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Chapter 17 Statistical Quality Control Mr.Mosab I. Tabash PowerPoint PPT Presentation


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Chapter 17 Statistical Quality Control Mr.Mosab I. Tabash. Learning Objectives. Students will be able to: Define the quality of a product or service. Develop four types of control charts

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Chapter 17 Statistical Quality Control Mr.Mosab I. Tabash

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Chapter 17 statistical quality control mr mosab i tabash

Chapter 17

Statistical Quality Control

Mr.Mosab I. Tabash

17-1


Learning objectives

Learning Objectives

Students will be able to:

  • Define the quality of a product or service.

  • Develop four types of control charts

  • Understand the basic theoretical underpinnings of statistical quality control, including the central limit theorem.

  • Know whether a process is in control.

17-2


Chapter outline

Chapter Outline

17.1 Introduction

17.2 Defining Quality and TQM

17.3 Statistical Process Control

17.4 Control Charts for Variables

17.5 Control Charts for Attributes

17-3


Introduction

Introduction

Quality is a major issue in today’s organizations.

Quality control (QC), or quality management, tactics are used throughout the organization to assure deliverance of quality products or services.

Statistical process control (SPC) uses statistical and probability tools to help control processes and produce consistent goods and services.

Total quality management(TQM) refers to a quality emphasis that encompasses the entire organization.

17-4


Definitions of quality

Definitions of Quality

  • “Quality is the degree to which a specific product conforms to a design or specification.”

  • “Quality is the totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs.”

  • “Quality is fitness for use.”

  • “Quality is defined by the customer; customers want products and services that, throughout their lives, meet customers’ needs and expectations at a cost that represents value.”

  • “Even though quality cannot be defined, you know what it is.”

17-5


Statistical process control spc

Statistical Process Control (SPC)

  • Statistical technique used to ensure process is making product to standard. It can also monitor, measure, and correct quality problems.

  • Control charts are graphs that show upper and lower limits for the process we want to control.

    Thus, SPC involves taking samples of the process output and plotting the averages on a control chart.

17-6


Statistical process control spc continued

Statistical Process Control (SPC) (continued)

All processes are subject to variability.

  • Natural causes: Random variations that are uncontrollable and exist in processes that are statistically ‘in control.’

  • Assignable causes: Correctable problems that are not random and can be controlled.

    • Examples: machine wear, unskilled workers, poor material.

      The objective of control charts is to identify

      assignable causes and prevent them from

      reoccurring.

17-7


Statistical process control steps

Statistical Process Control Steps

No

Produce Good

Start

Provide Service

Assign.

Take Sample

Causes?

Yes

Inspect Sample

Stop Process

Create

Find Out Why

Control Chart

17-8


Control chart patterns

Control Chart Patterns

Upper control

chart limit

Target

Normal behavior.

One point out above.

Investigate for

cause.

One point out below.

Investigate for

cause.

Lower control

chart limit

17-9


Control chart patterns continued

Control Chart Patterns (continued)

Upper control

chart limit

Target

Two points near upper control. Investigate

for cause.

Two points near lower

control. Investigate

for cause.

Run of 5 points above central line.

Investigate for cause.

Lower control chart limit

17-10


Control chart patterns continued1

Control Chart Patterns (continued)

Upper control

limit

Target

Erratic behavior.

Investigate.

Run of 5 points below

central line.

Investigate for cause.

Trends in either

Direction.

Investigate for cause of progressive change.

Lower

control limit

17-11


Control chart types

Control Chart Types

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control

Charts

Variables

Attributes

Charts

Charts

R

P

C

X

Chart

Chart

Chart

Chart

17-12


Control chart types continued

Control Chart Types(continued)

17-13


Control charts for variables clt

Control Charts for Variables - CLT

The central limit theorem

(CLT) says that the distribution

of sample means will follow a

normal distribution as the sample

size grows large.

µ = µ and δ = δ

n

-

-

x

x

x

17-14


Sampling distribution of sample means

Sampling Distribution of Sample Means

99.7% of all x

fall within ± 3 x

95.5% of all x fall within ± 2 x

17-15


Control charts for variables

Control Charts for Variables

_

X charts measure the central tendency of a process and indicate whether changes have occurred.

R charts values indicate that a gain or loss in uniformity has occurred.

X charts and R charts are used together to monitor variables.

-

17-16


Steps to follow in using x and r charts

Steps to Follow in Using X and R Charts

__

1. Collect 20 - 25 samples of n = 4, or n = 5 from a stable process. Compute the mean and range of each sample.

2. Compute the overall means. Set appropriate control limits - usually at 99.7 level. Calculate upper and lower control limits. If process not stable, use desired mean instead of sample mean.

3. Graph the sample means and ranges on their respective control charts. Look to see if any fall outside acceptable limits.

17-17


Steps to follow in using x and r charts continued

Steps to Follow in Using X and R Charts (continued)

__

4. Investigate points or patterns that indicate the process is out of control. Try to assign causes for the variation, then resume the process.

5. Collect additional samples. If necessary, re-validate the control limits using the new data.

17-18


Setting control limits for the x chart

Setting Control Limits for the X Chart

Control Limits

From Table

Sample Range at Time i

Sample Mean at Time i

# of Samples

17-19


Setting control limits for the r chart

Setting Control Limitsfor the R Chart

From Table

Sample Range at Time i

# Samples

17-20


Table factors for control chart limits

Table Factors for Control Chart Limits

17-21


Super cola example x and r chart

Super Cola Example: x and R Chart

Super Cola bottles soft drinks labeled “net weight 16 ounces.” Several batches of 5 bottles each revealed the following:

Each batch has 5 bottles of cola

_

Construct a X and R chart for the data

17-22


Chapter 17 statistical quality control mr mosab i tabash

Super Cola Example: x and R Chart

Step 1: Collected 20 samples with 5 bottles in each. Compute the mean and range of each batch.

The data are given on the previous slide.

17-23


Chapter 17 statistical quality control mr mosab i tabash

Super Cola Example: x and R Chart

Step 2: Compute the overall means and range (x , R), calculate the upper and lower control limits at the 99.7%:

Mean = 16.01 ounces

Range = 0.25 ounces

For X chart

UCL = 16.01 + (0.577)(0.25) = 16.154

LCL = 16.01 – (0.577)(0.25) = 15.866

For R Chart

UCL = (2.114)(0.25) = .5285

LCL = (0)(0.25) = 0

_

_

17-24


Chapter 17 statistical quality control mr mosab i tabash

Super Cola Example: x and R Chart

Step 3: Graph the sample means and determine if they fall outside the acceptable limits.

17-25


Chapter 17 statistical quality control mr mosab i tabash

Super Cola Example: x and R Chart

Step 4: Investigate points or patterns that indicate the process is out of control.

Are there any points we should investigate??

17-26


Chapter 17 statistical quality control mr mosab i tabash

Super Cola Example: x and R Chart

Step 5: Collect additional data and revalidate the control limits using the new data.This is particularly important for Super Cola because the original control limits were obtained from ‘unstable’ data.

17-27


Control charts for attributes

Control Charts for Attributes

p chartsmeasure the percent defective in a sample and are used to control attributes that typically follow the binomial distribution.

c chartsmeasure the count of the number defective and are used to control the number of defects per unit. The Poisson distribution is its basis.For example:

  • % of mortalities per month versus # of mortalities per month.

  • % of typed pages with mistakes vs. # of mistakes per page.

  • % of hamburgers without pickles per shift vs. # of missing pickles per shift.

17-28


Setting control limits for p chart

Setting Control Limitsforp Chart

-

p

(

1

p

)

=

+

UCL

p

z

P

n

-

p

(

1

p

)

=

-

UCL

p

z

P

n

z = 2 for 95.5% limits; z = 3 for 99.7% limits

# Defective items in sample i

Size of sample i

17-29


Arco p chart example

ARCO p Chart Example

Data entry clerks at ARCO key in thousands of insurance records each day. One hundred records were obtained from 20 clerks and checked for accuracy.

p = 0.04

17-30


Arco p chart example continued

ARCO p Chart Example (continued)

-

p

(

1

p

)

=

+

= 0.04 – 3 (.04)(.96)

= 0.04 + 3 (.04)(.96)

UCL

p

z

P

n

100

100

-

p

(

1

p

)

=

-

UCL

p

z

P

n

So,

UCL = 0.10

LCL = 0… cannot have a negative percent defective

17-31


Arco s p chart example continued

ARCO’s pChart Example (continued)

UCLp = 0.10

p-Chart

.12

.11

.10

.09

Fraction Defective

.08

.07

.06

.05

.04

.03

.02

.01

1

2

3

4

5

6

7

8

9

1

0

1

1

1

2

1

3

1

4

1

5

1

6

1

7

1

8

1

9

2

0

.00

LCLp = 0.00

Sample Number

What can you say about the accuracy of ARCO’s clerks???

17-32


Setting control limits for c chart

Setting Control Limitsforc Chart

UCL = c + z cLCL = c – z c

z = 2 for 95.5% limits; z = 3 for 99.7% limits

Where c = average of all of the samples

17-33


Red top cab c chart example

Red Top Cab c Chart Example

Red Top Cab Company is interested in studying the number of complaints it receives about the poor cab driver behavior. For nine days the manager recorded the total number of calls he received.

c = 6 complaints per day

UCL = 6 + 3 ( 6 ) = 13.35

LCL = 6 – 3 ( 6 ) = 0… cannot have negative mistakes.

17-34


Red top cab company c chart example continued

Red Top Cab Company c Chart Example (continued)

After the control chart was posted prominently, the number of complaints dropped to an average of 3 per day. Can you explain why this may have occurred???

17-35


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