The TQM Magazine Simulating c and u control schemes Jim FreemanGeorge Mintzas
Article information: To cite this document: Jim FreemanGeorge Mintzas, (1999),"Simulating c and u control schemes", The TQM Magazine, Vol. 11 Iss 4 pp. 242 - 248 Permanent link to this document: http://dx.doi.org/10.1108/09544789910256984
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Introduction
Techniques Simulating c and u control schemes
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Jim Freeman and George Mintzas
The authors Jim Freeman specialises in computer simulation. Before taking up his lectureship at UMIST in 1981, he was statistician at the Distributive Industry Training Board (DITB) where he held responsibility for computer-based training. He has published widely in his field and been involved in developing a large number of management simulation packages. George Mintzas was recently awarded an MSc degree in Operations Management at the Manchester School of Management. Keywords Computer-based training, Control charts, Simulation, Training Abstract Control charts are a vital quality management tool. Attribute schemes are of particular (though not exclusive) interest to the customers of manufacturing organisations. A new computer assisted, experiential approach to training staff in attribute (defects) sampling methods is described. The package in question is standalone and allows a variety of chart options to be simulated. Schemes can be appraised both individually and on a pairwise basis. ``Live'' results from the simulation can be compared with standard benchmark information incorporated in the program. A gaming facility additionally provides trainees with a means of assessing changes in their skill level and performance.
The TQM Magazine Volume 11 . Number 4 . 1999 . pp. 242±247 # MCB University Press . ISSN 0954-478X
Over the years many different approaches have been applied to the management and control of quality. Whereas early efforts focussed on inspection (covering activities such as measuring, examining, testing, gauging one or more characteristics of a product or service and comparing these with specified requirements to determine conformity) and quality control (the operational techniques and activities used to fulfil requirements for quality), nowadays the emphasis is firmly on prevention. Hence, the current popularity of quality assurance (all the planned and systematic activities necessary to provide adequate confidence that a product or service will satisfy given requirements for quality) and total quality management (the management approach of an organisation centred on quality, based on all its members and aiming at long-term success through customer satisfaction and benefits to all members of the organisation and to the society (British Standards Institute, 1995), (Dale, 1994) (see Figure 1).
Statistical process control The best-known statistical tool in quality management is statistical process control (SPC) ± described by the British Standards Institute (1995) as ``the in-process application of statistical data analysis methods to identify out of tolerance conditions for a specific production process and to notify the operator of the current or impending problem''. The fundamental objective of SPC is to reduce the variation inherent in most processes. On-line process control is performed at the product design stage before production and manufacturing. In preventative (as opposed to screening) mode, the process is inspected to avoid defective items being produced. The priority is correcting both special and common causes of process variation (see Table I) (Rauwendaal, 1993). Off-line SPC on the other hand, is concerned with re-engineering the process or product to make it less sensitive to (primarily) common causes of variability. With SPC, a thorough data recording system is essential. In addition to the basic elements of a quality system which provide a framework for recording data, a number of tools exist which can be used to derive the maximum value from data (see Table II).
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Figure 1 Stages in the evolution of quality management
Table II SPC methods and their purpose
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By far the most commonly used of these tools are:
SPC tools
Purpose
Process flowcharting
Revealing what is done
Check sheets/tally charts
Showing how often it is done
Histograms and charts
Summarising pictorially the numbers involved
Pareto analysis
Determining the relative importance of problems
Cause and effect analysis and brainstorming
Finding out what causes problems
Scatter diagrams
Exploring relationships between factors
Control charts
Highlighting discrepancies outside the range of sample variation
Figure 2 A typical Shewhart (variables) control chart
Control charts Statistical quality control charts (see Figure 2) (Oakland and Followell, 1990) relate directly to the on-line process control function: Here, the centre line (CL) represents the mean or target value of process observations and the upper and lower control limits (UCL and LCL respectively) are the lines between which plotted values would be expected to fall if the process were considered to be in control. This type of (Shewhart) chart is well suited to handling variables data. Such data result from using some kind of measuring system e.g. a pressure gauge, thermometer, odometer etc. Measurements may refer to product characteristics e.g. length, weight, diameter, arrival time, or to process parameters e.g. temperature, pressure, pH, In practice, it is found charts based on the latter variables give earlier feedback and lead to better diagnosis of the causes for variation than for the former (Grant and Leavenworth, 1996), (Amsden et al., 1986).
In contrast to variables data, attributes data are the result of an assessment using go/no-go gauges (as a proxy for measured data) or pass/ fail criteria (e.g. conforming/non-conforming). To assist those employed in this activity, the boundaries of acceptance and rejection must be clearly defined. Reference standards or illustrations may help in this respect and where possible the accept/reject characteristics should also be agreed with the customer. The distinction between non-conforming items/units and non-conformities is also important: a non-conformity may be a blemish
Table I Characteristics of common and special causes of variation Common cause
Special cause
Inherent or natural to the process
Unnatural
Predictable
Unpredictable
Stable
Unstable
Source
Many small ``groups''
One or a few major sources
Effect
Slight
Can be strong
Improvement action
Reduce common cause variability
Eliminate
Responsibility of improvement action
Management
Operator/supervisor
Nature
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Jim Freeman and George Mintzas
Control charts provide important information about process capability and the stability of key process parameters over time. Such information is vital to product and process designers.
or the presence of some non-preferred feature (e.g. a surface scratch). A non-conforming unit, however, may fail to meet the assessment criteria because of one or more nonconformities. An important property of control chart schemes is the average run length (ARL) which enables the performance of alternative chart types to be easily compared. The ARL ± also referred to as the mean action time (MAT) ± is defined as the average number of points to be plotted before an out of control signal is generated. An ideal control chart scheme will have a large ARL when the process is in control (corresponding to a very low incidence of ``false alarms'') but a small ARL when the process drifts out of control so that detection of problem points is swift.
Adopting SPC methods is not always without its difficulties. Most commonly cited problems are summarised below: . Lack of knowledge/expertise in SPC. . Lack of action from senior management. . How to apply SPC to a particular process. . Resistance to change from people in the organisation. . How to decide which product characteristic and/or process parameter to chart.
Benefits of control charts
The SQCC_DEF simulation
The benefits of using control charts in manufacturing are legion (Oakland and Followell, 1990), (Messina, 1987), (Grant and Leavenworth, 1996). As on-line tools in process monitoring they provide instantaneous feedback for operators, engineers and managers which can be applied retrospectively or prospectively. By interpreting control chart patterns, the manufacturing manager can help reduce nonconformities and rejections that occur on-line and thus assist with the prevention of quality problems. Scrap and rework are the primary productivity ``killers'' so if these can be reduced, productivity increases, costs decrease and production capacity (measured as the number of conforming parts per time period) increases. The pattern of points in a flow chart often contains information of diagnostic value to the manager or engineer. By making appropriate changes to the manufacturing setup, process performance can frequently be improved. Control charts are used to determine when to adjust a process ± also when to prevent unnecessary adjustments. Control charts distinguish between background ``noise'' and abnormal variation better than any other means, including even the most experienced human operator. Humans have a tendency to over-react to background noise. Frustratingly this can result in many unnecessary adjustments and actual deterioration in process performance.
SQCC_DEF was developed for training managers in the use of control charts for handling data on nonconformities (defects). This new simulation prototype (Oakshott, 1997) complements that for dealing with control charts for variables (Freeman, 1993) and defectives (Freeman and Evangeliou, 1996). With SQCC_DEF, two different chart options are considered, relating to: (1) the number (c); and (2) the proportions (u).
Problems in implementing and using SPC
of non-conformities (defects). C charts are used when the sample size used is the same all the time, u charts correspondingly when the sample size can fluctuate (Montgomery, 1991), (Wetherill and Brown, 1991). C and u charts can also be used in nonmanufacturing applications of SPC e.g. plot errors on engineering drawings, plans or documents, software bugs etc. In contrast to the variables situation ± illustrated earlier in Figure 2 ± the lower control limit (LCL) for attribute schemes is usually not a consideration (significantly low levels of defects or defectives being regarded as non-problematic). With c and u charts, the theoretical probability distribution adopted is the Poisson (Messina, 1987). This distribution is based on the assumption that while the number of opportunities or potential opportunities for non-conformity is infinitely large the
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probability of a non-conformity at any location is small but constant. If the average rate of occurrence of defects or other events is low, the sampling interval may contain very few incidences for non-conformity. In such cases it may then be appropriate (if not essential) to use moving averages so that sample intervals are effectively aggregated. SQCC_DEF enables trainees to: . Obtain first-hand experience of Shewhart and Modified Shewhart c and u charts; for c-type data based on numbers of nonconformities the CUSUM scheme is also covered. An experimental CuScore option is provided in each case for additional interest (see Figure 3 for details). . Evaluate and appreciate the strengths and weaknesses of each type of control chart scheme ± as shown for example by Figures 4 and 5. Note that the ARL test option enables the ARLs of chosen schemes to be derived by simulation. These can then be compared with theoretical values (British Standards Institute, 1980a); (British Standards Institute, 1980b); (British Standards Institute, 1983). The Direct monitor facility in contrast is strictly experimental, allowing users to see directly and chart responses to deliberate changes in process parameters. . Gain expertise in interpreting control charts. In particular the management game option presents randomly generated
observations which may or may not involve a shift in parameter. The user has to determine whether or not a shift has occurred. Also by how many multiples of the standard deviation and at what point of the observation series this took place (see Figure 6). A scoring system enables trainees to monitor improvements in their performance.
Conclusions The value of simulation methods in quality management training should be under-estimated. Significant inroads ± see for example Aghaie and Popplewell (1997) and Freeman and Lythgoe (1996) ± are now under way and this trend, if anything, is accelerating. SQCC_DEF is the latest in a range of simulation-based tools for developing SPC skills. The package, as currently configured, focuses specifically on the use of c and u type charts. In the future, it could be advantageous to integrate the simulation with two sister packages dealing respectively with x, R and s, and p and np schemes. The result would be a training resource covering effectively every mainstream quality chart contingency. SQCC_DEF was written in Turbo Pascal 7.0 and runs as a DOS application. Converting the package for use in a Windows environment would permit standard facilities such as
Figure 3 Alternative c chart options
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Figure 4 ARL characteristics of different c chart schemes
Figure 5 Simulation-based ARL results
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Figure 6. Sample output from management game facility
multi-tasking and multiple windows etc. to be fully exploited. A particular benefit of this would be access to mainstream statistics and database software which could be used to greatly extend the analysis options, presently available. A further enhancement under active consideration is a World Wide Web version of the package. As well as vastly extending the potential take-up of this new computer aided learning (CAL) opportunity it would lift it to, what in training terms, is widely seen as the current state-of-the-art.
References Aghaie, A. and Popplewell, K. (1997), ``Simulation for TQM ± the unused tool?'', The TQM Magazine, Vol. 9 No. 2 pp. 111-16. Amsden, R.T., Butler, H.E. and Amsden, D.M. (1986), SPC Simplified: Practical Steps to Quality, Kraous International Publications, White Plains, New York, NY. British Standards Institute (1980a), BS 5701, Guide to Number Defective Charts for Quality Control, British Standards Institute, London. British Standards Institute (1980b), BS 5704 Part 4, Guide to Data Analysis and Quality Control using CuSum Techniques, British Standards Institute, London.
British Standards Institute (1983), BS 5703 Part 4, CuSum for Counted/Attributes Data, British Standards Institute, London. British Standards Institute (1995), BSEN Quality Vocabulary: Part 1; International Terms (ISO 9402), British Standards Institute, London. Dale, B. (1994), Managing Quality, Prentice-Hall International, London. Freeman, J. (1993), ``Simulation for quality improvement'', Quality Forum, Vol. 19 No. 3, pp. 155-9. Freeman, J. and Evangeliou, N. (1996), ``Simulation for training in quality control'', Training for Quality, Vol. 4 No. 1, pp. 27-31. Freeman, J. and Lythgoe, P. (1996), ``CAL courseware for training in statistical quality control'', Proceedings of the First International Research Conference on Quality Management, Monash University, Melbourne. Grant, E. and Leavenworth, R. (1996), Statistical Quality Control, McGraw Hill, London. Messina, W. (1987), Statistical Quality Control for Manufacturing Managers, John Wiley and Sons Inc., Canada. Montgomery, Douglas (1991), Introduction to Statistical Quality Control, John Wiley and Sons Inc., New York, NY. Oakland, J. and Followell, R. (1990), Statistical Process Control, Heinemann Newnes, Oxford. Oakshott, L. (1997), Business Modeling and Simulation, Pitman Publishing, London. Rauwendaal, C. (1993), SPC Statistical Process Control in Extrusion, Hanser Publishers, Munich. Wetherill, B. and Brown, D. (1991), Statistical Process Control: Theory and Practice, Chapman and Hall, London.
Commentary A useful statistical technique explained clearly. 247
