Statistical Quality Control Chapter 4 Statistical Quality Control © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e

Quality Control Approaches Statistical process control (SPC) Monitors production process to prevent poor quality Acceptance sampling Inspects random sample of product to determine if a lot is acceptable © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Statistical Process Control Take periodic samples from process Plot sample points on control chart Determine if process is within limits Prevent quality problems © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Variation Common Causes Variation inherent in a process Can be eliminated only through improvements in the system Special Causes Variation due to identifiable factors Can be modified through operator or management action © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Types Of Data Attribute data Product characteristic evaluated with a discrete choice Good/bad, yes/no Variable data Product characteristic that can be measured Length, size, weight, height, time, velocity © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

SPC Applied To Services Nature of defect is different in services Service defect is a failure to meet customer requirements Monitor times, customer satisfaction © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Service Quality Examples Hospitals timeliness, responsiveness, accuracy Grocery Stores Check-out time, stocking, cleanliness Airlines luggage handling, waiting times, courtesy Fast food restaurants waiting times, food quality, cleanliness © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Control Charts Graph establishing process control limits Charts for variables Mean (X-bar), Range (R) Charts for attributes p and c © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Process Control Chart Upper control limit Process average Lower 1 2 3 4 5 6 7 8 9 10 Sample number © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

A Process Is In Control If No sample points outside limits Most points near process average About equal number of points above & below centerline Points appear randomly distributed © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Development Of Control Chart Based on in-control data If non-random causes present discard data Correct control chart limits © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Charts For Attributes p Charts Calculate percent defectives in sample c Charts Count number of defects in item © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e p-Chart © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

The Normal Distribution 95% 99.74% -3 -2 -1 =0 1 2 3 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Control Chart Z Values Smaller Z values make more sensitive charts Z = 3.00 is standard Compromise between sensitivity and errors © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e p-Chart Example 20 samples of 100 pairs of jeans Sample # # Defects Proportion Defective 1 6 .06 2 0 .00 3 4 .04 … … … 20 18 .18 200 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e p-Chart Calculations © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Example p-Chart 0.2 0.18 0.16 0.14 0.12 0.1 Proportion defective 0.08 0.06 0.04 0.02 2 4 6 8 10 12 14 16 18 20 . . Sample number © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e c-Chart © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e c-Chart Example Count # of defects in 15 rolls of denim fabric Sample # # Defects 1 12 2 8 3 16 … … 15 15 190 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e c-Chart Calculations © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Example c-Chart . 3 6 9 12 15 18 21 24 2 4 8 10 14 Sample number Number of defects © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Charts For Variables Mean chart (X-Bar Chart) Uses average of a sample Range chart (R-Chart) Uses amount of dispersion in a sample © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Range (R) Chart © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

R-Chart Example Slip-ring diameter (cm) Sample 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 … … … … … … … … 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

3 Control Chart Factors Sample size -chart R-chart n A2 D3 D4 2 1.88 0 3.27 3 1.02 0 2.57 4 0.73 0 2.28 5 0.58 0 2.11 6 0.48 0 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e R-Chart Calculations © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Example R-Chart © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e x Chart Calculations © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e x-Chart Example © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Using x- and R-Charts Together Each measures process differently Process average and variability must be in control © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Example x-Chart © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Chart Patterns UCL UCL LCL LCL Sample observations consistently below the center line Sample observations consistently above the center line © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Chart Patterns UCL UCL LCL LCL Sample observations consistently increasing Sample observations consistently decreasing © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Chart Patterns UCL UCL LCL LCL Sample observations consistently below the center line Sample observations consistently above the center line © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Zones For Pattern Tests Values for example 4.4 UCL 5.08 Zone A 5.05 Zone B 5.03 Zone C 5.01 Zone C 4.98 Zone B 4.965 Zone A 4.94 LCL © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Control Chart Patterns 1. 8 consecutive points on one side of the center line. 2. 8 consecutive points up or down across zones. 3. 14 points alternating up or down. 4. 2 out of 3 consecutive points in zone A but still inside the control limits. 5. 4 out of 5 consecutive points in zone A or B. © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Performing A Pattern Test Sample x Above/below Up/down Zone 1 4.98 B -- B 2 5.00 B U C 3 4.95 B D A 4 4.96 B D A 5 4.99 B U C 6 5.01 -- U C 7 5.02 A U C 8 5.05 A U B 9 5.08 A U A 10 5.03 A D B © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Results Of Pattern Test 2 of 3 consecutive points in zone A Samples 3 and 4 Process should be checked © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Sample Size Determination Attribute control charts 50 to 100 parts in a sample Variable control charts 2 to 10 parts in a sample © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Process Capability Range of natural variability in process Measured with control charts. Process cannot meet specifications if natural variability exceeds tolerances 3-sigma quality specifications equal the process control limits. 6-sigma quality specifications twice as large as control limits © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Process Capability Process cannot meet specifications Process can meet specifications PROCESS Natural variation specifications Design PROCESS Natural variation specifications Design Process capability exceeds specifications © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Acceptance Sampling Accept/reject entire lot based on sample results Not consistent with TQM of Zero Defects Measures quality in percent defective © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Sampling Plan Guidelines for accepting lot Single sampling plan N = lot size n = sample size (random) c = acceptance number d = number of defective items in sample If d <= c, accept lot; else reject © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Producer’s & Consumer’s Risk TYPE I ERROR = P(reject good lot)  or producer’s risk 5% is common TYPE II ERROR = P(accept bad lot)  or consumer’s risk 10% is typical value © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Quality Definitions Acceptance quality level (AQL) Acceptable fraction defective in a lot Lot tolerance percent defective (LTPD) Maximum fraction defective accepted in a lot © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Operating Characteristic (OC) Curve Shows probability of lot acceptance Based on sampling plan quality level of lot Indicates discriminating power of plan © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Operating Characteristic Curve AQL LTPD  = 0.10  = 0.05 Probability of acceptance, Pa { 0.60 0.40 0.20 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.80 Proportion defective 1.00 OC curve for n and c © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Average Outgoing Quality (AOQ) Expected number of defective items passed to customer Average outgoing quality limit (AOQL) is maximum point on AOQ curve © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e AOQ Curve 0.015 AOQL Average Outgoing Quality 0.010 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AQL LTPD (Incoming) Percent Defective © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Russell/Taylor Oper Mgt 3/e Double Sampling Plans Take small initial sample If # defective < lower limit, accept If # defective > upper limit, reject If # defective between limits, take second sample Accept or reject based on 2 samples Less costly than single-sampling plans © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Multiple (Sequential) Sampling Plans Uses smaller sample sizes Take initial sample If # defective < lower limit, accept If # defective > upper limit, reject If # defective between limits, resample Continue sampling until accept or reject lot based on all sample data © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc

Choosing a Sampling Method An economic decision Single sampling plans high sampling costs Double/Multiple sampling plans low sampling costs © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e 2000 by Prentice-Hall, Inc