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BS 5702-3:2008

BS 5702-3:2008

$142.49

Guide to statistical process control (SPC) charts for variables – Charting techniques for short runs and small mixed batches

Published By Publication Date Number of Pages
BSI 2008 40
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This part of BS 5702 describes ways of applying measured data statistical process control (SPC) charts to short runs and small mixed batches where the sample size for monitoring is restricted to one. It provides a set of tools to facilitate the understanding of sources of variation in such processes so that the processes can be better managed.

The charts described are process- rather than product-focused. The user can plot, monitor and control similar characteristics on different items, or different characteristics on an item, on a single control chart.

PDF Catalog

PDF Pages PDF Title
3 Contents
Introduction 1
1 Scope 2
2 Normative references 2
3 Terms, definitions, abbreviations and symbols 3
4 How to select the correct type of Shewhart control chart for measured data 5
5 How to prepare for short-run, small mixed batch control charting 8
6 How to establish and apply short-run, small mixed batch, control charts 17
Annexes
Annex A (informative) Reproducible copies of control chart forms and normal probability worksheet 28
Bibliography 34
List of figures
Figure 1 – Diagram distinguishing between a population parameter and a sample statistic 3
Figure 2 – Shewhart control chart selection flow chart for measured data 6
Figure 3 – Control chart selection flow chart for short runs and small batches 7
Figure 4 – Four different scenarios with a single observed measurement 10
Figure 5 – Preliminary process stability check 15
Figure 6 – Normal probability worksheet 16
Figure 7 – Variable aim, individual and moving range control chart 19
Figure 8 – Variable aim, moving mean and moving range control chart 21
Figure 9 – Universal individual and moving mean chart 25
Figure 10 – Universal moving mean chart for short runs 27
Figure A.1 – Variable aim, individual and moving range chart 29
Figure A.2 – Variable aim, moving mean and moving range control chart 30
Figure A.3 – Universal, individual and moving range chart 31
Figure A.4 – Universal, moving mean and moving range control chart 32
Figure A.5 – Example normal probability worksheet 33
List of tables
Table 1 – Chart selection table for short runs and small batches 7
Table 2 – Four scenarios when a single measurement is taken at set up 11
Table 3 – Range of critical set up acceptance values for t 11
Table 4 – % probability plotting positions for sample sizes of 3 to 20 14
Table 5 – Data for normal probability plot 15
Table 6 – Key data for constructing a variable aim, individual and moving range chart 18
Table 7 – Data and calculations for variable aim, individual and moving range chart 19
4 Table 8 – Key data for constructing a Variable aim, moving mean and moving range control chart 21
Table 9 – Data and calculations for variable aim, moving mean and moving range chart 21
Table 10 – Key data for constructing a universal individual and moving range chart 23
Table 11 – Data and calculations for universal individual and moving range chart 24
Table 12 – Key data for constructing a universal moving mean and moving range control chart 26
Table 13 – Data and calculations for universal moving mean and moving range chart 27
5 Foreword
7 Introduction
8 1 Scope
2 Normative references
9 3 Terms, definitions, abbreviations and symbols
3.1 General
Figure 1 Diagram distinguishing between a population parameter and a sample statistic
a) The lower case Greek letter sigma, s, a population parameter, represents the standard deviation of a population;
b) S, a sample statistic, represents the sample estimate of the standard deviation;
c) s represents the realized, or measured value, of the sample statistic, S.
10 1) the lower case Greek letter mu, m, a population parameter, represents the arithmetic mean of the population;
2) , a sample statistic, represents the sample estimate of the arithmetic mean;
3) represents the realized, or measured, value of the sample statistic .
3.2 Terms and definitions
3.3 Abbreviations and symbols
11 4 How to select the correct type of Shewhart control chart for measured data
4.1 General
4.2 How to select the correct type of Shewhart control chart for measured data generally
a) If the characteristic is ongoing with a targeted constant aim and precision, and the feasible sample size is greater than one, refer to BS 5702-1.
b) If the characteristic is ongoing with a targeted constant aim and precision, and the sample size is limited to one, refer to BS 5702-2.
c) If the characteristics or multiple-dimensioned items do not have a constant aim and/or precision, and the sample size is limited to one, 4.3.
d) If the characteristics or multiple-dimensioned items do not have a constant aim and/or precision and the feasible sample size is greater than one, specialist guidance should be sought.
12 Figure 2 Shewhart control chart selection flow chart for measured data
4.3 How to select the correct type of Shewhart control chart for short runs and small batches
a) Variable aim, individual and moving range charts.
b) Variable aim, moving mean and moving range charts.
c) Universal, moving mean and moving range charts.
d) Universal, individual and moving range charts.
13 Figure 3 Control chart selection flow chart for short runs and small batches
Table 1 Chart selection table for short runs and small batches (sample size, n = 1)
14 5 How to prepare for short-run, small mixed batch control charting
5.1 Focus on the process
a) the same drilling process produces different nominal size diameter and depth holes;
b) the same heading machine produces bolts with various size heads, length and diameter;
c) the same press produces stampings with various slot widths;
d) the same mixing process produces different solutions with different chemical elements and ratios;
e) the same extruder extrudes tube with different nominal outer and inner diameters and wall thickness;
f) the same coiner produces blanks in multiple cavity dies;
g) the same soldering operation produces small batch size printed circuit board assemblies with different nominal solder strengths per board.
1) 100% final inspection. This is an expensive and after-the-event activity.
2) First-off inspection based on a single measurement. This provides limited set-up information and does not take into account process changes over time.
15 3) Last off inspection. This is a high-risk strategy, taken after the event, which provides too little information too late.
4) Separate control chart for each feature and nominal dimension. This is not cost-effective and is administratively cumbersome to operate. An excessive number of charts are produced, often with too few data points to properly interpret.
5.2 Typical applications
5.3 Preliminary process diagnosis
a) Source material dominance; where the incoming material or previous operation has a major influence.
b) Set-up dominance; where the characteristic is highly reproducible once properly set-up.
c) Operator dominance; where the process is highly dependent on the skill, care and attention of operational personnel.
d) Time dominance; where the process can drift, e.g. with tool wear and lack of replenishment of solution mix ratios.
e) Fixture or pallet dominance; where the fixtures or pallets holding the parts are a large source of inconsistency.
f) Process dominance; where the output is dependent on process parameters, e.g. depth and speed of cut, temperature, humidity.
g) Information dominance; where variation and nonconformities are caused by frequent job and specification changes.
h) Singular process never to be repeated.
16 5.4 Procedure to establish the correct initial setting of a process characteristic
5.4.1 Purpose
5.4.2 Scope and/or limitations
5.4.3 Reasons for need of procedure
Figure 4 Four different scenarios with a single observed measurement
17 Table 2 Four scenarios when a single measurement is taken at set up
5.4.4 Method
Table 3 Range of critical set up acceptance values for t
18 5.4.5 Example
5.4.6 Background to the test
5.5 Procedure to pre-establish controls for SPC charts for short-run, small batch, processes
5.5.1 Purpose
5.5.2 Scope of application
19 5.5.3 Reasons for need of procedure
5.5.4 Method
a) After the set-up is judged acceptable, run, measure, and record in production sequence, the number of items considered practicable, as a basis for establishing SPC charts.
b) Plot the individual values, on standard graph paper, in production sequence. If there are obvious abnormalities seek out the reasons. When there is no obvious abnormality present, proceed with this method.
c) Tabulate the values in ascending order against the percentage plotting positions for the appropriate sample size given in Table 4.
d) Plot the results on a normal probability worksheet (Figure A.5).
2) If it is more appropriate to draw a smooth curve through the data points this indicates a skew distribution. Consult BS 600:2000, 11.3.3, for further interpretation.
3) If it is not reasonable to draw a straight or smooth curve through the plotted points on the probability worksheet, on the ba…
20 Table 4 % probability plotting positions for sample sizes of 3 to 20
5.5.5 Example
a) Check for process stability.
21 Figure 5 Preliminary process stability check
b) Check for process normality.
Table 5 Data for normal probability plot
22 Figure 6 Normal probability worksheet
23 c) Estimate the process mean and standard deviation.
6 How to establish and apply short-run, small mixed batch, control charts
6.1 Introduction
6.2 Variable aim, individual and moving range chart
6.2.1 Purpose
a) the sample size is 1;
b) a process, running items of various size or dissimilar characteristics with different aims, or nominal values, is to be monitored;
c) the extent of the variation of the characteristics is expected to be constant throughout;
d) a timely response is required to any sudden change in the characteristics monitored.
6.2.2 Scope/application
a) the sample size is restricted to 1;
b) it is necessary to reduce the number of control charts when a number of different characteristics are being monitored at the same work station;
c) the process parameter or product characteristic is continually changing in nominal value, for example, as with short runs on generically similar items of different sizes processed at the same work station;
24 d) the process variation of the characteristics is expected to be constant throughout;
e) a timely response is required to any change in process level;
f) the pattern of variation of the characteristics plotted is approximately normal.
6.2.3 Method
a) Establish an aim value for each item or characteristic. This is usually the nominal value, the desired value, or the overall average value experienced.
b) In the individuals plot, each plot point is based on a single measurement. Plot deviations from the relevant aim value, for example, X p nominal, or X p overall average value, as applicable.
c) As each individual measurement becomes available progressively construct a tally chart of (X p aim) in the section marked ‘distribution’. Check that the distribution shape is approximately normal (symmetrical bell-shaped).
d) In the moving range chart, plot the absolute value of the difference between each two consecutive (X p aim) plot points.
e) Calculate centre lines and control limits using Table 6. Continue and monitor for process control as in BS 5702-2:2007, Clause 7.
Table 6 Key data for constructing a variable aim, individual and moving range chart
6.2.4 Example
25 Table 7 Data and calculations for variable aim, individual and moving range chart
Figure 7 Variable aim, individual and moving range control chart
26 6.3 Variable aim, moving mean and moving range chart
6.3.1 Purpose
a) the sample size is 1;
b) a process, running items of various size or dissimilar characteristics with different aims, or nominal values, is to be monitored;
c) the extent of the variation of the characteristics is expected to be constant throughout;
d) the detection of trends is more important than response to sudden changes.
6.3.2 Scope/application
a) the sample size is restricted to 1;
b) it is necessary to reduce the number of control charts when a number of different characteristics are being monitored at the same work station;
c) the process parameter or product characteristic is continually changing in nominal value, for example, as with short runs on generically similar items of different sizes processed at the same work station;
d) it is more important to determine trends than sudden changes;
e) the pattern of variation of individuals is non-normal.
6.3.3 Method
a) Establish an aim value for each item or characteristic. This is usually the nominal value, the desired value or the overall average value experienced.
b) In the moving mean plot, calculate and plot each point from two consecutive (X p aim) values. Plot the moving mean of X p nominal, or X p overall average value, as applicable.
c) As each measurement becomes available, progressively construct a tally chart of (X p aim) in the section marked ‘distribution’. Take note of the distribution shape as described in BS 5702-2:2007, Clause 8.
d) In the moving range chart, plot the absolute value of the difference between each two consecutive (X p aim) plot points.
e) Calculate centre lines and control limits using Table 8.
f) Continue and monitor for process control and capability as in BS 5702-2:2007, Clause 8.
27 Table 8 Key data for constructing a Variable aim, moving mean and moving range control chart
6.3.4 Example
Table 9 Data and calculations for variable aim, moving mean and moving range chart
Figure 8 Variable aim, moving mean and moving range control chart
28 6.4 Universal, individual and moving range chart
6.4.1 Purpose
a) the sample size is 1;
b) a process, running items of various size or dissimilar characteristics with different aims, or nominal values, is to be monitored;
c) there is a significant change in the value of the average range, or standard deviation, with differing characteristics or size of the aim or nominal;
d) a timely response is required to any sudden change in the characteristics monitored.
6.4.2 Scope/application
a) the sample size is restricted to 1;
b) it is necessary to reduce the number of control charts when a number of different characteristics are being monitored at the same work station;
c) the process parameter or product characteristic is continually changing in nominal value, for example, as with short runs on generically similar items of different sizes processed at the same work station;
d) the extent of the process variation changes with the type of characteristic and/or size of an item;
e) a timely response is required to any change in process level;
f) the pattern of variation of the individual values plotted is approximately normal (symmetrical bell-shaped).
29 6.4.3 Method
a) Establish aim or reference values in the form of both the nominal, desired or overall average value and measure of variation,…
b) In the individuals chart each plot point is based on a single measurement. Plot deviations from the relevant aim value, after standardizing for Raim, namely, plot (X p aim)/Raim.
c) As each individual measurement becomes available, progressively construct a tally chart of (X p aim)/Raim in the section marked ‘distribution’. Check that the distribution shape is approximately normal (symmetrical bell-shaped).
d) In the moving range chart, plot the absolute value of the difference between each two consecutive (X p aim)/Raim plot points.
e) Insert the centre lines for the individual and range chart at the values shown in Table 10, namely, at 0 and 1, respectively.
f) Calculate control limits using Table 10. Enter in graph.
g) Continue and monitor for process control and capability as in BS 5702-2:2007, Clause 7.
Table 10 Key data for constructing a universal individual and moving range chart
6.4.4 Example
30 Table 11 Data and calculations for universal individual and moving range chart
31 Figure 9 Universal individual and moving mean chart
6.5 Universal, moving mean and moving range chart
6.5.1 Purpose
a) the sample size is 1;
b) a process, running items of various size or dissimilar characteristics with different aims, or nominal values, is to be monitored;
c) there is a significant change in the value of the average range, or standard deviation, with differing characteristics or size of the aim or nominal;
d) detection of trends is more important than response to sudden changes.
32 6.5.2 Scope/application
a) the sample size is restricted to 1;
b) it is necessary to reduce the number of control charts when a number of different characteristics are being monitored at the same work station;
c) the process parameter or product characteristic is continually changing in nominal value, for example, as with short runs on generically similar items of different sizes processed at the same work station;
d) the extent of the process variation changes with the type of characteristic and/or size of an item;
e) it is more important to determine trends than sudden changes.
6.5.3 Method
a) Establish aim or reference values in the form of both the nominal, desired or overall average value and the previously establ…
b) In the moving mean plot, calculate and plot each point from the mean of each two consecutive (X p aim)/Raim values.
c) As each individual measurement becomes available, progressively construct a tally chart of (X p aim)/Raim in the section marked “Distribution of Xvariable”. Check that the distribution shape is approximately normal (symmetrical bell-shaped).
d) In the moving range chart, plot the absolute value of the difference between each two consecutive (X p aim)/Raim plot points.
e) Insert the centre lines for the moving mean and moving range chart at the values shown in Table 12, namely, at 0 and 1, respectively.
f) Calculate control limits using Table 12. Enter in graph.
g) Continue and monitor for process control and capability as in BS 5702-2:2007, Clause 8.
Table 12 Key data for constructing a universal moving mean and moving range control chart
33 6.5.4 Example
Table 13 Data and calculations for universal moving mean and moving range chart
Figure 10 Universal moving mean chart for short runs
34 Annex A (informative) Reproducible copies of control chart forms and normal probability worksheet

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BS 5702-3:2008
$142.49