Chapter 6.1- Statistical Process Control-2009(Rev1)
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Chapter 6.1 Statistical Process Control (Week 8) L2 & L3 - X-bar and R Charts
Transcript of Chapter 6.1- Statistical Process Control-2009(Rev1)
Chapter 6.1
Statistical Process Control(Week 8)
L2 & L3 - X-bar and R Charts
2Jan 2008
Week 8 :
Learning Outcomes:At the end of the lesson student should be able to
- understand the concept of SPC especially for X-bar and R charts
- calculate and plot X-bar and R charts - calculate the process mean and standard
deviation
3Jan 2008
Introduction to Statistical Process Control (SPC)What is Quality Control?:
Quality control is designed to prevent the production of products that do not meet certain acceptance criteria.
Action could be taken by rejecting those products or
Some products would go on to be reworked, (it means that a process is costly and time consuming).
In many cases, rework is more expensive than producing the product.
Thus results in decreased productivity, customer dissatisfaction, loss of competitive position, and higher cost.
4Jan 2008
Introduction to Statistical Process Control (SPC) Statistical process control (SPC), is a powerful tools
that implement the concept of prevention as a shift from the traditional quality by inspection/correction.
SPC is a technique that employs statistical tools for controlling and improving processes.
SPC is an important ingredient in continuous process improvement (CPI) strategies. It uses simple statistical means to control, monitor, and improve processes.
5Jan 2008
Introduction to Statistical Process Control (SPC) Among the most commonly used tools of
SPC:histograms cause-and-effect diagrams Pareto diagrams control charts scatter or correlation diagrams run charts process flow diagrams
6Jan 2008
Control Chart The most important SPC tool is called control
charts:
graphical representations of process performance over time
concerned with how (or whether) processes vary at different intervals and identifying nonrandom or assignable causes of variation.
provide a powerful analytical tool for monitoring process variability and other changes in process mean
7Jan 2008
Figure 8-1
A typical control chart.
A typical control chart.
8Jan 2008
X-bar and R Charts
X-bar and Range, R Charts are a set of control charts for variables data (data that is both quantitative and continuous in measurement, such as a measured dimension or time).
The X-bar chart monitors the process location over time, based on the average of a series of observations, called a subgroup.
The Range chart monitors the variation between observations in the subgroup over time.
9Jan 2008
When to Use an X-bar / R Chart :
X-bar / Range charts are used when you can rationally collect measurements in groups (subgroups) of between two and ten observations.
The charts' x-axes are time based, so that the
charts show a history of the process.
The data is time-ordered; that is, entered in the sequence from which it was generated.
10Jan 2008
X Bar Chart Calculations
The average, sometimes called X-Bar, is calculated for a set of n data values as:
11Jan 2008
X Bar Chart Calculations Sub-grouped data: the average of the subgroups' averages,
sometimes called the estimate process mean,
where n is the subgroup size and m is the total number of subgroups included in the analysis.
12Jan 2008
X Bar Chart Calculations
UCL – Upper Control Limit:
rAXUCLX 2
where the constant A2 is tabulated for various sample sizes in Appendix A Table VII.
13Jan 2008
X Bar Chart Calculations
LCL - Lower Control Limit:
where the constant A2 is tabulated for various sample sizes in Appendix A Table VII.
rAXUCLX 2
14Jan 2008
R Chart Calculations
Average Range
The average of the subgroup ranges –(R-bar) – centre line
15Jan 2008
R Chart Calculations
UCL - Upper Control Limit:
where R-bar is the sample average range, and the constants D4 is tabulated for various sample sizes in Appendix A Table VII.
16Jan 2008
R Chart Calculations
LCL - Lower Control Limit:
where R-bar is the sample average range, and the constants D3 is tabulated for various sample sizes in Appendix A Table VII.
17Jan 2008
Process Mean and Process Standard Deviation Process mean:
Estimated by
Process standard deviation: Estimated by
m
xX
m
ii
1̂
nAd
dr
22
2
3 where
ˆ
