Statistical Process Control Workshop. An Introduction to the Principles behind SPC. Ilca Croufer. Workshop Outline. 1. Statistical Process Control a ) Definition b) Benefits & Tools 2. Process a) Definition b) Common & Special Cause Variation 3. Statistics Revision
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Statistical Process Control Workshop
An Introduction to the Principles behind SPC
Ilca Croufer
1. Statistical Process Control
a) Definition
b) Benefits & Tools
2. Process
a) Definition
b) Common & Special Cause Variation
3. Statistics Revision
a) Mean, Variance and Standard Deviation
b) Normal Distribution
4. Control Charts
5. Control Chart Construction
6. Examples of Root Cause Analysis Techniques
a) 5 Whys
b) Fishbone Diagram
Statistical process control (SPC) is a methodology focused on quality control and improvement, using data analysis
It consists of using valid statistical data analysis to determine and eliminate variation due to assignable causes.
It is based on the following principles:
- measuring the process
- identifying and eliminating unusual variation
- improving the process to its best target value
- monitoring the process performance over time
Process improvement
In-depth management decision making
Better understanding of process performance
Establish process baselines
Better control on variables that impact a process
Gain More predictability
Histograms
Scatter Diagrams
Run Charts
Pareto Charts
Control Charts
An activity which transforms inputs into outputs; (F(x) = Y)
X f(X) Y
Example: making a cup of tea, baking a cake, getting to work, etc.
Any process will have a certain degree of variation; some variation will be inherent to the process, some will not.
Variation in a Process = Common Cause Variation + Special Cause variation
INPUTS
ACTIVITY
OUTPUTS
Common Cause Variation:
- Irregular variation within an historical experience base
- Naturally present within the system
- Usually insignificant and predictable
Special Cause Variation
- Variation outside the historical experience base
- Assignable to a root cause
- Usually significant and unpredictable
Distribution: arrangement of values of a variable showing their observed or theoretical frequency of occurrence.
E.g.: 21 25 33 33 45 47 51 55 55 61
A distribution is usually characterised by its mean, standard deviation and shape
In Statistics, different types of distribution exist, with the Normal Distribution being the most well-known and commonly used.
Mean = ∑ (sum of observed values)
Number of observations
Variance = ∑ (observed value – mean)2
Number of observations
Standard Deviation ( ) = √ (Variance)
Consider the following distribution:
11, 17,25, 28, 34
Calculate the mean, variance and standard deviation.
Mean = (11+17+25+28+34) = 23
5
Variance = (11-23)2+(17-23)2+(25-23)2+(28-23)2+(34-23)2 = 66
5
Standard Deviation = √66 = 8.12
Mean = (1.0+0.8+0.8+1.2) = 0.95
4
Variance = (1.0-0.95)2+(0.8-0.95)2+(0.8-0.95)2+(1.2-0.95)2 = 0.0275
4
Standard Deviation = √0.0275 = 0.17
Bell-shaped curve
Symmetrical around the mean
Defined by its mean and standard deviation
68.3% of data found within one standard deviations away from the mean
95.5% of data found within two standard deviations away from the mean
99.7% of data found within three standard deviations away from the mean
Statistical tool used to
monitor the stability
of a process over time
Key features:
- UCL (Upper Control Limit) = mean + 3*sigma
- LCL (Lower Control Limit) = mean – 3*sigma
- central line (mean of data set)
A process is said to be in control when data points fall within limits of variation (i.e.: between Upper and Lower Control Limits)
Rule1: Any point falls beyond 3 sigma from the centre line
Rule2: Two out of three consecutive points fall beyond 2 sigma
on the same side of the centre line
Rule3: Four out of five consecutive points fall beyond 1 sigma
on the same side of the centre line
Rule4: Nine or more consecutive points fall on the same side
of the centre line
Consider the next set of control charts and identify whether the process is “in-control” or “out of control”:
(a) (b)
(c) (d)
Type I errors occur when a point falls outside the control limits even though no special cause is operating.
Type II errors occur when you miss a special cause because the chart isn't sensitive enough to detect it
All process control is vulnerable to these two types of errors.
Control charts can measure two types of data:
- Continuous Data(can be measured)
E.g.: temperature, volume, weight, height, time
- Discrete Data(can be counted)
E.g.: How many people in this room?
How many defects in an inspected unit?
There are different control charts to choose from depending on what data is available.
Before assessing the stability of a process over time using control charts, it is important to identify the type of data at hand, and how to consistently collect and validate it:
1. Decide what to collect: what metrics?
2. Determine the needed sample size
3. Identify source/location of data
4. Is the data in a useable form?
5. Identify how to collect the data consistently and validate it
6. Decide who will collect the data
7. Consider what you’ll have to do with the data (sorting, graphing,
calculations)
8. Execute your data collection plan
5 Whys: a problem solving tool that helps understand the root cause
of a problem. The 5 Whys technique is usually very quick
and focused.
Key Points:
The 5 Whys strategy is an easy and often-effective tool for
uncovering the root cause of a problem.
Because it's simple, you can adapt it quickly and apply it to
almost any problem.
However, it is important to remember, if an intuitive answer is hard
to find, then other problem-solving techniques may need to be considered.
Fishbone diagrams: diagram-based technique, which combines brainstorming with a type of mind map, and forces to consider all possible causes of a problem, rather than just the ones that are most obvious. Fishbone diagrams encourage broad thinking.
Key Points:
1. Identify the problem.
2. Work out the major factors involved.
3. Identify possible causes.
4. Analyse your diagram.
When used correctly, control charts are powerful instruments that can give you visual understanding on the stability of your process
Control charts cannot tell you what is wrong with your process, they can only let you know when something in your process has changed
Control charts can confirm the impact of process improvement activities
Ilca Croufer
2 Occam Court
Surrey Research Park
Guildford, Surrey
GU2 7QB
Tel: +44 1483 595 000