Statistical Process Control (SPC) Definitions

Overview Process Data Data Characteristics Chronologically arranged data. Nature or Shape of the Distribution Representative Value - Mean Statistically Stable ( Within Statistical Control ) Measure of Variation - Standard Deviation Only random variation, no patterns or cycles. Pattern of Change with respect to Time Variation Quality Control Random Variation - Due to chance, inherent in any process. Consistency (limited variation from unit to unit) Assignable Variation - Results from identifiable causes.

Concept of Statistical Quality Control SPC - Data Charts

Run Chart Only when a process is statistically stable can the data be Sequential plot of individual data values over time. treated as if it came from a single population. Control Charts (Quantitative & Qualitative) One method of maintaining quality is to reduce the amount of Sequential plot of average values over time. assignable variation. Control values indicate central tendency and the limits of acceptable excursions. Minimum Assignable Variation implies a stable process; Upper Control Limit ( UCL ) a stable process is indicative of a quality product or service. Center Line Lower Control Limit ( LCL ) Data charts are useful tools for monitoring the stability of a Quantitative ( R, X, s ) process, and hence help maintain quality. Qualitative ( p, c )

Control Charts R Charts (Range)

Quantitative Control Charts R Charts are used to monitor variation R Charts - Monitor Variation (Range) (plots of sample ranges, not individual values)

s Charts - Monitor Variation ( Standard Deviation) Notation X Charts - Monitor Means (Averages) n = size of each sample R = mean of sample ranges

Qualitative Control Charts Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) p Charts - Monitor Proportions of Characteristic Value Upper Control Limit (UCL) = D4R c Charts - Monitor Number of Characteristic Values Note: p Charts & c Charts are often used to track the Center Line = R

proportion or number of defective items per lot. Lower Control Limit (LCL) = D3R s Charts (Standard Deviations) X Charts (Means) s Charts are used to monitor variation X Charts are used to monitor sample means (plots of sample standard deviations) (plots of sample means, based on ranges)

Notation Notation n = size of each sample n = size of each sample s = mean of sample standard deviations 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) = B4s Upper Control Limit (UCL) = X + A2R Center Line = s Center Line = X

Lower Control Limit (LCL) = B3s Lower Control Limit (LCL) = X - A2R

X Charts (Means) p Charts (Proportion)

X Charts are used to monitor sample means p Charts are used to monitor attribute’s proportionality (plots of sample means, based on standard deviations) (plots of sample attribute proportions)

Notation Notation n = size of each sample n = size of each sample X = mean of sample means = mean of all samples p = pooled estimate of attribute’s overall proportion

Control Limits ( 99.7 % confidence intervals { 3 SD’s} ) Control Limits ( 99.7 % confidence intervals { 3 SD’s} )

1/2 Upper Control Limit (UCL) = X + A3s Upper Control Limit (UCL) = p + 3 [ p ( 1 - p ) / n ] Center Line = X Center Line = p

1/2 Lower Control Limit (LCL) = X - A3s Lower Control Limit (LCL) = p - 3 [ p ( 1 - p ) / n ]

c Charts (Count) Out-of-Control Criteria c Charts are used to monitor attribute’s numerical quantities Obviously apparent non-random pattern, trend, or cycle. (plots of sample attribute numbers)

Notation Outlying point beyond upper or lower control limit. n = size of each sample c = pooled estimate of attribute’s overall quantity Run-of-#-Points Rule Eight consecutive points above or below the centerline. Control Limits ( 99.7 % confidence intervals { 3 SD’s} )

1/2 Upper Control Limit (UCL) = c + 3c Six consecutive points all increasing or all decreasing. Center Line = c Fourteen consecutive points alternating above and below Lower Control Limit (LCL) = c -3c 1/2 the center line.