = X - A2R =X Lower Control Limit (LCL) = X - A3s 9 10 p Charts (Proportion) c Charts (Count) p Charts are used to monitor attribute’s proportionality (plots of sample attribute proportions) c Charts are used to monitor attribute’s numerical quantities (plots of sample attribute numbers) Notation n = size of each sample p = pooled estimate of attribute’s overall proportion Notation n = size of each sample c = pooled estimate of attribute’s overall quantity Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Upper Control Limit (UCL) = p + 3 [ p ( 1 - p ) / n Center Line Upper Control Limit (UCL) = c + 3 c 1/2 ]1/2 =p Lower Control Limit (LCL) = p - 3 [ p ( 1 - p ) / n Center Line =c Lower Control Limit (LCL) = c - 3 c 1/2 ]1/2 11 12