Q2-Statistical Process Control

Statistical Process Control SPC monitors a production process to detect and prevent poor quality. Does the process vary from what it is supposed to be doing? Key Tool is a Control Chart: • Periodically take a sample from a process • Calculate a statistic of interest from the sample • Plot the statistic on a control chart • Determine if the process is in control • Prevent quality problems Process Control Chart Signs of a process in control: a.No sample points outside limits b.Most points near process average c. About equal number of points above and below center line d.Points appear randomly distributed (no discernible pattern) Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 1 1 2 3 4 5 6 7 8 9 10 Sample number Process average Violations: b. c. d.

If the process is in control, the sampling distribution of the plotted statistic should be ~Normal (and the Empirical Rule applies) This class will always set the control limits 3 σ from the process average Types of Variation Observed Assess the chart to determine if the variation present is inherent to the process or if it needs to be removed Common Causes of Variation  ever-present factors that contribute to small, random shifts in output  difficult to track to a source Special Causes of Variation  identifiable factors that induce variation beyond the inherent variation in the system  can usually be tracked to a source Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 2  =0 1  2  3  -1  -2  -3 

Initial Construction of a Control Chart The control chart built for a process should be a benchmark for when the process is “in-control” Steps: • Decide what to measure or count Attribute Data product characteristic evaluated with a discrete choice Variable Data product characteristic that can be measured on a continuous scale • Collect the sample data • Calculate and plot the control limits & center line • Plot the samples on the control chart • Evaluate: if special-cause variation is present, discard the data and remove special-cause variation before collecting a new set of data Control Charts for Attribute Data p - charts percentage of defects found in a sample Example Sample 1: test 100 light bulbs and find that 4 don’t work c - charts count the number of defects found in an item Example Sample 1: inspect a roll of carpet and find 6 blemishes Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 3 0 . 0 8 0 . 0 7 0 . 0 6 0 . 0 5 0 . 0 4 0 . 0 3 0 . 0 2 0 . 0 1 1 2 3 4 5 Sample 8 7 6 5 4 3 2 1 1 2 3 4 5

Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 4

p - Chart Example p - Chart Formulas Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 5 total # defects total # observations p = 0.00 Sample 0 2 4 6 8 10 12 14 16 18 20 0.10 0.20 p p(1 – p) = p + Z n = p - Z p(1 – p) n n p(1 – p) Each day a sample of 100 towels is randomly selected. The number of towels found defective in the sample is recorded. Sample # # Defects 1 3 2 2 3 4 4 8 5 6 6 4 7 12 8 10 9 8 10 10 Sample # # Defects 11 13 12 11 13 14 14 11 15 9 16 16 17 12 18 15 19 18 20 18 Total = 204 UCL P LCL P where: Z = # standard deviations = standard deviation of the proportion sampling distribution = 0.1020 – 3 √ 0.1020 ( 1 − 0.1020 ) 100 = 0.01121