advisory system for control chart selection

Comput. & Indus. Engng Vol. 10, No. 3, pp. 171-177, 1986 0360-8352/86 $3.00 + 0.00 Printed in Great Britain Pergamon Journals Ltd

A D V I S O R Y S Y S T E M F O R C O N T R O L C H A R T S E L E C T I O N

S. M. ALEXANDER Department of Industrial Engineering, University of Louisville, Louisville, KY 40292,

U.S.A.

and

V. JAGANNATHAN Boeing Computer Services, Seattle, WA 98124-0346, U.S.A.

(Received for publication 10 February 1986)

A b s t r a c t - - T h i s paper presents a framework of a computer based advisory system that can be used to assist in the selection, design, and construction of control charts. The system is developed using expert systems technology. This paper illustrates the framework by providing a trace of a demonstration system that has been constructed and shows planned enhancements to the sys tem.

Control Charts are widely used for manufacturing process control, establishing process parameters, and evaluating process capability. Many different control chart schemes have been proposed in the literature, for example see Page[l], Moore[2], Roberts[3], and Ferrell[4]. Gibra[5] gives a review of control chart developments. The different control chart schemes have been shown to have varied performance characteristics as measured by the frequency of type I and type II errors, sensitivity to detecting shifts in the process mean, sensitivity to detecting changes in the process variance, the average run length to detect shifts in the process, etc.; see Gibra[5], Freund[6], and Ewan[7]. This suggests that control chart selection should be done after thoroughly reviewing the requirements of each potential application.

However, the typical organization, which considers implementing control charts, invariably selects standard Shewhart ~ and R charts with three sigma limits (Mayer[8]). This is often due to a lack of knowledge of the existence of other types of control chart schemes, and the lack of appropriate expertise in the organization. Gibra[5] emphasizes this fact when he remarks that the more recent literature tends to underemphasize the cost of learning, applying, and supervising complicated statistical tools (referring to the different control chart schemes that have been proposed).

Standard Shewhart ~ and R charts with three sigma limits may suffice if the lack of sensitivity to small shifts and the resulting type II errors are not expensive. On the other hand, if high sensitivity to the detection of small shifts in the process average is desirable, such as in the production process of a product with tight specifications, the standard Shewhart chart, without modifications, may not be appropriate. Hence, in these situations, modified Shewhart charts with warning limits have been suggested by researchers (see for example, Page[9], Weiler[10], Weindling et al.[11]).

In some situations, such as when the time required to measure the quality characteristic is so large that repeated observations cannot be considered, the Shewhart charts may not be feasible. Further, Shewhart charts, like most other control charts, are constructed and interpreted on the basis that the characteristic measurements are uncorrelated. In practice this is not always true. Heikes and Montgomery[12] suggest the use of autoregressive integrated moving average (ARIMA) methods (Box and Jen- kins[13]) for taking autocorrelation into consideration in designing control chart schemes. The authors (Heikes et al.) state that in general more representative schemes lead to better process monitoring. They suggest that in the current era of increased competition and stringent customer requirements, precise procedures that have been

171

172 S.M. ALEXANDER and V. JAGANNATHAN

theoretically well developed should be used rather than those that are just popular. They state, "the fact that they (the precise procedures) are rarely, if ever, found in use requires a query as to why?" . Their thesis is that the main reason for the lack of application of sophisticated control chart schemes is the lack of knowledge and understanding by practitioners. Many small businesses, for instance, hire consultants for the implementation of even standard Shewhart 2 and R charts.

This paper is written to illustrate a solution which alleviates the lack of knowledge problem and greatly enhances the application of precise and suitable process monitoring procedures. The solution suggested is an expert advisory system for control chart selection and construction. This paper illustrates the framework, provides a trace of a demonstration system, which has been constructed, and shows planned enhancements to the system. The system is developed using expert systems technology.

Expert systems are programs that solve substantial problems employing facts and heuristics used by experts. For a review of expert systems see Stefik e t a/.[14]. Struc- turally, expert system programs consist of a knowledge base, a working memory or "global database" and an inference mechanism.

The knowledge base or knowledge source contains facts and heuristics associated with the problem. The knowledge about a problem domain is most commonly repre- sented as rules, though other representations are also used. Expert systems differ from conventional computer programs in that the domain knowledge can easily be updated without having to modify other portions of the system.

The working memory is a contextual database used for keeping track of the state of the "world". This includes input data for the particular problem, the problem status, and relevant history of what has been done.

The inference mechanism is the control structure that defines the way the knowledge base is used to reach a solution. The common inference paradigms are forward chaining and backward chaining. Forward chaining is the process of working from known facts towards a goal state (i.e. the process is data driven). Backward chaining is the process of selecting a hypothesis and determining if the hypothesis is supported by the context (i.e. goal driven).

Expert systems are very difficult to develop. The need to reduce the time and effort required to develop expert systems prompted the development of a number of expert systems construction tools. These tools (expert shells) in essence provide domain independent inference engines which reduce dramatically the time spent in building expert systems. The expert shell used in this implementation was GENIE[15, 16] developed at Vanderbilt University. The demonstration system was developed on an IBM PC T M with an IQ LISP environment.

The expert system framework suggested can also be used in control chart design. Saniga and Shirland[t7] and Chiu and Wetherill[18] report very few implementations of economic models for the design of control charts. The main reason for this as per- ceived by Montgomery[ 19] is the difficulty for practitioners to understand and use the models. The expert system framework suggested allows for the design of optimal models based on inputs by the user. The system has the explanation capability to enhance user understanding and acceptance. Gibra[5] suggests the need for the development of statistical computer programs for data analysis and the optimization of complex cost functions. The suggested expert system framework could be extended to access statistical computer programs and optimization routines for data analysis and design optimization.

A FRAMEWORK FOR AN EXPERT ADVISORY SYSTEM FOR CONTROL CHARTS

The basic framework for the expert advisory system for control chart selection, design, construction, and data analysis is illustrated in Fig. 1. The expert advisory system suggests appropriate control charts to use based on information about the sit- uation. Information on control chart construction and interpretation can be obtained through database query. The system framework also enables control chart design

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174 S . M . ALEXANDER and V. JAOANNATHAN

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through interface with an optimization routine and the input of appropriate cost functions and parameters.

Control chart selection rules in the knowledge base were derived from the literature. In this demonstration system no effort was made to make the set of rules comprehensive. A typical rule in the program, which was developed using the expert shell GENIE and IQ LISP, and its English translation are shown in Table 1. The set of control chart selection rules, in plain English, which were used in the program are shown in the Appendix. In order to illustrate the user interface with the expert system during the control chart selection phase, a sample trace of an interaction session is shown in Table 2.

Once the selection phase is over the user is queried by the system as to whether he requires assistance with chart construction and interpretation. If his answer is yes, a procedural call is made to a relational database for information on the specific control charts selected. Sample information in the data base for ~ and R charts is illustrated

Table 2. Trace of an interaction session

What is the value of;

MEASUREMENTS-NOT-POSSIBLE

Please enter value. > > F A L S E

FALSE CF: 1

What is the value of:

MEASUREMENTS-NOT-PRACTICAL


FALSE CF: 1

Advisory system for control chart selection

Table 2. (Continued)

175


LARGE-NUMBER-OF-CRITICAL-CHARACTERISTICS

Please enter value. > >FALSE

FALSE CF: 1


CHART-BASED-ON-ONE-HUNDRED-%-CHECKING


FALSE CF: 1

CONCLUDE (RECOMMENDATION) USE VARIABLE CHARTS


TIME-REQUIRED-TO-OBTAIN-MEASUREMENTS-IS-SMALL

Please enter value. > > T R U E

TRUE CF: 1


DESIRE-TO-DETECT-SHIFTS-IN-PROCESS-MEAN


TRUE CF: !


DESIRE-TO-DETECT-SHIFTS-IN-PROCESS-VARIANCE


TRUE CF: 1


RELATIVELY-LARGE-VALUES-OF-TYPE-I-ERRORS-ACCEPTABLE


FALSE CF: 1


HIGH-SENSITIVITY-TO-SMALL-PROCESS.SHIFTS-CRITICAL


CONCLUDE (FINAL-RECOMMENDATION) USE CUMULATIVE-SUM-CHARTS 1


ASSISTANCE-REQUIRED-IN.CHART-CONSTRUCTION-AND-INTERPRETATION


176 S. M. ALEXANDER and V. JAGANNATHAN

Table 3. Information on Shewhart x and R chart construction and chart interpretation

Chart Construction Size of subgroups: Subgroups should be selected so that the opportunity for variation to occur within

subgroups is small. For an initial study subgroups could typically consist of 4 or 5 consecutively produced pieces from the same process stream (e.g. same tool, die cavity, etc.).

Frequency of subgroups: Subgroups should be selected often enough to detect any process changes.

Number of subgroups: Enough subgroups should be gathered so that major sources of variation have had the opportunity to appear. Typically 25 or 30 subgroups are sufficient to establish the control chart.

Chart Interpretation A point above the upper control limits is generally a sign that: rathe control limit or plot point has been miscalculated. rathe piece to piece variability has increased. mthere is a shift in the process mean. --the measurement system has changed (e.g. new inspector or gauge).

A point below the control limit is generally a sign that: rathe control limits or plotted points are in error. rathe spread of the distribution has decreased. ~there is a shift in the process mean. --the measurement system has changed.

A run of 7 or 8 points on one side of the average... A run above the average generally signifies: --a greater spread in the output values. --a shift in the process mean. ~ a change in the measurement system.

A run below the average generally signifies: ~ a smaller spread in the output values. ~ a shift in the process mean. --a change in the measurement system.

in Table 3. The general framework for integrating knowledge representation schemes such as frames, rules and databases can be found in the literature, for example see Swenson[20].

A design module is planned for the enhanced system. After control chart selection, if the user desires an optimal chart design he would be able to select from standard cost functions or input his own functions and appropriate parameters. An optimization routine would then be accessed for the design of the control chart scheme.

As in other expert system developments, e.g. see Weis et al.[21], it is possible to interface the expert system with statistical analysis software for data analysis. This data analysis could be used as another input for correct control chart selection. For example, process data could be analyzed for normality and autocorrelation before a control chart scheme is selected.

CONCLUSION

The framework suggested and partially implemented is feasible and has many advantages. The framework is feasible since the domain considered is defined and small. Also, there are many expert systems with structured selection capabilities that have been developed. The framework has many advantages, in that:

I. It allows for the implementation of correct and sophisticated control methodologies on the shop floor.

2. It provides a means of adding to and increasing the knowledge of process control personnel.

3. It allows for the use of both comprehensive knowledge and sophisticated com- putation in an integrated structure.

4. The inference mechanism allows the system to ask the user only appropriate ques- tions based on the user 's prior responses,

Advisory system for control chart selection 177

REFERENCES

1. E. S. Page, Cumulative sum charts. Technometrics 3, 1-9 (1961). 2. P. G. Moore, Some properties of runs in quality control procedures. Biometrika 45, 89-95 (1958). 3. S. W. Roberts, Control charts based on geometric moving averages. Technometrics 1, 239-250 (1959). 4. E. B. Ferrell, A median, midrange chart using run-size subgroups. Indus. Quality Control 20, 1-4 (1964). 5. I. N. Gibra, Recent developments in control chart techniques. J. Quality Technol. 7, 183-192 (1975). 6. R. A. Freund, Acceptance control charts, lndas. Quality Control 14, 13-23 (1957). 7. W. D. Ewan, When and how to use cu-sum charts. Technometries 5, 1-22 (1963). 8. R. R. Mayer, Selecting control chart limits. Quality Progress XVI(9), 24-26 (1983). 9. E. S. Page, A modified control chart with warning limits. Biometrika 49, 171-176 (1962).

10. G. H. Weiler, The use of runs to control the mean in quality control. J. Amer. Statist. Ass. 48, 816-825 (1953).

11. J. 1. Weindling, S. B. Liltauer & J, Tiago DeOliveira, Mean action time of the T-control chart with warning limits. J. Quality Technol. 2, 79-85 (1970).

12. R. G, Heikes & D. C. Montgomery, Productivity is enhanced with statistical quality control. Indus, Engng 13, 52-75 (1981).

13. G. E. P. Box & G. M. Jenkins, Time Series Analysis, Farecasting and Control, revised edition. Holden- Day, San Francisco (1976).

14. M, Stefik, J, Aikins, R. Balzer, J. Benoit, L. Birnbaum, F. Hayes-Roth, & E. Sacerdoti, The organization of expert systems: a tutorial. Artifieial Intelligence 18, 135-174 (1982).

15. H. G. H. Sandell, A knowledge engineering tool for creating frame and rule based expert systems, Ph.D. dissertation, Vanderbilt University, August 1984.

16. H. G. H. Sandell, J. Bourne & R. Shiavi, GENIE: A Generic Inference Engine for Medical Applications, Proceedings of the Sixth Annual 1EEE Conference on Engineering, Medicine and Biology, 1984,

17. E. M. Saniga & L. E. Shirland, Quality control in practice--a survey. Quality Progress 10, 30-33 (1977). 18. W. K. Chiu & G. B. Wetherill, Quality control practices. Int. J. Production Res. 1.3, 175-182 (1975). 19. D. C. Montgomery, The economic design of control charts: A review and literature survey. J. Quality

Technol. 12, 75-87 (1980). 20. E.T. Swenson, A framework for knowledge integration. M.S. thesis. University of Louisville, May 1984. 21. S. Weis, C. Kulikowski, C. Apte, M. Uschold, J. Pachett, R. Brigham & B. Spitzer, Building expert

systems for controlling complex programs. Proc. 2rid Natn. Conf. on Artificial Intelligence. 322-326 (1982).

APPENDIX

Typical rules for control chart selection If measurements are not possible (only visual inspection is possible) or if measurements are not practical

(too expensive, too much time, or if the part has many critical characteristics) or if the chart is based on 100% checking, an attribute chart is recommended, otherwise variable charts are recommended.

Rules for attribute chart selection If an attribute chart is recommended and the product can be classified as defective or nondefective then

a percent defective (p-chart) is recommended. If the chart selected is based on attribute data and if it is not appropriate to classify the product as

defective or nondefective (owing to complexity or cost) then it is recommended to record a defects-based statistic.

If it is recommended that a defects-based statistic be recorded and if the opportunity for defects to occur in each production unit are infinite and the probability of a defect occurring at any place on the unit is relatively small and constant and all defect types are considered equal then the c-chart or the number of defects chart is recommended.

If the c-chart is recommended, but the inspection unit is not the same as the production unit then a u- chart may be preferred. The u-chart records the number of defects per production unit.

If an attribute chart is recommended and a defects-based statistic is considered appropriate and if the defect types are not equally important then a D-chart is recommended.

If the D-chart is recommended, but the inspection unit is not the same as the production unit then a U- chart may be preferred. The U-chart records the average weighted number of defects per production unit.

Rules for variables chart selection If a variables chart is selected and if the time required to obtain measurements is small and if it is desired

to detect shifts in the process mean and process average and high sensitivity to process shifts is not critical, standard Shewhart Y and R charts and recommended.

If a variables chart is selected and if the time required to obtain measurements is small and if it is desired to detect shifts in the process mean and increased sensitivity is desired for small and large shifts, a modified Shewhart chart with warning limits is recommended.

If a variables chart is selected and it is desired to detect shifts in the process mean and the time required to measure a critical quality characteristic is so large that repeated observations cannot be combined to form a rational subgroup and if high sensitivity to small shifts is not critical, then the moving average chart is recommended.

If the moving average chart is recommended but sensitivity to small process shifts is desirable then the geometric moving average chart is recommended.

If a variables chart is selected and if increased sensitivity to small shifts in process mean and variance is desirable and very small values of type 1 errors are allowed, a cumulative sum chart is recommended.

advisory system for control chart selection

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