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Quality Management

Guanyi LuMay 3, 2023

Learning Objectives• Understand total quality management.• Understand the cost of quality.• Understand how processes are monitored with control

charts.• Calculate the capability of a process.• Understand six sigma philosophy.• Understand the lean manufacturing philosophy.

Total Quality Management • Total quality management (TQM): managing the entire

organization so that it excels on all dimensions of products and services that are important to the customer

• Two fundamental operational goals:– Careful design of the product or service– Ensuring that the organization’s systems can consistently

produce the design

Quality Specifications• Design quality: inherent value of the product in the

marketplace

• Conformance quality: degree to which the product or service design specifications are met – Quality at the source: the person who does the work takes

responsibility for making sure it meets specifications• The later a defect is detected, the more costly the defect is

Defects and Profit Losses

Defectsfound at:

Own Process

Next Process

End of Line

FinalInspection

End User’sHand

Impact to the company

Very minor

Minor delay

ReworkDelay

Significant reworkDelay in deliveryAdditional inspection

Warranty cost Administrative cost

Reputation

Loss of market share

Cost of Quality• Basic cost assumptions

– Failures are caused– Prevention is cheaper– Performance can be measured

• Cost of quality– Appraisal cost– Prevention cost– Internal failure cost– External failure cost

Statistical Process Control• Statistical Process Control (SPC) is a set of techniques

designed to evaluate quality from a conformance view.

• Can be applied to both manufacturing and service processes

• Statistics on variations– Process capability determines how good a process is at making parts

when it is running properly• Measure the overall variations

– Control charts are used to check continuously whether the process is running properly

• Differentiate two types of variations

Two Types of Variations• Assignable variation

– Variation that is caused by factors that can be clearly identified and possibly even managed

• Common variation– Variation that is inherent in the process

• The distinction between common variation and assignable variation is NOT a universal truth

General Form of Control Charts

1 5 9 13 17 21Sample No.

SampleValueUCL

Average

The Basics of Control Charts• Control charts are graphical tools to statistically

distinguish between assignable and common variations

• Attribute charts versus variable charts– Attributes are quality characteristics that are classified as either

conforming or not conforming to specification• p charts

– Variables refer to measurable quality characteristics• X-bar charts and R charts

• Based on samples taken from the process

Sample Size• Control charts are plotted based on samples taken from

the process

• Sample size: the number of units (data points) included in a sample– Make the sample size large enough to expect to count the

attribute twice in each sample• If the defect rate were about 1%, an appropriate sample size would be 200

– Sample sizes for variable control charts are much smaller, typically from 2 to 10. Larger sample sizes may be necessary for detecting finer variations of a process

Attribute Control Chart: p Chart

• When it is difficult to comp up with a single variable that captures the degree of specification, it is desirable to track the percentage of defective items in a given sample

• Denote by p this percentage and by the average percentages of defects over all samples

Control Limits For p Chart

(1 )sample sizepp ps

p pUCL p zs

p pLCL p zs

z=3 (for 99.7% confidence)z=2.58 (for 99% confidence)

, or 0, whichever is larger

Example: p Chart

• Facing intense competitions, the manager of Cheesy Pizza is thinking of implementing a “30-minute delivery” policy which promises a customer a free pizza if the delivery time exceeds 30 minutes. Before publicizing the policy, the manager sets up a p-chart based on 6 samples of 50 deliveries. (z=3) Is the delivery process in control or out of control?

SAMPLE Number of Fraction ofbelated deliveries belated deliveries

#1 4#2 9#3 4 #4 5#5 2#6 6

Example: p Chart

1 2 3 4 5 6

p value

Variable Control Charts:X-bar Chart and R chart

• X-bar chart• The x-axis corresponds to sample numbers• The y-axis corresponds to the mean of each sample

• R chart• The x-axis corresponds to sample numbers• The y-axis corresponds to the range of each sample

Construct X-bar Chart and R Chart

• The mean of each sample

• The range of each sample– R = max{x1, x2, …, xn} - min{x1, x2, …,xn}

• : the average of

• : the average range

1 2 ...X

nnx x x

X-bar Chart and R Chart Control Limits

UCL A R

LCL A R

RD LCL

RD UCL

Control Chart Parameters(99.7% confidence)

SampleSize (n)

Factor forX-bar chart

Factor forLCL in R chart

Factor for UCL in R chart (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

9 0.34 0.18 1.82

10 0.31 0.22 1.78

Example: X-bar Chart and R Chart

#1 6.2 6.1 5.9 6.0 #2 5.8 6.0 6.1 6.0 #3 6.0 6.0 6.0 6.0 #4 5.2 5.8 6.1 6.0

#6 6.3 6.1 5.9 5.7

Sample Item NumberNumber 1 2 3 4

#5 5.9 5.9 6.0 6.1

Example: X-bar Chart and R Chart

1 2 3 4 5 6

average

1 2 3 4 5 6

average

Process Capability

• In control vs. meet quality requirement• Running properly vs. making good products

• A design specification includes– An upper tolerance level (UTL)– A lower tolerance level (LTL)

• A process is capable if it can produce output according to

the design specifications

• Measure: Process Capability Index Cpk

Process Capability Index

where X = Estimated process average

σ = Estimated Process Standard Deviation

Cpk = min [(X-LTL)/3s, (UTL –X) /3σ]

Example

• We are the maker of this cereal. Consumer reports has just published an article that shows that we frequently have less than 16 ounces of cereal in a box.

• Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.

• Upper Tolerance Limit = _____

• Lower Tolerance Limit = _____

• We examine 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of 0.529 ounces. Cpk = _____

Interpretations

• An index that shows how well the units being produced fit within the specification limits

• The greater the Cpk is, the more capable the process is in terms of producing quality products

• Threshold Cpk = 1.3 • Six-sigma companies want 2.0!

Six Sigma

Six Sigma quality – 3.4 defects per million opportunities (DPMO)

Six Sigma

• Six Sigma is a business management strategy, initially implemented by Motorola, that today enjoys widespread application in many sectors of industry (Source:Wikipedia.org)

• Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects (errors) and variability in manufacturing and business processes

Six Sigma Standard

• Metric: defects per million opportunities (DPMO)

• When the process mean is centered there are only 2 defects per billion

• If, for some reason, the process mean is shifted off the center by 1.5 sigma, there are 3.4 defects per million

• If the process goes out of control (adjustment) it might be identified before ‘bad’ units are produced

GE's Six-Sigma Program

• Employing statistical tools in a systematic project-oriented fashion through the define, measure, analyze, improve and control (DMAIC) cycle.

• Six Sigma at GE– In 1995, percentage of quality products was about 97% (3-4

sigma). – Started the Six Sigma program in Jan. 1996– Achieved $320 million in productivity gains and profits in 1997– Generated $750 million in Six Sigma savings over and above

the investment by 1998– Earned $1.5 billion in savings in 1999

DMAIC Methodology• Define -- Identify customers and their priorities; Identify a project; Identify

critical-to-quality characteristics

• Measure -- Determine how to measure the process; Identify key internal processes

• Analyze -- Determine most likely causes of defects; Understand why key defects are generated

• Improve -- Identify means to remove causes of defects; Confirm the key variables; Identify the maximum acceptance ranges; Modify process to stay within acceptable range

• Control -- Determine how to maintain improvements; Put tools in place to track key variables

The Fundamental Element of Lean Manufacturing

Eliminating waste

through continuous improvement

High Inventory Level

Low Inventory Level

The Kanban System

• Kanban system refers to a production and inventory control system, in which production instructions and parts delivery instructions are triggered by the consumption of parts at the downstream step

Push vs. Pull System

Finished Goods

CustomerDemand

RawMaterialSupplier

FinalAssembly

RawMaterialSupplier

FinalAssembly

Finished Goods

Material FlowInformation Flow

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