Lean six sigma process improvement tools and techniques by donna summers chapter 18

Walter Shewhart 1891-1967 – Father of Statistical Process Control – Inventor of Control Charts – Proposed concept of common cause and special cause variation... Variables Control Chart

Variables Control Chart

Chapter 18

Variables Control Chart

• Dr Walter Shewhart (1891-1967)

– Father of Statistical Process Control

– Inventor of Control Charts

– Proposed concept of common cause and

special cause variation

Variables Control Chart

• Dr Walter Shewhart (1891-1967)

– A phenomenon will be said to be controlled

when, through the use of past experience, we can predict, at least within limits, how the

phenomenon may be expected to vary in the

future Here it is understood that prediction

within limits means that we can state, at least

approximately, the probability that the

observed phenomenon will fall within the

given limits.

Variables Control Chart

• Controlled variation, chance, or common

causes

– variation present in a process due to the very

nature of the process.

– small random changes in the process that

cannot be avoided

– consistently affect the process and its

performance day after day, every day.

– This type of variation can be removed from

the process only by changing the process

Variables Control Chart

• Uncontrolled variation, special or assignable

causes

– comes from sources external to the process.

– This type of variation is not normally part of the

process

– Assignable causes are variations in the process that

can be identified and isolated as the specific cause of

a change in the behavior of the process.

– This type of variation arises because of special

circumstances.

Variables Control Chart

Control charts serve two basic functions:

1 Decision-making tools They provide an economic basis for making a decision as to whether to investigate for potential problems, to

adjust the process, or to leave the process alone.

a Control charts provide information for timely decisions concerning recently produced items

b Control chart information is used to determine the process

capability, or the level of quality the process is capable of producing Samples of completed product can be statistically compared with

the process specifications This comparison provides information

concerning the process’s ability to meet the specifications set by the product designer.

Variables Control Chart

2 Problem-solving tools They point out where

improvement is needed.

a Control chart information can be used to help

locate and investigate the causes of the

unacceptable or marginal quality By observing the patterns on the chart the investigator can

determine what adjustments need to be made.

b During daily production runs, the operator can

monitor machine production and determine when

to make the necessary adjustments to the process

or when to leave the process alone to ensure

quality production.

Variables Control Chart

Several types of variation are tracked with

statistical methods These include:

1.Within-piece variation, or the variation within

a single item or surface

2.Piece-to-piece variation, or the variation that

occurs among pieces produced at

approximately the same time

3.Time-to-time variation, or the variation in the

product produced at different times of the

day.

Variables Control Chart

• The centerline of a variables control

chart shows where the process

average is centered, the central

tendency of the data

• The upper control limit (UCL) and

lower control limit (LCL) describe

the spread of the process

Variables Control Chart

To construct a variables control chart:

1 Define the Problem 

2 Select the Quality Characteristic to Be Measured    

3 Choose a Rational Subgroup Size to Be Sampled  

4 Collect the Data  

5 Determine the Trial Centerline for the X-bar Chart  

6 Determine the Trial Control Limits for the X-bar Chart

7 Determine the Trial Control Limits for the R Chart  

8 Examine the Process: Interpret the Control Chart     

Variables Control Charts

X =

X i

i = 1

m

∑

m UCL X = X + A 2 R LCL X = X − A 2 R

R =

R i

i = 1

m

∑

m UCL R = D 4 R LCL R = D 3 R

Variables Control Chart

A control chart exhibits a state of control when:

1 Two-thirds of the points are near the center

value.

2 A few of the points are on or near the center

value.

3 The points appear to float back and forth across

the centerline.

4 The points are balanced (in roughly equal

numbers) on both sides of the centerline.

5 There are no points beyond the control limits.

6 There are no patterns or trends on the chart.