Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and l Chapter 18 l Quality Control: Recognizing and Managing Variation

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Processes Control  Process Any business activity transforms inputs into outputs e.g., manufacturing products e.g., restaurant meals e.g., information processing  Statistical Process Control Use of statistical methods to monitor the functioning of a process Fix when necessary, otherwise leave it alone! Detect problems and fix them before defects are produced Variation is due to different causes

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Causes of Variation  Assignable Cause of Variation Due to identifiable causes, e.g. Dust contamination Incomplete training of workers  Random Cause of Variation Due to causes not worth identifying, e.g. Even a process that is “in control” and working properly still shows some variation in its results Perhaps there is no reason to ensure that each cookie has the exact same number of chocolate chips in it, so long as there are enough!

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and In Control  A Process is In a State of Statistical Control (or, Simply, In Control) When all assignable causes of variation have been identified and eliminated Only random causes of variation remain  What to do with a Process that is In Control? Monitor it with control charts Leave it alone, so long as it stays in control Fix it when it goes out of control

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and The Pareto Diagram  Pareto Diagram Shows Where to Focus Attention For a group of defective components Each defect is classified according to its cause Pareto Diagram displays the causes in order from most frequent to least frequent Also shows the cumulative percentage of defects (e.g., due to the top 3 causes) Pareto Diagram includes a bar chart, showing the number of defects due to each cause, most to least Together with their cumulative sum

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Example: Pareto Diagram  Defect Causes and Frequencies Solder joint: 37 defects, Plastic case: 86 defects, Power supply: 194 defects, Dirt: 8 defects, Shock: 1 defect % 59.5% 85.9% 100% Power supply Plastic case Solder joint DirtShock Number of defective items Percent of defective items Fig

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Control Chart  Displays successive measurements of a process, together with Center line Control limits (upper and lower)  To Help You Decide if the Process is In Control A hypothesis test H 0 : The process is in control H 1 : The process is not in control The false alarm rate (type I error) How often will you intervene when the system is really OK? The 5% level is too high In quality control, 3  limits are often used (as compared to 2  )

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and A Process that is In Control  If Process is In Control, Control chart stays within the control limits Variation within the control limits is to be expected Variation should be random, without systematic patterns Group Number Measurement Upper control limit Lower control limit Center line Data

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and A Process that is Not In Control  If Control Chart Extends Beyond a Control Limit Or if there is a systematic pattern within the limits  Then the Process is Not In Control Group Number Measurement Group Number Measurement

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and X -Bar Chart  A Control Chart for Averages of Successive Measurements Tells you about the stability of the size of measurement Often taken in groups of 4 or 5 at a time Control Chart plots the averages of successive groups Center line is the grand mean of all measurements Unless an external standard is given Upper and lower limits are found using multipliers

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and R Chart  A Control Chart for Ranges of Successive Measurements Tells you about stability of the variability of process Range is largest minus smallest Often taken in groups of 4 or 5 at a time Control Chart plots the ranges of successive groups Center line is the mean range for all groups Unless an external standard is given Upper and lower limits are found using multipliers

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Example: Weight of Detergent Fig  25 Groups of 5 measurements each Find average and range for each group Plot with center line and control limits It’s In Control! Group Number Averages Group Number Ranges

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Percentage Chart  A Control Chart for the Percent Defective Tells you about the stability of the defect rate Plot the percent defective for successive samples How to choose n, the sample size? You should expect at least 5 defective items in a sample Center line is the average defect rate Unless an external standard is given Upper and lower limits are set at 3 binomial standard deviations above and below the center line

Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and Example: Purchase Order Errors  25 batches of n = 300 purchase orders each Find percent defective for each batch Plot with center line and control limits It’s not in control 0% 5% 10% Group Number Percent of purchase orders in error Fig