Quality Improvement

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Definitions

• Quality product or service: A product or service that meets or exceeds the expectations of the customer.

• Process: Any combination of people, machinery, material, and methods that is intended to produce a product or service.

• Quality Characteristics: Features of a product that describe its fitness for use .Introduction to Business

Statistics, 5e

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(c)2000 South-Western College Publishing

Definitions

• Statistical Process Control (SPC): The application of statistical quality-

control methods to measure and analyze the variation found in a process.

• Control Chart: A statistical chart used to monitor various aspects of a

process and to determine if the process is in control or out of control.Introduction to Business

Statistics, 5e

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(c)2000 South-Western College Publishing

Malcolm Baldrige National Quality Award Criteria

• Leadership System

• Strategic Planning

• Customer and Market Focus

• Information and Analysis

• Human Resource Focus

• Process Management

• Business ResultsIntroduction to Business Statistics, 5e

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Quality Improvement Tools

• Flowcharts

• Cause-and-Effect Diagrams

Introduction to Business Statistics, 5e

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Flowchart

Figure 12.2

Introduction to Business Statistics, 5e

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Cause-and-Effect Diagram

Figure 12.3

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Process Variation and Control Charts: Sources of Variation

• Machinery

• People

• Materials

• Production Methods

• The Environment

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Deming Funnel Experiment: Strategies

• Strategy 1: Do not react to this random variation and do not move the funnel.

• Strategy 2: Measure the distance from the marble’s resting place to the bull’s-eye. Move the funnel and equal distance, but

in the opposite direction.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Deming Funnel Experiment: Strategies

• Strategy 3: Measure the distance from the marble’s resting place to the

bull’s-eye. Move the funnel this distance, in the opposite direction, starting at the bull’s- eye.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Deming Funnel Experiment

Figure 12.5

Introduction to Business Statistics, 5e

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Control Charts

• A process is in control if the observed variation is due to inherent or natural variation. This variability is the cumulative effect of many small, essentially uncontrollable, causes.

• A process in out of control if a relatively large variation is introduced that can be traced to an assignable cause.

Introduction to Business Statistics, 5e

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General Form of a Control Chart

Figure 12.6

Introduction to Business Statistics, 5e

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Control Chart

Figure 12.7

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X and R Charts

X X 1 X 2 X m

m

ˆ R d2

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X and R Charts

Tables 12.2 & 12.3

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X and R ChartsProcess for Estimating

• Determine the average of the m values of R.

• Select the values of d2 from Table 12.3 using the corresponding sample size, n.

• Estimate using:

ˆ R d2

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

X and R ChartsControl Limits

UCL X 3ˆ n

X 3( R / d2)

n

Center Line X

LCL X 3ˆ n

X 3( R / d2)

n

Introduction to Business Statistics, 5e

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X and R ChartsControl Limits

Figure 12.9

Introduction to Business Statistics, 5e

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R Chart

sR R d3

d2

UCL R 3sR R 3R d3

d2

1 3

d3

d2

R

LCL R 3sR R 3R d3

d2

1 3

d3

d2

R

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

R Chart

D3 1 3d3

d2and D4 1 3

d3

d2

By defining

UCL D4 R

Center Line R

LCL D3 R Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Steps for Making X and R Charts

• Collect m samples of data, each of size n.

• Compute the average of each subgroup.

• Compute the range for each subgroup.

• Find the overall mean.

• Find the average range.

• Estimate .

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Steps for Making X and R Charts

• Compute the 3-sigma control limits for X.

• Compute the 3-sigma control limits for R

• Construct the control charts by plotting X and R points for each subgroup on the same vertical line.

Introduction to Business Statistics, 5e

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Pattern Analysis for X

Figure 12.12

Introduction to Business Statistics, 5e

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Minitab X Chart

Figure 12.13

Introduction to Business Statistics, 5e

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Control Chart for the Proportion Nonconforming: The p chart

Reasons for Using a p Chart

• Quality measurements are not possible.

• Quality measurements are not practical.

• Many characteristics on each part are being judged during inspection

• The main question of interest is: “will the process be able to produce conforming products over time?”

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Steps for Making p Charts

• Collect m samples of data, each of size, n.

• Determine the proportion nonconforming for each sample.

• Find p, the overall proportion nonconforming.

• Compute the 3-sigma control limits

• Draw the control lines and plot the values of pi.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

p Chart Equations

UCL p 3p (1 p )

n

CL p

LCL p 3p (1 p )

n

pi Ti

n

p Ti

mnp

total number of nonconforming units

total sample size

Introduction to Business Statistics, 5e

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p Chart for Ex. 12.3

Figure 12.17

Introduction to Business Statistics, 5e

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The c Chart Construction

• Collect m samples of data, each of size, n.

• Determine the number of nonconformities for the ith unit. Call this value ci.

• Find the average number of nonconformities per unit, c.

• Compute the 3-sigma control limits.

• Construct the chart.Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

c Chart Equations

c ci

m

UCL c 3 c

Center Line c

LCL c 3 c Introduction to Business Statistics, 5e

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Process Capability

• Specification Limits: process requirements

• Lower spec limit (LSL): the lower limit of the process output that meets the process requirements.

• Upper spec limit (USL): the upper limit of the process output that meets the process requirements.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Process Capability

Figure 12.20

The difference between 12.01 and 12.19 is referredto as the process spread.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Process Capability

Figure 12.21

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Process Capability Ratio Cp

Assumptions:

• The process is centered within specifications.

• The process is normally distributed.

• The process is stable.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Cp

Cp USL LSL

6 ˆ

Cp USL X 3 ˆ

(upper spec limit only)

Cp X LSL

3 ˆ (lower spec limit only)

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Process Capability Ratio Cpk

Assumptions

• The process may or may not be centered in spec.

• The process is normally distributed.

• The process is stable.

• Control charts will be used to monitor the process over time.

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Figure 12.22

Introduction to Business Statistics, 5e

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(c)2000 South-Western College Publishing

Procedure for Finding Cpk

1. Determine RL X LSL

3 ˆ

2. Determine RU USL X

3ˆ 3. Cpk Minimum of RL and RU

Introduction to Business Statistics, 5e

Kvanli/Guynes/Pavur

(c)2000 South-Western College Publishing

Figure 12.23

Introduction to Business Statistics, 5e

Kvanli/Guynes/Pavur

(c)2000 South-Western College Publishing