FDFPPL4005A
Establish Process Capability
Contents
Introduction and Unit Details ………….………………………………….... 4
Element 1: Prepare to Conduct a Capability Study…………………….
7
Preparation and Sampling………………….………………………………....
8
Considerations for the Statistical Process Control Chart………………….
9
Element 2: Analyse Data to Determine Process Capability..…………
17
Process Control Charts………………………………………………………..
18
Process Capability…..………………………………………………………...
24
Analysis and Interpretation of the Control Chart..…………………………..
28
Capability Index……………………………………….……………………....
34
Continuing Improvement …………………………………………………….
40
Activity Answers…………………………………………………………….
41
Appendix 1…………………………………………………………………….
43
Appendix 2…………………………………………………………………….
47
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Element 1: Prepare to Conduct a Capability Study.
Learning
Objectives
When you have finished this section you should be
able to:
 Identify the purpose and scope of the process to
be investigated
 Design a control chart which collects
representative data of the defined process
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Preparation and Sampling
Control charts are widely used to establish and maintain statistical control of a process.
They are also effective devices for estimating process parameters, particularly in processcapability studies. The use of a control chart requires the analyst to select a sample size, a
sampling frequency or interval between samples and the control limits for the chart. The
selection of these three parameters is usually called the design of the control chart.
It is not always possible to give an exact solution to the problem of control chart design, as
detailed information is needed on:
 Statistical characteristics of the control chart tests
 Economic factors that affect the problem
A complete solution of the problem would require knowledge of the
 Cost of sampling and testing include the out-of-pocket expenses of inspectors and
technicians' salaries and wages, the costs of any necessary test equipment and in
the case of destructive testing the unit cost of the items sampled. 1
 Cost associated with production of a product that does not meet specifications
Models for the economic design of control charts can be calculated2 but this is beyond the
scope of this unit of competency.
Traditionally control charts have been designed with respect to statistical criteria only. This
usually involves selecting the sample size and control limits such that the power to detect a
particular shift in the quality characteristics and the probability of a ‘false alarm’ (type I
error) are equal to specified values. Obviously you would not have this information if there
has never been a statistical evaluation of the process.
Control charts do not control the process, they are tools used to improve the process.
Generally processes do not operate in a state of statistical control and consequently routine
and attentive use of control charts will identify assignable causes. If these causes can be
eliminated from the process, variability will be reduced and the process will be improved.
The control chart will only detect assignable causes. Management, operator, and
engineering action will be necessary to eliminate the assignable cause. 3
Two concepts which are fundamental in the control of quality are measurement and
variation. Measurement of some kind is necessary in describing product quality (goods and
services), whether on a continuous scale producing variable data or a number counting
resulting in attribute data.
After-all, what can’t be measured can’t be controlled and if it can’t be controlled , it
can’t be improved.
1
(Montgomery, 1991, pp. 112-113)
(Montgomery, 1991, pp. 413 - 443)
3 (Montgomery, 1991, p. 106)
2
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3 δ either side of the mean
contains 99.73% of the values
The two tails contain the remainder of
2.7% or 0.0027 of the values (that is
100% - 99.73% = 2.7%)
370 is the average run length of the x-bar chart when the process is in control. That is, even
if the process remains in control, an out-of-control signal will be generated every 370
samples on average. Consider the example used earlier of the opening diameter of a glass
jar and suppose sampling occurred every hour. In this instance a false alarm would occur
approximately every 370 hours.
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4 Taking the sample
Samples need to be random and there be an equal chance of being selected.
A representative sample contains the relevant characteristics of the population in the same
proportion as they are included in that population.
If one accepts that a main objective of keeping a control chart is to detect a sustained
change in the process mean ,(that is, the average value of the characteristic being
investigated), then samples, should be chosen ‘instantaneously’ so that each sample is as
homogeneous as possible.
In such a situation, the sample should consist of a number, say 5, of successively produced
items to maximise the opportunity for variation between samples and increase the
sensitivity of the chart to detect a disturbance. On the other hand, if the control chart is to
be used to detect short-lived or compensating changes in the mean (that is, where the
change may occur after one ‘instantaneous’ sample but be corrected before the next), then
the sample should be chosen at random from all items produced over a suitable given time
period so that it is representative of production over that time period. 4
To establish the inherent variation in the process, allow the process to run untouched (that
is, according to procedures).
Culturally, staff collecting the data must feel ‘safe’ to report data as they find it, even if it
gives undesirable results otherwise the staff with their familiarity with the machinery will
collect biased data. An example of this is with the hamburger patty assessment question. If
only two samples were taken, the staff might know which two samples would give the
desired weight (as the former may deposit heavy in the middle and lighter on the edges)
5 Create charts / sheets for data collection
Sheets for the collection of data will need to be designed / created. They can be created to
collect the raw data which is then later analysed or once having established control limits
also used to monitor the process.
The data collection forms should also include provision for recording any unusual events
that occur (which would then be used to eliminate assignable causes).
An example of such a sheet is on the following page and in Appendix 1.
4
(Ogle, 1994)
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Process Control Chart
The process control chart has been covered in considerable detail in the pre-requisite
units of competency FDFOP2015A Apply Principles of Statistical Process Control and
FDFTEC4007A Describe and analyse data using mathematical principles.
The histogram is related to the control chart. Like a histogram, a normally distributed
control chart will have almost all its values with +/- 3 standard deviations from the mean.
Below is a diagramatic representation of how variation (or the spread of the data),
usually represented by the normal distribution curve, can be translated into a control
chart.
UL
3δ
3δ
LL
3 δ either side of 𝒙 is a total of 6 δ
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Rule 4
The proportion of points within the middle 1/3 of the region between the
control limits differs excessively from 2 out of 3
Special Causes - Rule 4
2 out of 3 fall outside or inside the third (1δ) lines
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0
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9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Additional Criteria
1.
Two of three consecutive points outside the 2-sigma warning limits but still
inside the control limits
Special Causes - 2 out of 3 points exceed warning limits
18
16
UNL (3δ)
14
UWL (2δ)
12
(1δ)
10
Value
8
Avg
6
(1δ)
4
LWL (2δ)
2
LNL (3δ)
0
1
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
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conforming if the process is not satisfactorily centered in respect to the
specifications.
Cp <1 This implies that specifications are not being met in which case three
courses of action arise:
o Change specifications. In some situations specifications may be set more
tightly than necessary. It may be possible to make headway through
negotiation
o Reduce process variability. This may involve an analysis of the sources of
variation in the process. In turn, this may lead to changes to particular
aspects of the process, for example, method, materials or equipment
used. A further capability study may be required.
o Accept the status quo. Of course, this alternative is hardly a course of
action. However, if such a situation is unavoidable (hopefully) in the shortterm, management must accept that some process outcomes will continue
to fall short of what is required so that the economics of the operation
become paramount. What is the percentage of non-conforming outcomes?
Where should the process be centered in order to minimize scrap/rework
costs?
Cpk = 1 , both specifications are at least three standard deviations from the
process centre. Such a process could be described as having 3δ (3-sigma)
capability. Similarly, values of Cpk = 1.33, 1.67 and 2 would correspond to
capabilities of 4δ , 5δ and 6δ respectively.
Cpk < 1 defective material is being made
Cpk, Cpl and Cpu measure not only the process variation with respect to the
allowable specification, they also take into account the location of the process
average.
NOTE: The indices Cpl and Cpu can be used for single-sided specification limits
If the process is not capable, form a team to identify and correct common causes of the
variation in the process.
 Process capability, based on individual data for the process population is used to
determine if a process is capable of meeting customer requirements or
specifications. It represents a ‘snapshot’ of the process for some specific period
of time.
 Control charts use small sample sizes over time and look at averages. The
control limits are natural limits of variation of the averages within the sample.
These limits are not be confused with specification limits, which are for individual
data points in the population.
Attribute Control Charts.
The process capability of an Attribute Data Control chart is represented by the process
averages p , n p , c and u .
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Continuing Improvement
Process control charts and process capability studies in themselves do not solve quality
problems but as management tools they assist in focusing attention on the issues of
quality and productivity improvement.
Once the initial process control chart and capability analysis has been undertaken it is
necessary to”:
1. Determine any special causes if the process is considered out of control. Special
causes can include changes in raw materials or methods, damaged or worn
equipment, faulty gauges or human errors, poor lighting, badly designed work
stations, inadequate supervision and training. Some of the causes can be
corrected ‘locally’ by appropriate personnel, others will require resolution by
senior management.
o Further statistical process control techniques (such as pareto, cause and
effect diagrams etc) along with other general methods (such as quality
circles, brainstorming) may also be employed to identify special causes,
reduce variation and improve processes.
2. Once the special causes have been determined and eliminated, the control limits
for a process control chart will need to be recalculated
3. Rectifying any special causes may have a flow on effect and also improve
process capability. Modifications to equipment, the process or the design of the
product can improve process capability; if this is not the case the following should
be considered
o Change specifications. In some situations specifications may be set more
tightly than necessary. It may be possible to make headway through
negotiation
o Reduce process variability. This may involve an analysis of the sources of
variation in the process. In turn, this may lead to changes to particular
aspects of the process, for example, method, materials or equipment
used. A further capability study may be required.
o Accept the status quo. Of course, this alternative is hardly a course of
action. However, if such a situation is unavoidable (hopefully) in the shortterm, management must accept that some process outcomes will continue
to fall short of what is required so that the economics of the operation
become paramount. What is the percentage of non-conforming outcomes?
Where should the process be centered in order to minimize scrap/rework
costs?
4. Sampling and analysis for process control should be ongoing and as special
causes are gradually removed, benefits will be received comprising of greater
profits, better quality and increased productivity. The reasons for such
improvements include reductions in scrap and rework, preventative actions rather
than remedial and a better understanding of process capability.
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