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Statistical process control for the process industries
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Statisti©a| Pro©ess Contre| for t h e P r o © e s s | n d u s t r | e s John A. Shaw Statistical quality control (SQC) and statistical process control (SPC) have been used in the discrete parts manufacturing industries as a tool for improving the ~mality of manufactured items. ,Statistical methods are now being used in the chemical and petroleum industries for quality improvement. Certain concepts of SQC and SPC are applicable to certain processes, but they are not universally applicable to all processes. Successful application o f the tools requires an understanding of the methods and the limitations. This paper explains the concepts of statistical quality control and examines its use in batch and continuous processes. INTRODUCTION Statistical process control, a technique whose advocates e×pect will improve the quality of products in all industries, was developed in the "discrete parts" manufacturing industry. Its use is being examined in the chemical and petroleum industries. Distributed control manufacturers are including SPC capability in control systems designed for the process industries. Its succe~ is unquestioned in the manufacturing industries, but ~,,qii its promise be met in the chemical process industries? ISSN 0019-0578191101100991~$2.50© ISA 1991
Statistical methods are not new to the chemical process industries or to chemical engineering. Many statistical applications are intended for use in analyzing, experimental data.O) Digital filtering techniques, used to remove noise from process measurements, have been studied and applied for over twenty years. For SPC to be used in the process industries, its basic foundation, the assumptions on which it is based, and its need should be fully examined in the framework of the needs and characteristics of the proces,~ :-~d,s~es.
Deflnigon Statistical process control (or statistical quality control) is a sta~s.ffcal method for analyzing certain product characteristics to determine the likel|hood that improvements can be made in the process to reduce variability and achieve higher quality.(2, 3) While often the terms "statistical quality control" (SQC) and "statistical process control" (SPC) are used interchangeably, many in the fidd define them differently. SQC refers to the gathering of data for analysis at a later time, while SPC refers to on-line data gathering and h-m'nediate analysis.(4) Some practitioi~ers avoid the distinction altogether by referring to these methods as SPQC
(statistical process quality control). The name statistical process control ofte__~causes the incorrect inference that SPC is a control algorithm, or that it can be used to provide feedback to the process. SPC is a stalistics-based analysis method that is used to analyze process data and, it is hoped, assist the process or control engineer in making improvements to the process. SPC is not synonymous with quality control. It does not measure quality directly. Instead, it is a.-, analytical tool that indicates the Likelihood that there is some correctable condition that is causing undesirable variation in product quality and that corrective action may reduce this variation. SPC methods comprise a variety of analysis tools, including cause and effect diagrams, Pareto charts, and control charts. This paper will concentrate on control charts because of the ability of some dis~buted control systems used in the process indus~es to produce such charts.
gaSiC Theory The basic theory of SPC is that there will inevitably be variations of a product from one sample to another that are due to inherent (or "built-in") variations in the process. Variations other than these inherent variations are clue VOLUME 30 o NUMBER 1 G 1991
STATISTICALPROCESS CONTROL
to "assignable causes," which can be corrected. A statistical analysis of quality measurement should reveal any assigv_.ab!e cause vaff.ation. If there are no assignable cause variations and the only variations are inherent, the process is said to be "in statistical control." Otherwise, it is "out of statistical control" and should be corrected. SPC is based on samples of the product and the data resulting from the measurement of these samples. Charts are made from the data to assist in the analysis. Key to the operation of the SPC calculations and charts is the p~'emise that the chance or inherent variations will affect every measurement and will be stable over time. Variations that are greater than the short term variations or appear only over a longer
term must be due to "assignable causes." (5, 6) The idea is to reduce product variability rather than strive solely for conformance to specifications that all the product will be as close to aim as possible. (7)
BASIC SPC CALCULATIONS AND CHARTS Normal Distribufion'"'Bell-shaped curve" One very key concept to SPC is that of "normal distribution." A key theorem of statistics is that samples of the product will follow the standard bell-shaped normal distribution curve; that is, more of the samples will be close to the center of the range of the distribu-
Figure 1--NormalDistribution"Bell Curve"
103
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tion than toward the outside (see Figure 1).
Shewhart ControlCharts Shewhart suggested plotting the data on a chart to show variation above and below a mean. This, of course, is very similar to a trend recording very familiar to anyone in the chemical process control business. However, Shewhart suggested drawing limits (upper and lower control limits, UCL a n d LCL) at three standard deviations above and below the mean. When the process crosses either limit it is considered "out of statistical control." This chart is not very sensitive to small variations, so it is common to use various "run" tests in addition to the limits.
SPC FOR THE PROCESS iNDUSTRIES
X.R Charts
The Shewhart control chart is more commonly known as an X (X bar) chart often combined with an R chart. To build the X chart, the product is periodically sampled with several (typically four or five) individual m e a s u r e m e n t s taken. This set of measm ements is known as a "subgroup." The individual samples areaveraged to produce the number X (or average X). The individual samples are also compared to determine their range, or R. The control chart is plotted as a b o v e except that, rather than using theindividual samples, the average X is plotted. The upper and lower control limits are de,ermined using the range of the individual samples in a subgroup. The upper and lower control limits are derived from X % 3 standard deviations of the subgroup. The exact calculations are shown in Figure 2b. An important concept is that the variation of individual measurements within a subgroup is due to chance causes only. In a typical chemical process, this variation would be considered measurement or instrument noise. Longer term variations from one subgroup to another that are significantly larger (more than 3 standard deviations) than the variations within the subgroup are probably due to assignable causes.
The X and R charts show that the process is "not in statistical control" when the X value falls outside either of the control lh~ts. Some run rules also will identify out of control values. For example, eight or more consecutive values on the same side of the mean signals an out of control condition. Process ~pab#ity
Another result of the SPC analysis of the process data is what is known as "process capability."
Process capability asks the question, "Based on the spread in the measurements, will the process be capable of staying within specifications almost all the time?" By basing the standard deviation on the average range of the subgroups (R) rather than on the distribution of all the measurements, we will base the capability index on the inherent variability. This supposes that the subgroup variability represents the inherent variability and the overall variability includes assignable causes.
Example Shown in Figure 2a are data taken from a hypothetical continuous chemical process. The measurements of density are made by an on-line analyzer everX 10 minutes. To construct the X-R chart we will take 4 consecutive measurements every hoar. We then average the four measurements in each hourly subgroup and plot the average on the X chart. We plot the range of each subgroup on the R chart. Next we must determine the upper and lower control limits ushag the calculations shown in Figure 2b. Horizontal lines are drawn (Figure 2c) to indicate the UCL and LCL on the X chart and the UCL on the R chart. We can then see that at several points X exceeds the upper control limit, h~dicating that the process is out of statistical control.
D
Vadatlon of X An important part of the X chart is the subgrouping of four to five measurements that are averaged to provide one point on ~ e chart. The concept is that the natural inherent varmfion will be reflected in the average range of the subgroup, while the difference between one subgroup and a n o ~ e r will, ff it is greater than a certain a m o u n t , reflect the assignable cause.
Sometimes there is no way to obtain a rationalsubgroup that reflects all the inherent variation. Here the subgrouping is omitted, and each measurement is plotted on a chart of hqdividuals. The control limits are determined by the variation between one measurement and the next.
USE OF SPC DATA So how do the charts and numbers improve the q,,ali~_. . of the product, reduce rerun material, and make our processes better? They don't. What they do is provide information about the process that can be used in the process analysis to determine ways to improve the process. The charts and data tell us when the variability is due to assignable, perhaps correctable, causes. They also provide clues such as when the variability has changed. For example, ff the process is out of statistical control only during one shift and the time changes with shift rotation, we may want to look at the procedures used by those operators.
SPC lntegraOon
into ControlSystem
Modem digital distributed control systems have the capability of measuring the process parameters at designated rates, storing the measurements, and processing them. One addition that can be made _toa control syste~ is to provide SPC c o m p u ~ f i o ~ and "charts as an integral part of the system. Such a system wal allow the operator to quickly display an SPC chart for a process variable.
SPC~ One application of SPC is to produce alarms when the measured v~-iable is out of statistical control. This feature can easily be a part of the SFC capability in a dish'ibu~d control system.(8) VOLUME 30 • NUMBER 1 • 1991
101
S"TATISTICAL PROCESS CONTROL
=S_ 99.736 98.740 100.206 101.424 101.311 102.601 99.447 104.152 103.391 100.765 102.969 101.209 99.647 100.59 101.959 99.840 100.839 101.179 101.782
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SAMPL,,.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
98.349 100.455 99.282 101.677 102.481 102.362 102.876 104.029 102.35 101.68 104.403 102.216 98.976 99.611 102.737 98.142 98.244 98.793 99.260
101.99 98.957 99.285 102.469 101.461 101.927 103.314 102.,~95 99.920 103.358 104.369 100.355 100.404 99.511 99.404 97.744 97.613 99.642 100.71
97.777 102.522 100.197 90.526 102.615 98.530 99.989 102.499 100.901 102.905 103.856 103.731 101.658 102.929 98.850 98.153 99.390 99.809 101.365
4.21 3.78 0.92 2.94 1.30 4.07 3.87 1,66 3.47 2.59 1.43 3.3S 2.6'~ 3.42 3.89 ,,,~ -'.10 3,23 2.39 2.52
___.R_ 99.463 100.169 99.743 101.274 101.967 !0!.355 101.407 103.294 ~01.640 102.177 103.899 101.878 100.171 i00.661 100.738 98.470 99.022 99.856 100.779
X (average ?,f) = lnn.q_5
R (Average range) = 2.83 Figure 2a-Exampleof an X R Chart (a) is the data, (b)is the calculation, and (c) is the completed charts
Upper Control Limit
UCL
=
X+0.73xR
Lower Control Limit
LCL
=
X- 0.73xR
Range Control Limit
UCL(R) = 2.28 x R
Figure 2b-Example on an X R Chart (a) is the data, (b)is the calculations, and (c) is tl~e,completed charts Several types of SPC alarms are trend alarms when fl~e X points increase or decrease for too many samples, alarms when any X is uu .....d~: the upper or lower control limits, and alarms when the accumulated value above or below the median is too ~eat.
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SPC IN THE MANUFACTURING iNDUSTRiES SPC has been adopted in the manufacturing industries (often known as the "discrete parts" industries) to the extent that SPC is almost synonymous with quality
control. SPC is the primary means of determiaing product variability and determining if corrective action or process improvement is required. Certain characteristics of the m a n u f a c t u r i n g industries have encouraged the development of
SPC FOR THE PROCESS INDUSTRIES
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Figure 2c-Example of an X R Chart (a) is the data, (b) is the calculations, and (c) is the complmed charts SPC as the primary method of qaality control. These industries produce large quantifies of dis~ete parts using a variety of machines, m o s t of w h i c h are involved in cutting, stamping, or shaping solid material. The most common measurement of a part is dimensional (size). i3ecause the measurement of a part is a manual operation, the parts are usually sampled, with measurements from the samples being used to judge the production. Sar l?lir~g technology is based on the ~aathematics and theory of statislScs. In typical manufacturing operations, t h e r e m a ) b e a large amount of automatic con~ol"numerically operated m~chines and programmed robots'1~ut there is very little of the feedback control like that used in the chemical industry. Variations in a product measurement are not automafi-
cally used to manipulate the machines. Instead, variations may be used by supervision to make certain changes, such as machine adjustments or operator retraining. A~corddng to SPC theory, if the v~-iation is inherent or the result of a constant cause (that is, always present), the process should be left alone. If fl~e variation is due to a s s i g n a b l e cause (because it changes over time), the cause s h o u l d be i d e n t i f i e d a n d removed. (9)
ularly chemical plants and refineries, are important to statistical analysis.d0,11,12) In the typical discrete parts factory where many parts are made, only a small number are sampled for testing. Except for certain effects, such as different workers on different shifts and temperatu~ changes wihhin a day, most of the parts selected for sampling can be considered statistically independent. That is, the difference between part #101 and #102 should be the same a~ the difference between part #102 and part #11301.
SPC iN THE CHEWCAL AND PETROLEUM iNDUSTRY
In continuous chemical processes there is normally a degree of backmixing of the product stream due to storage of the product Jn vessels that are a part of the process. This storage "smooths" the charactedsrfics of the material. The process measurements are often continuous or sampled at a
Differences between Chemical Processing and Manufacturing Several major differences between the discrete p~rts ~ d u ~ and the process industries, partic-
VOLUME 30 • NUMBER 1 o 199!
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STATISTICALPROCESS CONiROL
time period less than (sampled faster than) the holdup time in the relevant parts of the process. This removes the statistical independence of the samples. The result is what is known as "correlated" (or auto correlated) data. Conventional control charts do not apply to correlated data. Another difference between m o s t typical m a n u f a c t u r i n g plants and most chemical process plants is the degree of feedback control. In most chemical plants the key product variables are measured and, using the PID control algorithms, fed back to control the process. The control algorithms work to move the controlled variable to a set point. Thus, the concept of controlling to an "aim" has always been the standard practice in the process Industries.
ever, other, more minor, components come from impurities in raw materials, contaminants from the materials of construction, etc., and cannot be controlled directly. Sometimes product quality characte_,Ss.fics are measured by a~t analyzer on a very long sample. The analyzer may exhibit random
In certain situations, key product quality variables cannot be directly controlled. Typical among these are certain batch processes where the product continues to change even after the last control action has been taken ~nd there are no more opportunities to correct for error (the "end point control" problem). The situation also arises when the key quality variable cannot be measured on line for feedback control but is instead measured every several hours in a quality control laboratory. Another type of quality-related variables that are not controlled with the standard PID control loops are such secondary variables as small amounts of impurities in a product. A typical chemical process may have as its last unit operation a distillation column to separate the product from some other chemical. The control loops on the column will measure (using an analyzer or a tray temperature) and maintain the proper proportion of the major constituents of the product. How104,
ISA TRANSACTIONS
SPC has been used for batch chemical processes.(13) Certain considerations must be made. First is the use of rational subgroups and the number of samples. If the batch is a well-mixed liquid, the only difference be-
In certain situations, key product quality variables cannot be directly controlled. error, so each measurement cannot, by itself, be taken as an indication of the quality. SPC calculations may serve as a filter to "see t h r o u g h " the r a n d o m noise.
Fiat Sheet Industries Areas of ProbableAppflcation
Batch Processes
The "fiat sheet" industries indude paper, plastics, and other industries that produce fiat sheets of material through the extrusion of the material. The material usually moves from a machine at a very high speed, and certain characteristics are determined by scanning the material at a much slower speed. Because the holdup in the machine is very low, this scanning amounts to sampling of the characteristics. These flat sheet industries, from a statistical and sampling point of view, are very similar to the discrete parts manufacturing industries. SPC, in the classical sense and as used in manufacturing,, should apply directly. Other areas of the chemical process industries may be similar. These would be processes where there is very little holdup or backmixing in the process, where there are product characteristics that cannot be continuously measured but must be sampled, and where those characteristics cannot be easily controlled by standard process control techniques.
tween s~mples of the same batch is measurement error. We may, of course, wish to make several measurements of the same batch for accuracy, but if we base the control lirr'.its on these measurements, the control limits will be so dose to the mean (assuming little variation in the measurements) that any variation from one batch to another will be outside the control limits and the process will be considered to be out of statistical control. Another concern for batch SPC is statistical significance. With one true measurement per batch, we must have a significant number of batches before the SPC results can be reliable. Estimates about the number of samples differ. However, we cannot have confidence in the analysis of SPC data after only five batches. If analysis of the batch control is necessary after only a few batches, some other method will be needed.
Considem~ons in SPC Appffcatlons One basic tenet of statistical quality control also may limit :ts application in many processes: the assumption that short-term variations that affect measurements within a subgroup or ~,~. . . . . . . jacent measurements are inherent and not correctable, while longterm variations reflect assignable cause, that is, variations due to some operational or process prob-
SPC FOR THE PROCESS INDUSTRIE',
lem that can be corrected.(14,15) This assumption is reflected in the fact that the control limits, based on the subgroup variation, are applied to the average measurement over a longer time frame. Many continuous processes exhibit short-term variation in the m e a s u r e m e n t due to measurement error or noise, with actual process changes dampened out by mixing within vessels in the process. There will be longer term variations due to small oscillations in the process, changes in feed stock, or process upsets, which may be insignificant when compared to the product specifications but are many times larger than the short-term variations. Conversely, there may be situations, such as many batch processes, where short-term variations between adjacent batches are very significant in terms of product specifications, but because the variations are short-term and continue over a longer period of time they are not reflected in the control chart. Conventional control chart theory requires that three assumptions be met: (1) the process mean '.'s constant, (2) the process standard deviaf.m is constant, and (3) measurements are independent of one another (un. ~rrelated). If any of these is not true, then a conventional (ShewharO control chart probably will I,,i -~roduce reliable results. The first and third assumptions are particularly relevant to the continuous process industries. The mean, (that is, the average of any group of consecutive measurements), often will vary over a longer period. Also, continuous process variables tend to exhibit a large degree of correlation. This is not to say that SPC is not applicable to the chemical process industries but to emp~hasize that it is not urdver-~aUy applicable; it is up to the process engineer to determine how it can be applied to
his particular process and if SPC provides knowledge about the process not more easily obtainable through other methods. It is also incumbent upon the user to make use of knowledge gained through SPC to improve his or her process operation.
OTHERSTATISTICAL TECHNIQUES Statistical analysis of data taken from the process may help to locate the cause of the variation. Some variations (measurement noise, for example) are random, and can be identified by test for randomness. One such method is serial (or auto) correlation, in which each sample is correlated with the previous sample. A random noise exhibits very little correlation. A r a n d o m noise t h a t has been damped by passing through the process exhibits much greater correlation. This test may be able to determine if var~atmn results from measurement noise that occurs in the transmitter from the fluctuations that occur in the process. Standard SPC con[rol charts are often used to detect trends that are not otherwise apparent because the variation is less than the noise. In this application, the SPC chart is really being used as a type of digital filter.
engineer or control engineer to correct the variation if it is harmful. These methods will include digital filtering, correlation analysis techniques, and other methods that will use statistics and other mathematical methods. The goal should be to develop teclmiques that willallow the process engineer to analyze the performance of the process in order to improve product quality and process efficiency.
COHCLUSIOH Statistical process control has served as an important tool in the discrete parts manufacturing industries to improve product quality, r e d u c e variability, and decrease cost. It is being adopted by many companies in the chemical process industries, in part due to pressure from their customers. In some areas within the chemical industry, SPC has proven to be a useful and successful tool. Its applicability must be examined in all areas of the chemical industry, application by application. Two primary considerations should govern its ~cc_eptance for each individual application: the ability of SPC to produce meaningful results, and the need for SPC as compared to other statistical and non statistical tools.
REFERENCES ADDfflOHALIHVESTIGATIOH HEEDS
1.
Rather than simply adopting the SPC techniques of the manufacturing industries, the chemical process industries should choose statistical techniques tailored to their processes. Methods are available that w'll analyze process variations to locate the cause of the variation. Knowledge of the cause of the variation will assist the process
2.
Himmelblau, David M.,
Process Analysis by Statistical Methods, Wiley, 1970. Western Electric Company, Inc., ,Statistical Quality Control Handbook, D e l m a r Printing Company, Charlore, North Carolina, 1956, p. 3. 3. Grant, E. L., and Leavenw o r t h , R. S., Statistical Quality Control, McGrawHill, 1980, p. 3. VOLUME 30 o NUMBER 1 e 1991
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STATISTICAL PROCESS CONTROL
4.
Dybeck, Martin, "From SQC to SPC: An Economically Significant Step for Today's Process Industry,"
Advances In Instrumentat/on, Vol. 42 (ISA/87), p. 7i3. 5. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, McGrawHill, 1980, p. 1 and pp 7475. 6. Oft, E. R., Process Quality
Control, TroubZeshooting and Interpretation of Data, McGraw-Hill, 1975, pp 3-6. 7. Hess, J. L., and Bright, L. R., "Statistical Process control and Quality Partnerships,"
Advances In Instrumentation, Vol. 43 (ISA/88) p. 8.
106
107. Lee, J. L., "Application of
ISA TRANSACTIONS
Process Analysis by Statistical Methods, Wiley, 1970, p.
Statistical Process Conl~'ol Methods to the Establishment of Process Alarms in a Distributed Process Control System," Advances In Instrumentation, Vol. 43 (ISA/88), p. 1311. 9. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, McGrawHill, 1980, pp 74-75. 10. Hess, J. L., and Bright, LoR., "Statistical Process control and Quality Partnerships,"
79. 13. Marsh, C. E., and Tucker, T. W., "Application of SPC to Batch Units," Advances In Instrumentation, Vol. 43 (ISA/88), p. 1325. 14. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, 1980, McGraw-Hill, p. 5.
Advances In Instrumentation, Vol. 43 (ISA/88) p. 107. 11. American Society of Quality Control, Quality Assur-
ance for the Chemical and Process Industries, A Manual of Good Practices, 1987, p. 1. 12. Himmelblau, David M.,
@
15. Western Electric Company, Inc., Statistical Quality Control Handbook, Delmar Printing Company, Charlotte, North Carolina, 1956, p. 6.
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.
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.
.
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! !
Statisti©a| Pro©ess Contre| for t h e P r o © e s s | n d u s t r | e s John A. Shaw Statistical quality control (SQC) and statistical process control (SPC) have been used in the discrete parts manufacturing industries as a tool for improving the ~mality of manufactured items. ,Statistical methods are now being used in the chemical and petroleum industries for quality improvement. Certain concepts of SQC and SPC are applicable to certain processes, but they are not universally applicable to all processes. Successful application o f the tools requires an understanding of the methods and the limitations. This paper explains the concepts of statistical quality control and examines its use in batch and continuous processes. INTRODUCTION Statistical process control, a technique whose advocates e×pect will improve the quality of products in all industries, was developed in the "discrete parts" manufacturing industry. Its use is being examined in the chemical and petroleum industries. Distributed control manufacturers are including SPC capability in control systems designed for the process industries. Its succe~ is unquestioned in the manufacturing industries, but ~,,qii its promise be met in the chemical process industries? ISSN 0019-0578191101100991~$2.50© ISA 1991
Statistical methods are not new to the chemical process industries or to chemical engineering. Many statistical applications are intended for use in analyzing, experimental data.O) Digital filtering techniques, used to remove noise from process measurements, have been studied and applied for over twenty years. For SPC to be used in the process industries, its basic foundation, the assumptions on which it is based, and its need should be fully examined in the framework of the needs and characteristics of the proces,~ :-~d,s~es.
Deflnigon Statistical process control (or statistical quality control) is a sta~s.ffcal method for analyzing certain product characteristics to determine the likel|hood that improvements can be made in the process to reduce variability and achieve higher quality.(2, 3) While often the terms "statistical quality control" (SQC) and "statistical process control" (SPC) are used interchangeably, many in the fidd define them differently. SQC refers to the gathering of data for analysis at a later time, while SPC refers to on-line data gathering and h-m'nediate analysis.(4) Some practitioi~ers avoid the distinction altogether by referring to these methods as SPQC
(statistical process quality control). The name statistical process control ofte__~causes the incorrect inference that SPC is a control algorithm, or that it can be used to provide feedback to the process. SPC is a stalistics-based analysis method that is used to analyze process data and, it is hoped, assist the process or control engineer in making improvements to the process. SPC is not synonymous with quality control. It does not measure quality directly. Instead, it is a.-, analytical tool that indicates the Likelihood that there is some correctable condition that is causing undesirable variation in product quality and that corrective action may reduce this variation. SPC methods comprise a variety of analysis tools, including cause and effect diagrams, Pareto charts, and control charts. This paper will concentrate on control charts because of the ability of some dis~buted control systems used in the process indus~es to produce such charts.
gaSiC Theory The basic theory of SPC is that there will inevitably be variations of a product from one sample to another that are due to inherent (or "built-in") variations in the process. Variations other than these inherent variations are clue VOLUME 30 o NUMBER 1 G 1991
STATISTICALPROCESS CONTROL
to "assignable causes," which can be corrected. A statistical analysis of quality measurement should reveal any assigv_.ab!e cause vaff.ation. If there are no assignable cause variations and the only variations are inherent, the process is said to be "in statistical control." Otherwise, it is "out of statistical control" and should be corrected. SPC is based on samples of the product and the data resulting from the measurement of these samples. Charts are made from the data to assist in the analysis. Key to the operation of the SPC calculations and charts is the p~'emise that the chance or inherent variations will affect every measurement and will be stable over time. Variations that are greater than the short term variations or appear only over a longer
term must be due to "assignable causes." (5, 6) The idea is to reduce product variability rather than strive solely for conformance to specifications that all the product will be as close to aim as possible. (7)
BASIC SPC CALCULATIONS AND CHARTS Normal Distribufion'"'Bell-shaped curve" One very key concept to SPC is that of "normal distribution." A key theorem of statistics is that samples of the product will follow the standard bell-shaped normal distribution curve; that is, more of the samples will be close to the center of the range of the distribu-
Figure 1--NormalDistribution"Bell Curve"
103
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tion than toward the outside (see Figure 1).
Shewhart ControlCharts Shewhart suggested plotting the data on a chart to show variation above and below a mean. This, of course, is very similar to a trend recording very familiar to anyone in the chemical process control business. However, Shewhart suggested drawing limits (upper and lower control limits, UCL a n d LCL) at three standard deviations above and below the mean. When the process crosses either limit it is considered "out of statistical control." This chart is not very sensitive to small variations, so it is common to use various "run" tests in addition to the limits.
SPC FOR THE PROCESS iNDUSTRIES
X.R Charts
The Shewhart control chart is more commonly known as an X (X bar) chart often combined with an R chart. To build the X chart, the product is periodically sampled with several (typically four or five) individual m e a s u r e m e n t s taken. This set of measm ements is known as a "subgroup." The individual samples areaveraged to produce the number X (or average X). The individual samples are also compared to determine their range, or R. The control chart is plotted as a b o v e except that, rather than using theindividual samples, the average X is plotted. The upper and lower control limits are de,ermined using the range of the individual samples in a subgroup. The upper and lower control limits are derived from X % 3 standard deviations of the subgroup. The exact calculations are shown in Figure 2b. An important concept is that the variation of individual measurements within a subgroup is due to chance causes only. In a typical chemical process, this variation would be considered measurement or instrument noise. Longer term variations from one subgroup to another that are significantly larger (more than 3 standard deviations) than the variations within the subgroup are probably due to assignable causes.
The X and R charts show that the process is "not in statistical control" when the X value falls outside either of the control lh~ts. Some run rules also will identify out of control values. For example, eight or more consecutive values on the same side of the mean signals an out of control condition. Process ~pab#ity
Another result of the SPC analysis of the process data is what is known as "process capability."
Process capability asks the question, "Based on the spread in the measurements, will the process be capable of staying within specifications almost all the time?" By basing the standard deviation on the average range of the subgroups (R) rather than on the distribution of all the measurements, we will base the capability index on the inherent variability. This supposes that the subgroup variability represents the inherent variability and the overall variability includes assignable causes.
Example Shown in Figure 2a are data taken from a hypothetical continuous chemical process. The measurements of density are made by an on-line analyzer everX 10 minutes. To construct the X-R chart we will take 4 consecutive measurements every hoar. We then average the four measurements in each hourly subgroup and plot the average on the X chart. We plot the range of each subgroup on the R chart. Next we must determine the upper and lower control limits ushag the calculations shown in Figure 2b. Horizontal lines are drawn (Figure 2c) to indicate the UCL and LCL on the X chart and the UCL on the R chart. We can then see that at several points X exceeds the upper control limit, h~dicating that the process is out of statistical control.
D
Vadatlon of X An important part of the X chart is the subgrouping of four to five measurements that are averaged to provide one point on ~ e chart. The concept is that the natural inherent varmfion will be reflected in the average range of the subgroup, while the difference between one subgroup and a n o ~ e r will, ff it is greater than a certain a m o u n t , reflect the assignable cause.
Sometimes there is no way to obtain a rationalsubgroup that reflects all the inherent variation. Here the subgrouping is omitted, and each measurement is plotted on a chart of hqdividuals. The control limits are determined by the variation between one measurement and the next.
USE OF SPC DATA So how do the charts and numbers improve the q,,ali~_. . of the product, reduce rerun material, and make our processes better? They don't. What they do is provide information about the process that can be used in the process analysis to determine ways to improve the process. The charts and data tell us when the variability is due to assignable, perhaps correctable, causes. They also provide clues such as when the variability has changed. For example, ff the process is out of statistical control only during one shift and the time changes with shift rotation, we may want to look at the procedures used by those operators.
SPC lntegraOon
into ControlSystem
Modem digital distributed control systems have the capability of measuring the process parameters at designated rates, storing the measurements, and processing them. One addition that can be made _toa control syste~ is to provide SPC c o m p u ~ f i o ~ and "charts as an integral part of the system. Such a system wal allow the operator to quickly display an SPC chart for a process variable.
SPC~ One application of SPC is to produce alarms when the measured v~-iable is out of statistical control. This feature can easily be a part of the SFC capability in a dish'ibu~d control system.(8) VOLUME 30 • NUMBER 1 • 1991
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S"TATISTICAL PROCESS CONTROL
=S_ 99.736 98.740 100.206 101.424 101.311 102.601 99.447 104.152 103.391 100.765 102.969 101.209 99.647 100.59 101.959 99.840 100.839 101.179 101.782
B~gf..
SAMPL,,.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
98.349 100.455 99.282 101.677 102.481 102.362 102.876 104.029 102.35 101.68 104.403 102.216 98.976 99.611 102.737 98.142 98.244 98.793 99.260
101.99 98.957 99.285 102.469 101.461 101.927 103.314 102.,~95 99.920 103.358 104.369 100.355 100.404 99.511 99.404 97.744 97.613 99.642 100.71
97.777 102.522 100.197 90.526 102.615 98.530 99.989 102.499 100.901 102.905 103.856 103.731 101.658 102.929 98.850 98.153 99.390 99.809 101.365
4.21 3.78 0.92 2.94 1.30 4.07 3.87 1,66 3.47 2.59 1.43 3.3S 2.6'~ 3.42 3.89 ,,,~ -'.10 3,23 2.39 2.52
___.R_ 99.463 100.169 99.743 101.274 101.967 !0!.355 101.407 103.294 ~01.640 102.177 103.899 101.878 100.171 i00.661 100.738 98.470 99.022 99.856 100.779
X (average ?,f) = lnn.q_5
R (Average range) = 2.83 Figure 2a-Exampleof an X R Chart (a) is the data, (b)is the calculation, and (c) is the completed charts
Upper Control Limit
UCL
=
X+0.73xR
Lower Control Limit
LCL
=
X- 0.73xR
Range Control Limit
UCL(R) = 2.28 x R
Figure 2b-Example on an X R Chart (a) is the data, (b)is the calculations, and (c) is tl~e,completed charts Several types of SPC alarms are trend alarms when fl~e X points increase or decrease for too many samples, alarms when any X is uu .....d~: the upper or lower control limits, and alarms when the accumulated value above or below the median is too ~eat.
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SPC IN THE MANUFACTURING iNDUSTRiES SPC has been adopted in the manufacturing industries (often known as the "discrete parts" industries) to the extent that SPC is almost synonymous with quality
control. SPC is the primary means of determiaing product variability and determining if corrective action or process improvement is required. Certain characteristics of the m a n u f a c t u r i n g industries have encouraged the development of
SPC FOR THE PROCESS INDUSTRIES
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Figure 2c-Example of an X R Chart (a) is the data, (b) is the calculations, and (c) is the complmed charts SPC as the primary method of qaality control. These industries produce large quantifies of dis~ete parts using a variety of machines, m o s t of w h i c h are involved in cutting, stamping, or shaping solid material. The most common measurement of a part is dimensional (size). i3ecause the measurement of a part is a manual operation, the parts are usually sampled, with measurements from the samples being used to judge the production. Sar l?lir~g technology is based on the ~aathematics and theory of statislScs. In typical manufacturing operations, t h e r e m a ) b e a large amount of automatic con~ol"numerically operated m~chines and programmed robots'1~ut there is very little of the feedback control like that used in the chemical industry. Variations in a product measurement are not automafi-
cally used to manipulate the machines. Instead, variations may be used by supervision to make certain changes, such as machine adjustments or operator retraining. A~corddng to SPC theory, if the v~-iation is inherent or the result of a constant cause (that is, always present), the process should be left alone. If fl~e variation is due to a s s i g n a b l e cause (because it changes over time), the cause s h o u l d be i d e n t i f i e d a n d removed. (9)
ularly chemical plants and refineries, are important to statistical analysis.d0,11,12) In the typical discrete parts factory where many parts are made, only a small number are sampled for testing. Except for certain effects, such as different workers on different shifts and temperatu~ changes wihhin a day, most of the parts selected for sampling can be considered statistically independent. That is, the difference between part #101 and #102 should be the same a~ the difference between part #102 and part #11301.
SPC iN THE CHEWCAL AND PETROLEUM iNDUSTRY
In continuous chemical processes there is normally a degree of backmixing of the product stream due to storage of the product Jn vessels that are a part of the process. This storage "smooths" the charactedsrfics of the material. The process measurements are often continuous or sampled at a
Differences between Chemical Processing and Manufacturing Several major differences between the discrete p~rts ~ d u ~ and the process industries, partic-
VOLUME 30 • NUMBER 1 o 199!
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STATISTICALPROCESS CONiROL
time period less than (sampled faster than) the holdup time in the relevant parts of the process. This removes the statistical independence of the samples. The result is what is known as "correlated" (or auto correlated) data. Conventional control charts do not apply to correlated data. Another difference between m o s t typical m a n u f a c t u r i n g plants and most chemical process plants is the degree of feedback control. In most chemical plants the key product variables are measured and, using the PID control algorithms, fed back to control the process. The control algorithms work to move the controlled variable to a set point. Thus, the concept of controlling to an "aim" has always been the standard practice in the process Industries.
ever, other, more minor, components come from impurities in raw materials, contaminants from the materials of construction, etc., and cannot be controlled directly. Sometimes product quality characte_,Ss.fics are measured by a~t analyzer on a very long sample. The analyzer may exhibit random
In certain situations, key product quality variables cannot be directly controlled. Typical among these are certain batch processes where the product continues to change even after the last control action has been taken ~nd there are no more opportunities to correct for error (the "end point control" problem). The situation also arises when the key quality variable cannot be measured on line for feedback control but is instead measured every several hours in a quality control laboratory. Another type of quality-related variables that are not controlled with the standard PID control loops are such secondary variables as small amounts of impurities in a product. A typical chemical process may have as its last unit operation a distillation column to separate the product from some other chemical. The control loops on the column will measure (using an analyzer or a tray temperature) and maintain the proper proportion of the major constituents of the product. How104,
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SPC has been used for batch chemical processes.(13) Certain considerations must be made. First is the use of rational subgroups and the number of samples. If the batch is a well-mixed liquid, the only difference be-
In certain situations, key product quality variables cannot be directly controlled. error, so each measurement cannot, by itself, be taken as an indication of the quality. SPC calculations may serve as a filter to "see t h r o u g h " the r a n d o m noise.
Fiat Sheet Industries Areas of ProbableAppflcation
Batch Processes
The "fiat sheet" industries indude paper, plastics, and other industries that produce fiat sheets of material through the extrusion of the material. The material usually moves from a machine at a very high speed, and certain characteristics are determined by scanning the material at a much slower speed. Because the holdup in the machine is very low, this scanning amounts to sampling of the characteristics. These flat sheet industries, from a statistical and sampling point of view, are very similar to the discrete parts manufacturing industries. SPC, in the classical sense and as used in manufacturing,, should apply directly. Other areas of the chemical process industries may be similar. These would be processes where there is very little holdup or backmixing in the process, where there are product characteristics that cannot be continuously measured but must be sampled, and where those characteristics cannot be easily controlled by standard process control techniques.
tween s~mples of the same batch is measurement error. We may, of course, wish to make several measurements of the same batch for accuracy, but if we base the control lirr'.its on these measurements, the control limits will be so dose to the mean (assuming little variation in the measurements) that any variation from one batch to another will be outside the control limits and the process will be considered to be out of statistical control. Another concern for batch SPC is statistical significance. With one true measurement per batch, we must have a significant number of batches before the SPC results can be reliable. Estimates about the number of samples differ. However, we cannot have confidence in the analysis of SPC data after only five batches. If analysis of the batch control is necessary after only a few batches, some other method will be needed.
Considem~ons in SPC Appffcatlons One basic tenet of statistical quality control also may limit :ts application in many processes: the assumption that short-term variations that affect measurements within a subgroup or ~,~. . . . . . . jacent measurements are inherent and not correctable, while longterm variations reflect assignable cause, that is, variations due to some operational or process prob-
SPC FOR THE PROCESS INDUSTRIE',
lem that can be corrected.(14,15) This assumption is reflected in the fact that the control limits, based on the subgroup variation, are applied to the average measurement over a longer time frame. Many continuous processes exhibit short-term variation in the m e a s u r e m e n t due to measurement error or noise, with actual process changes dampened out by mixing within vessels in the process. There will be longer term variations due to small oscillations in the process, changes in feed stock, or process upsets, which may be insignificant when compared to the product specifications but are many times larger than the short-term variations. Conversely, there may be situations, such as many batch processes, where short-term variations between adjacent batches are very significant in terms of product specifications, but because the variations are short-term and continue over a longer period of time they are not reflected in the control chart. Conventional control chart theory requires that three assumptions be met: (1) the process mean '.'s constant, (2) the process standard deviaf.m is constant, and (3) measurements are independent of one another (un. ~rrelated). If any of these is not true, then a conventional (ShewharO control chart probably will I,,i -~roduce reliable results. The first and third assumptions are particularly relevant to the continuous process industries. The mean, (that is, the average of any group of consecutive measurements), often will vary over a longer period. Also, continuous process variables tend to exhibit a large degree of correlation. This is not to say that SPC is not applicable to the chemical process industries but to emp~hasize that it is not urdver-~aUy applicable; it is up to the process engineer to determine how it can be applied to
his particular process and if SPC provides knowledge about the process not more easily obtainable through other methods. It is also incumbent upon the user to make use of knowledge gained through SPC to improve his or her process operation.
OTHERSTATISTICAL TECHNIQUES Statistical analysis of data taken from the process may help to locate the cause of the variation. Some variations (measurement noise, for example) are random, and can be identified by test for randomness. One such method is serial (or auto) correlation, in which each sample is correlated with the previous sample. A random noise exhibits very little correlation. A r a n d o m noise t h a t has been damped by passing through the process exhibits much greater correlation. This test may be able to determine if var~atmn results from measurement noise that occurs in the transmitter from the fluctuations that occur in the process. Standard SPC con[rol charts are often used to detect trends that are not otherwise apparent because the variation is less than the noise. In this application, the SPC chart is really being used as a type of digital filter.
engineer or control engineer to correct the variation if it is harmful. These methods will include digital filtering, correlation analysis techniques, and other methods that will use statistics and other mathematical methods. The goal should be to develop teclmiques that willallow the process engineer to analyze the performance of the process in order to improve product quality and process efficiency.
COHCLUSIOH Statistical process control has served as an important tool in the discrete parts manufacturing industries to improve product quality, r e d u c e variability, and decrease cost. It is being adopted by many companies in the chemical process industries, in part due to pressure from their customers. In some areas within the chemical industry, SPC has proven to be a useful and successful tool. Its applicability must be examined in all areas of the chemical industry, application by application. Two primary considerations should govern its ~cc_eptance for each individual application: the ability of SPC to produce meaningful results, and the need for SPC as compared to other statistical and non statistical tools.
REFERENCES ADDfflOHALIHVESTIGATIOH HEEDS
1.
Rather than simply adopting the SPC techniques of the manufacturing industries, the chemical process industries should choose statistical techniques tailored to their processes. Methods are available that w'll analyze process variations to locate the cause of the variation. Knowledge of the cause of the variation will assist the process
2.
Himmelblau, David M.,
Process Analysis by Statistical Methods, Wiley, 1970. Western Electric Company, Inc., ,Statistical Quality Control Handbook, D e l m a r Printing Company, Charlore, North Carolina, 1956, p. 3. 3. Grant, E. L., and Leavenw o r t h , R. S., Statistical Quality Control, McGrawHill, 1980, p. 3. VOLUME 30 o NUMBER 1 e 1991
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STATISTICAL PROCESS CONTROL
4.
Dybeck, Martin, "From SQC to SPC: An Economically Significant Step for Today's Process Industry,"
Advances In Instrumentat/on, Vol. 42 (ISA/87), p. 7i3. 5. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, McGrawHill, 1980, p. 1 and pp 7475. 6. Oft, E. R., Process Quality
Control, TroubZeshooting and Interpretation of Data, McGraw-Hill, 1975, pp 3-6. 7. Hess, J. L., and Bright, L. R., "Statistical Process control and Quality Partnerships,"
Advances In Instrumentation, Vol. 43 (ISA/88) p. 8.
106
107. Lee, J. L., "Application of
ISA TRANSACTIONS
Process Analysis by Statistical Methods, Wiley, 1970, p.
Statistical Process Conl~'ol Methods to the Establishment of Process Alarms in a Distributed Process Control System," Advances In Instrumentation, Vol. 43 (ISA/88), p. 1311. 9. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, McGrawHill, 1980, pp 74-75. 10. Hess, J. L., and Bright, LoR., "Statistical Process control and Quality Partnerships,"
79. 13. Marsh, C. E., and Tucker, T. W., "Application of SPC to Batch Units," Advances In Instrumentation, Vol. 43 (ISA/88), p. 1325. 14. Grant, E. L., and Leavenworth, R. S., Statistical Quality Control, 1980, McGraw-Hill, p. 5.
Advances In Instrumentation, Vol. 43 (ISA/88) p. 107. 11. American Society of Quality Control, Quality Assur-
ance for the Chemical and Process Industries, A Manual of Good Practices, 1987, p. 1. 12. Himmelblau, David M.,
@
15. Western Electric Company, Inc., Statistical Quality Control Handbook, Delmar Printing Company, Charlotte, North Carolina, 1956, p. 6.
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