Chapter 14 Methods for Quality Improvement Quality, Processes, and - - PowerPoint PPT Presentation

Chapter 14

Methods for Quality Improvement

Quality, Processes, and Systems

Quality of a good or service – the extent to which it satisfies user needs and preferences 8 Dimensions of Quality

• Performance
• Features
• Reliability
• Conformance
• Durability
• Serviceability
• Aesthetics
• Other perceptions that influence judgment of quality

Quality, Processes, and Systems

Process – series of actions or operations that transforms input into outputs over time

Quality, Processes, and Systems

System – collection of interacting processes with an ongoing purpose

Quality, Processes, and Systems

Two important points about systems

• 1. No two items produced by a process are

the same

• 2. Variability is an inherent characteristic of

the output of all processes

Quality, Processes, and Systems

6 major sources of Process Variation

1. People 2. Machines 3. Materials 4. Methods 5. Measurement 6. Environment

Statistical Control

Control Charts – graphical devices used for

• monitoring process variation
• Identifying when to take action to

improve the process

• Assisting in diagnosing the

causes of process variation

run chart, or time series plot

Statistical Control

Run Chart enhanced by

• Adding centerline
• Connecting plot

points in temporal

• rder

Enhancements aid the eye in picking out any patterns

Statistical Control

Output variable of interest can be described by a probability distribution at any point in time. Particular value of output variable at time t can be thought of as being generated by these probability distributions The distribution may change over time, either the mean, the variance or both. Distribution of the process – distribution of the

• utput variable

Statistical Control

A process whose output distribution does not change over time is said to be in statistical control, or in control. Processes with changing distributions are out of statistical control, or out

• f control, or lacking stability.

Statistical Control

Patterns of Process Variation Patterns of Process Variation – changing distributions

Statistical Control

The output of processes that are in statistical control still have variability associated with them, but there is no pattern to this variability. It is random.

Statistical Control

Statistical Process Control – keeping a process in statistical control or bringing a process into statistical control through monitoring and eliminating variation Common Causes of variation – methods, materials, machines, personnel and environment that constitute a process and the inputs required by the process

Statistical Control

Special Causes of Variation (Assignable Causes) – events or actions that are not part of the process design. Processes in control still exhibit variation, from the common causes. Processes out of control exhibit variation from both common causes and special causes of variation Most processes are not naturally in a state

• f statistical control

Statistical Control

The Logic of Control Charts

Control charts are used to help differentiate between variation due to common and special causes When a value falls outside the control limits, it is either a rare event or the process is out of control

Mean when process is in control

The Logic of Control Charts

Hypothesis testing with control charts:

H0: Process is under control Ha: Process is out of control

Another view:

H0:  = centerline Ha:   centerline Ha here indicates that the mean has shifted

The Logic of Control Charts

Control limits vs. Specification limits Specification limits – set by customers, management, product designers. Determined as “acceptable values” for an output. Control limits are dependent

• n the process,

specification limits are not.

A Control Chart for Monitoring the Mean of a Process: The x-Chart

• control chart

that plots sample means

• Often used in concert

with R-chart, which monitors process variation

• More sensitive to

changes in process mean than a chart of individual measurements

x c h a r t 

A Control Chart for Monitoring the Mean of a Process: The x-Chart

To construct, you need 20 samples of a sample size of at least 2.

where A2 is found in a Table of Control Chart Constants, and R is the mean range of the samples

1 2 3

... :

k

x x x x C e n te r lin e x k     

2

: L o w er co n tro l lim it x A R 

2

: U p p er co n tro l lim it x A R 

A Control Chart for Monitoring the Mean of a Process: The x-Chart

Two important decisions in Constructing an x-chart

1.Determine sample size n 2.Determine the frequency with which samples are to be drawn Rational Subgroups – subgroups chosen with sample size n and frequency to make it likely that process changes will happen between rather than within samples Rational Subgrouping strategy maximizes the chance for measurements to be similar within each sample, and for samples to differ from each other.

A Control Chart for Monitoring the Mean of a Process: The x-Chart

Summary of x-chart Construction

1. Collect at least 20 samples with sample size n ≥ 2, utilizing rational subgrouping strategy 2. Calculate mean and range for each sample 3. Calculate mean of sample means x and mean of sample ranges R 4. Plot centerline and control limits 5. Plot the k sample means in the order that the samples were produced by the process

A Control Chart for Monitoring the Mean of a Process: The x-Chart

Constructing Zone Boundaries These zone boundaries are used in conjunction with Pattern-Analysis rules to help determine when a process is out

• f control

Using 3-sigma control limits Upper A-B Boundary:

 

2

2 3 x A R 

Lower A-B Boundary:

 

2

2 3 x A R 

Upper B-C Boundary:

 

2

1 3 x A R 

Lower B-C Boundary:

 

2

1 3 x A R 

Using estimate standard deviation of x ,

2

R d n

Upper A-B Boundary:

2

2 R d x n       

Lower A-B Boundary:

2

2 R d x n       

Upper B-C Boundary:

2

R d x n       

Lower B-C Boundary:

2

R d x n       

A Control Chart for Monitoring the Mean of a Process: The x-Chart

Any of the 6 rules being broken suggests an out of control process

A Control Chart for Monitoring the Variation of a Process: The R-Chart

R-chart used to detect changes in process variation R-chart plots and monitors the variation of sample ranges

A Control Chart for Monitoring the Variation of a Process: The R-Chart

To construct, you need 20 samples of a sample size of at least 2.

where D3 and D4 are found in a Table of Control Chart

• Constants. When n ≤ 6, there is only an upper control limit

1 2 3

... :

k

R R R R C e n te rlin e R k     

3

: L o w e r c o n tro l lim it R D

4

: U p p e r c o n tro l lim it R D

A Control Chart for Monitoring the Variation of a Process: The R-Chart

Summary of R-Chart Construction

1. Collect at least 20 samples with sample size n ≥ 2, utilizing rational subgrouping strategy 2. Calculate the range for each sample 3. Calculate mean of sample ranges R 4. Plot centerline and control limits. When n ≤ 6, there is

• nly an upper control limit

5. Plot the k sample ranges in the order that the samples were produced by the process

A Control Chart for Monitoring the Variation

• f a Process: The R-Chart

Constructing Zone Boundaries These zone boundaries are used in conjunction with Pattern-Analysis rules 1-4 to help determine when a process is out of control

Upper A-B Boundary:

3 2

2 R R d d       

Lower A-B Boundary:

3 2

2 R R d d       

Upper B-C Boundary:

3 2

R R d d       

Lower B-C Boundary:

3 2

R R d d       

Note: when n ≤ 6, the R-chart has no lower control limit, but boundaries can still be plotted if non-negative

A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart

p-chart used to detect changes in process proportion when output variable is categorical As long as process proportion remains constant, process is in statistical control

A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart

Sample-Size determination

Choose n such that where n = Sample Size p0 = an estimate of the process proportion p

 

9 1 p n p  

A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart

Calculations for p-chart Construction

฀

N u m b er o f d efective item s in sa m p le p N u m b er o f item s in sa m p le  : T o ta l n u m b e r o f d e fe c tiv e ite m s in a ll k sa m p le s C e n te rlin e p T o ta l n u m b e r o f u n its in a ll k sa m p le s 

 

1 : 3 p p U p p e r c o n tro l lim it p n  

 

1 : 3 p p L o w e r c o n tro l lim it p n  

A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart

Summary of p-Chart Construction

1. Collect at least 20 samples utilizing rational subgrouping strategy and appropriate sample size 2. Calculate proportion of defective units for each sample 3. Plot centerline and control limits. 4. Plot the k sample proportions on the control chart in the order the samples were produced by the process

A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart

Constructing Zone Boundaries These zone boundaries are used in conjunction with Pattern-Analysis rules 1-4 to help determine when a process is out of control

Upper A-B Boundary:

 

1 2 p p p n  

Lower A-B Boundary:

 

1 2 p p p n  

Upper B-C Boundary:

 

1 p p p n  

Lower B-C Boundary:

 

1 p p p n  

Note: when LCL is negative it should not be plotted. Lower zone boundaries can be plotted if non-negative

Diagnosing the Causes of Variation

If monitoring phase identifies that problems exist, diagnosis is needed to determine what the problems are.

Diagnosing the Causes of Variation

Cause-and-Effect diagrams used to assist in process diagnosis Basic Cause-and-Effect diagram:

Diagnosing the Causes of Variation

Cause-and-Effect diagram applied to specific problem:

Capability Analysis

Used when a process is in statistical control, but level of variation is unacceptably high.

Capability Analysis

• A Capability Analysis

diagram is used to assess process capability.

• This diagram builds on

a frequency distribution

• f a large sample of

individual measurements from the process by adding specification limits and target value

Capability Analysis

From this, 2 approaches

• 1. Report percentage of outcomes that fall
• utside of specification limits
• 2. Construct a capability index Cp where

     

6

p

S p e c ific a tio n s p r e a d U S L L S L C P r o c e s s S p r e a d    

Capability Analysis

Interpretation of Cp

If Cp=1, (specification spread = process spread) process is capable If Cp>1, (specification spread > process spread) process is capable If Cp<1, (specification spread < process spread) process is not capable

If the process follows a normal distribution

Cp=1.00 means about 2.7 units per 1000 will be unacceptable Cp=1.33 means about 63 units per million will be unacceptable Cp=1.67 means about .6 units per million will be unacceptable Cp=2.00 means about 2 units per billion will be unacceptable