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Chapter 5 Quality Control

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Quality Control Purpose: monitor and maintain quality levels of products/services/processes, and try to improve product/service/process designs in ways that result in better quality products, services, and processes Quality Control Departments: Traditional focus inspections Newer focus quality training, improvements, working with suppliers, few inspections

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Quality Control Process variation causes a process to be less consistent, resulting in lower quality W. Edwards Deming 2 causes of variation Common causes: normal (typical) variation, inherent to the process, difficult/expensive to reduce; example– a machine is not very accurate because it is old Special causes: due to a specific problem, not inherent to process, usually easy/cheap to fix; example– a machine’s quality level is lower one morning, and after you investigate you discover that operator has hangover To improve quality, identify and fix special causes of variation first (low hanging fruit)

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Process Variation 2 different machines can do the same operation. Which should be used? 10,000 units of a gear shaft needed – set up machine and do test run of 100 units. 9.00 9.05 9.1 9.15 8.95 8.9 8.85 specs diameter (mm) machine A 20% out of spec

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**Process Variation Which should be used, machine A or machine B? 9.00**

9.05 9.1 9.15 8.95 8.9 8.85 specs diameter (mm) machine B 50% out of spec

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**Quality Control Throughout Productive Systems**

Raw Materials, Parts, and Supplies Production Processes Products and Services Acceptance Tests Control Charts Quality of Inputs Monitoring Quality of Partially Completed Products Outputs Conversion

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**Monitoring Process Quality**

Run Diagrams useful when starting a process (most likely time for errors) measure every piece plot measurements look for outliers and patterns to investigate process is in-control if no outliers or patterns (just typical randomness)

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**Run Diagram—1st Attempt Outer Diameters of 30 Pieces**

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**Run Diagram—2nd Attempt Outer Diameters of 30 Pieces**

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**GP4890 ROSEBURG FOREST PRODUCTS SHIPPING TEMPERATURE 1/21/93 – 2/15/93**

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**Control Charts X chart and R chart**

when measuring a variable (e.g., length, weight, volume, viscosity) assumes normal distribution of sample means X is the measurement of one unit X is the mean measurement of one sample X is the expected value of the measurement R is the range of one sample (high – low) R is the expected value of the range

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Control Charts p chart when measurement has only two outcomes (e.g., yes/no, defective/nondefective, good/bad) assumes binomial distribution p is fraction or percent of bad parts in a sample p is the expected value of p

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Control Charts c chart when measuring the total number of defects in a sample sample size is 2 or more units assumes Poisson distribution c is number of defects in a sample c is the expected value of c

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Control Charts u chart when measuring the number of defects on one unit sample size is one unit assumes Poisson distribution u is number of defects on one unit u is the expected value of u only difference between u and c charts is sample size (1 or many)

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**Control Limits X chart – for sample means**

Upper control limit (UCL) = X + AR Lower control limit (LCL) = X – AR X = expected value of X (average over many samples) R = expected value of R (average over many samples) A = a constant from Table

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**Control Limits R chart – for sample ranges UCL = D2R LCL = D1R**

D1 and D2 are constants from Table

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**Control Limits p chart – for fraction/percent defectives in sample**

p = expected fraction/percent defectives in samples n = size of one sample (number of units)

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**Control Limits c chart – for total number of defects in a sample**

c = expected number of defects in samples X and R chart example: Suppose a company wants to start using X and R control charts. They have collected 25 samples of 5 units in each sample to estimate X and R.

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Sample # 1st unit 2nd unit 3rd unit 4th unit 5th unit Average X-bar Range R 1 10.60 10.40 10.30 9.90 10.20 10.28 .70 2 9.98 10.25 10.05 10.23 10.33 10.17 .35 3 9.85 10.15 10.07 .40 4 10.10 9.95 10.09 5 10.24 10.50 10.31 .30 6 10.16 7 10.12 .50 8 10.27 9 10.34 10 11 9.50 10.35 .85 12 10.36 9.80 10.14 13 10.70 .80 14 15 10.54 10.55 10.00 .55 16 10.29 .60 17 10.80 10.42 18 9.96 1.00 19 10.22 20 10.38 21 9.60 22 23 9.88 24 10.18 25

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**Compute Control Limits**

X chart: for n=5 in Table (p.671), A=0.577 UCL,LCL = ± A( ) = LCL = and UCL = X R R chart: for n=5 in Table, D1=0 and D2=2.116 LCL = D1 = UCL = D2 = R R

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X Chart UCL 10.56 LCL 9.86 X=10.21

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R Chart LCL=0 UCL=1.27 R=0.6

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Control Chart Problems to Investigate

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**GP4890 ROSEBURG FOREST PRODUCTS % CAUSTIC 1/15/93 – 2/13/93**

UPPER CONTROL LIMIT LOWER CONTROL LIMIT 3 2.5 2 1.5 1 0.5

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**p Chart Example Process placing labels on jeans**

Label placement is either defective or non-defective. Typically, about 1.5% of labels are considered defective. Compute control limits for a p chart, with sample size = 200. If a sample has 6 bad labels, is this in-control?

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c Chart Example Twice a day, Ford takes a sample of 5 cars after the painting operation to count the number of bad spots on the freshly painted surfaces. The typical number of defects per sample is 3.1 bad spots. Compute 3σ control limits.

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**Good/Bad & Investigate or Not**

Above UCL Below LCL X chart R chart p chart c chart u chart

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**Guidelines for Determining Which Control Chart to Use**

Identify the item or product to be evaluated for quality. What characteristic is to be measured? Should every item be checked, or should a random sample be taken? Is the characteristic measured on a continuous scale? Is the item either good or bad, or is the number of defects on one item important? Should the random sample size be one unit, or should it be more than one unit?

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**Control Chart Examples**

1. A local building contractor builds large custom homes. He wants to use a control chart to monitor the number of problems that customers find in the finished homes. What type of control chart should be used? 2. A manufacturer of semiconductors chips plans to use a control chart to monitor the quality of chips they produce. Due to the complexity and density of circuits on each chip, typically 5% to 15% of the chips are faulty, which is about normal for the industry. Faulty chips are returned by customers for a full refund or replacement. What type control chart should be used? 3. A professional proofreader checks manuscript pages for typing errors. What type of control chart should be used to monitor the quality of their proofreading?

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**Control Chart Examples**

4. As cereal boxes are filled in a factory they are weighed for their contents by an automatic scale. The target is to put 10 ounces of cereal in each box. What type of control chart should be used to monitor how well they are achieving their target? 5. What type of control chart should Microsoft use to monitor the quality of their software programmers in developing computer code for assigned portions of larger software products? 6. What type of chart should a business school use to monitor the quality of incoming MBA students based on GMAT scores?

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BMM 3633 Industrial Engineering

BMM 3633 Industrial Engineering

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