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Chapter 9 Soil quality control
203 Chapter 9
SOIL QUALITY CONTROL F.J. PIERCE and D.C. GILLILAND
I. Introduction II. The Case for Statistical Quality Control in Soil Quality A. An overview B. Application to soil quality C. Basics of statistical process control D. Examples of control charts III. Potential for Statistical Quality Control to Regulate Soil QuaHty IV. Conclusions References
203 204 204 206 207 209 216 217 218
I. INTRODUCTION The search is on for acceptable methods to quantify soil quality and its change in response to land management practices (Larson and Pierce, 1991, 1994; Acton and Gregorich, 1995; Hatfield and Stewart, 1993; Doran and Parkin, 1994). This chapter proposes methodology for soil quality control based on an analogy with the quaUty control of manufactured products using statistical quality control (SQC) concepts and procedures. It introduces the fundamental principles and concepts of SQC in an effort to provide a basis for applying these principles to the task of sustaining and improving the quality of soils. A thorough discussion of SQC is not given, because SQC procedures are described in other readily available sources (Montgomery, 1985; Ryan, 1989; ASTM, 1992). We recognize that other techniques are available to assess soil quahty, including procedures to analyze spatial and temporal variation in soils (Shumway, 1988; Isaaks and Srivastava, 1989; Webster and Oliver, 1990; Mausbach and Wilding, 1991); these are discussed by Wendroth et al. (this volume). Quality control involves both monitoring and control. Monitoring is the regular surveillance of the condition of something, whereas control means to influence or regulate. Monitoring keeps track of quality but it does not change it, whereas the main objective of SQC is to change quahty. It does this by controlling the processes that determine product quality, systematically reducing variabiHty in the characteristics that define a good-quality product so that it meets the specifications and tolerances of the design (Montgomery, 1985). Because one goal of sustainable land management should be to achieve good soil quahty, it is necessary to go beyond simply monitoring and to focus on quahty management. For the purpose of this discussion, soil quahty means fitness for use, analogous to product quahty in
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manufacturing (Pierce and Larson, 1993). The analogy between product quality and soil quality is practical, because it allows the use of an extensive set of techniques in the field of SQC (ibid.). Thus, soil quahty control involves the three major components of SQC: experimental design, process monitoring and control, and continuous improvement. In terms of SQC, soil quaUty can be described as follows: for a given land use, soil quahty will be sustained or improved if the management system is well designed relative to the intended goals (quahty of design) and if the components of the system conform to specifications and tolerances that the design requires (quality of conformance) (ibid.). II. THE CASE FOR STATISTICAL QUALITY CONTROL IN SOIL QUALITY The use of SQC for soil quality evaluation was first proposed by Pierce and Larson (1993) as a means of developing criteria to evaluate sustainable land management. They recognized that although natural resource assessment programs, such as the National Resources Inventory and the Environmental Monitoring and Assessment Program in the U.S. (Campbell et al., 1994) and the Soil Quality Evaluation Program in Canada (Acton and Padbury, 1993), use monitoring as the primary assessment tool, monitoring itself does nothing to affect the condition of the target resource. They concluded that ''monitoring soil quality does not affect land (soil) quality unless this information is used to identify and implement opportunities for improvement.'' In the field of SQC, experimental design and process control are used to build quahty into the process to the point that quality assurance sampling (monitoring) of the product is minimized (Pierce and Larson, 1993). The focus shifts from monitoring to a goal of quality control or quality improvement. Thus, soil quality control must include the design of management systems that do not degrade soil quality (i.e., are inherently sustainable) and the development of process-control procedures that ensure that the processes within the management systems conform to the specifications and tolerances of that design. Soil quality is exactly analogous to SQC and is intuitively appealing. Also, SQC places control primarily in the hands of the manager and the operator, who alone can effect change in the operation of the management system. Compare SQC to traditional monitoring programs, which are generally institutional, costly, and designed for a specific purpose under a limited budget and thus hmited in scope, and which produce data that are often difficult to interpret. Our discussion focuses on the components of process control. A list of pertinent symbols and abbreviations is given in Table 9.1. A. An overview Statistical quahty control is a method to help control processes. It uses simple control charts, produced by sampling a quahty parameter over time, to determine if a specific process operates within the range of "natural variation". Natural variation is the cumulative effect of many uncontrollable causes. In SQC, a process is
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TABLE 9.1 List of symbols and abbreviations used to describe statistical quality control Symbol/Abbreviation
Description mean of distribution standard deviation of distribution sample average (for subgroup i) sample standard deviation (for subgroup i) average of sample averages average of sample standard deviations count at time i average of counts constant mean of Poisson distribution Statistical Quality Control Statistical Process Control Average Run Length Upper Control Limit Lower Control Limit
G
X
's C\
c C4
X SQC SPC ARL UCL LCL
considered to be "in statistical control" if it operates within the range of natural variation and is considered to be "out of control" if other variations resulting from "specific causes" are present in the process. Sample means and standard deviations of a quahty control parameter are plotted over time on a control chart (Fig. 9.1). The upper control limit (UCL) and lower control limit (LCL) are set based on estimated
UCL
.-
1 H
c
o4
IX
CO
0)
-1 H LCL
UCL
Sample # Fig. 9.1 Mean, x, and standard deviation, 5, control charts for 30 subgroups {n — 4) from a set of 120 independent normally distributed random variables.
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F.J. PIERCE and D.C. GILLILAND
means and variances or are known through some other means (Pierce and Larson, 1993). Montgomery (1985) described the use of SQC in the product-manufacturing process. The design phase in product manufacturing determines the specifications and tolerances desired in the product and designs the manufacturing process that will produce that product. ''The manufacturing process transforms inputs into a finished product that has several parameters that describe its quality or fitness for use'' (Montgomery, 1985). Some of the inputs are controllable, others are not. The primary output is the product, but measures of process quahty can also be output as part of the manufacturing process. Designed experiments, in conjunction with regression and time series analysis techniques, are used to identify the key variables influencing the quality characteristics of interest in the product and to determine the levels of the controllable variables that optimize the process performance. These key variables are then monitored and the process inputs adjusted as required to bring the process back to an in-control state using models that determine the nature and magnitude of the adjustments required. In dealing with a process, the stabihty of the process should be of primary concern; generally, little can be done to improve or manipulate a process until it is brought into control. B. Application to soil quality In this discussion, soil quality is denoted as Q and defined functionally as a set of soil attributes, q^ (Larson and Pierce, 1991). It is desirable to precisely define Q since the quality of two or more soils can then be compared. If Q is quantifiable, then the change in Q over time is a measure of the change in soil quality in response to management or land use. However, Q cannot be precisely defined, but some subset of q^s can be used to develop an estimate of Q, called Q'. If we view some subset of q[S as key characteristics or attributes of soil quality and define soil quahty as fitness for use, then SQC concepts and procedures can be applied to soil quality control. There are several aspects of SQC that apply to soil quality control. The first deals with the use of control charts to monitor each ^j and assess if soil quality is stable in response to the current management system. This statistical process-control approach indicates only that the process is either in control or not but does not in itself indicate how to bring the process back to an in-control state. If the control chart indicates that special causes of variation are present, then they should be identified and removed (if possible) to bring the process into control. Problemsolving skills, intimate knowledge of the process, and the gathering of relevant information help in identifying special causes. A second aspect of SQC applicable to soil quahty control concerns the identification of key variables influencing each qi of interest through research on the fundamental mechanisms of the process. Research involving designed experiments and computer simulation models can contribute to this basic understanding. A third aspect is the charting of the key variables and their control and adjustment to make desired changes in the q^, which is analogous to the engineering control of a chemical process through the monitoring and adjustment of critical variables.
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In the next section, we present some basics of statistical process control with examples using simulated and real data. Of course, in a given application the nature and number of variables to monitor with control charts will be determined by the nature of the application, the level of technical skills available, funding and the monitoring time frame. Our focus is on variation and whether soil quality is stable in response to management; we do not discuss experimental design and engineering control. C. Basics of statistical process control Soil properties and processes vary over time and space. A single measurement or set of measurements at a given time and place may carry Httle information about a soil property or the processes affecting it. Only by measuring a property over time and space can its nature be understood. The charting of measurements is a standard tool in Statistical Process Control (SPC). Charts provide a history of measured aspects of the process. Charts show variation and sometimes trends and cycles as well. Processes that have erratic behavior are unpredictable; they are called unstable or out of control. Processes that have regular behavior are predictable (within limits); they are called stable or in control. Action rules applied to control charts can operationally define whether the process is in control or not. Statistical process control encompasses a large set of techniques and ideas for dealing with data that vary in time. One technique involves plotting of means and standard deviations of a quantitative variable over time. Typically, the measurements come in subgroups that are close (local) in time, and it is the means, Xi, and standard deviations, ^i, of the subgroups that are plotted. These statistics provide local estimates of the mean and standard deviation of the variable being driven by the process. The action rules that determine whether the process is in control or not are functions applied to the data in these charts. The general model for a control chart as given by Montgomery (1985) is repeated here using terminology relative to soil quaUty, as follows. Let q^ be a soil quaHty attribute of interest, and let the mean of q{ be /iqj and the standard deviation of q^ be o-qi. Then the center fine, the upper control limit (UCL) and the lower control limit (LCL) become: UCL = /Iqi + A:(Tqi
(1)
Center line = /iqj LCL = jUqi - A:(Tqi (2) where k is the "distance" of the control limits from the center Une, expressed in standard deviation units. These hmits are commonly used today and may be referred to as the Shewhart limits (Deming, 1986). Although the general form of the Shewhart control limits is as given above, the equations for the center line and the control limits depend on the type of data being
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generated and plotted, and on the estimates. For sample means, x, and standard deviations, s, of subgroups of n measurements on a continuous variable, the Shewhart control limits for k = 3 are: jc-chart: UCL=f+3^/(c4V«)
(3)
Center line = ^ LCL=^-3s/{c4y/n)
(4)
^-chart: UCL = s + 3^{l-cl){s/c4)
(5)
Center line = s LCL = s-3^{\-cl){s/c4)
.
(6)
where x is the average of the subgroup means Xj, 5 is the average of the subgroup standard deviations ^i, and C4 is a constant that depends on the sample size n and adjusts for bias (see Ryan, 1989, Chapter 5). For « = 4, C4 = 0.9213. The estimates x and s/c4 are, respectively, unbiased estimated of the mean, /i, and the standard deviation, a, of the process if the process variable is normally distributed and the subgroup measurements are random samples of size n from the distribution. The Poisson distribution, in which the mean and the variance are equal, often describes the distribution of count data. If counts Cj are charted, the Shewhart k = 3 limits take the form, c-chart: VCL = fi^3{y/c)
(7)
Center line = c LCL = c-3{y/c) . (8) For the ^-chart and c-chart, the quantities being charted (.^i and q) are non-negative. If the LCL is negative, then it is usually stated as zero, and the chart effectively has no lower control limit. In some applications, it may be desirable to control within a specific level, that is, to specify standard values for the mean and standard deviation of soil quaUty attributes or indicators and to use these standards to establish the control charts. In this case, fi and a are given, and the control limits of the x chart are UCL = /i-h3(T/v'«
(9)
Center hne — fi LCL = fi-3a/y/n
.
(10)
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The selection of standards is important in soil quality control, since standards in measurement and for control limits will assist in the detection of real change in soil quality. D. Examples of control charts 1. Example 1: Generated data for in-control process To illustrate the use of control charts, we generated a data set of 120 independent normally distributed random variables and placed them in 30 subgroups {n = A). Envision these 30 subgroups to represent samples of a soil quality parameter, ^i, taken over a period of time. These subgroups have a mean, x = 0.0646952, and an average standard deviation, ^ = 0.9848. The subgroup means and standard deviations were plotted in control charts (as per Fig. 9.1). The upper and lower control limits for the x-chart were 1.66805 and -1.53866, respectively, and were 2.2316 and 0.0, respectively, for the ^--chart. The control charts in Figure 9.1 indicate that the process is "in control", because the variation of both the mean and standard deviation of the subgroup samples are within the range expected (within the control limits), and there are no apparent trends in the data (i.e., the variation is random and not dependent on the process). The appearance of trends in a soil quality data set should be evaluated, as they can occur even though the data fall within the control limits and are important in exposing a change in the process or system. There are a number of tests or action rules available to identify trends in control charts. Some commonly used tests are given in Table 9.2. The data in Figure 9.1 were subjected to these tests, and neither the mean nor the standard deviation charts exhibited any detectable trends. In Example 1, the data were generated as a stable process and the action rules indicated that the process was in control. In using control charts, there is a danger of over-analysis in the search for out-ofcontrol indications. Assume that points 3 through 7 were examined as part of a soil quality evaluation study. It would appear from these data that both the mean and standard deviation were decHning over time. In examining only these data, there would likely be a strong inclination to conclude that the process was changing in a TABLE 9.2 Some action rules for Statistical Process Control charts Test #
Description
1 2 3 4
Any point beyond the control limits Runs above or below the center line longer than 8 Runs up or down of length 7 or greater Sets of 5 consecutive points with 4 beyond 1 standard deviation in the same direction Sets of 3 consecutive points with 2 beyond 2 standard deviations in the same direction
5
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significant manner and that an adjustment in the system was needed. This conclusion would of course be incorrect, given the full data set in Figure 9.1. Any action to adjust the system would be detrimental, because tampering with a stable system will often make the system less stable (Deming, 1986). Thus it is necessary to know how measured quality variables vary over time (and space), so that real changes and special causes are detected. It is also necessary to stay with predetermined action rules rather than to selectively inspect the data and make intuitive decisions on an ad hoc basis. 2. Example 2: Generated data for a shifted process To further illustrate the use of control charts, we generated a second data set of 400 normal random variables to create 100 subgroups (« = 4). The first 200 variables were generated from a normal distribution with a mean of 0 and a standard deviation of 1. The second 200 variables were generated from a normal distribution with a mean of 0.5 and a standard deviation of 1 to simulate a change in the system. These data are plotted in the control charts in Figure 9.2. Note that the standard deviation remains stable, as expected, since the population variance was not altered. The shift in the mean is visually evident soon after the data from the shifted distribution are encountered. However, the subgroup means fall within the control limits until sample 77 and remain within the control limits for the remaining samples. Two of the other tests in Table 9.2 for detecting trends did reveal the shift in the
UCL
X
LCL
oi"
'i^l^iMifl^i'^N^
0)
^
UCL
2
S
LCL
0
\ 0
r 20
"T
T"
40^J 60
T
80
100
120
Change
Sample # Fig. 9.2 Mean, x, and standard deviation, s, control charts for 100 subgroups (n = 4) from a set of 400 independent normally distributed random variables, with the first 200 variables generated from a normal distribution with a mean 0 and standard deviation 1 and the second 200 variables from a normal distribution with a mean 0.5 and standard deviation 1.
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mean, but not until sample 77. Thus, a shift in the process was not detected for some time after the change had occurred. In SPC, the expected or average run length (ARL) until an action rule signals an out-of-control situation is a measure of the power of a rule to detect the change. Rules based on accumulated deviations from the center Hne in one direction or the other are known to have smaller ALRs than Action Rule 1 (Table 9.2) in the presence of small shifts of mean (see Ryan, 1989, Chapter 5). Of course, a shift would be detected much earlier by rules 1, 4, and 5 if the control limits were reduced. Thus, questions as to what should be the control limits relate in part to the level of change that must be detected and the cost of responding to false positives. In some cases, this change in the mean may be inconsequential and of limited importance to the quahty goals of the design, while in others, a change of this magnitude is important and must be detected early. Thus, standards for soil quality evaluation are critical to both the monitoring and interpretation of soil quaUty parameters. 3. Example 3: Generated data for a shifted count process Soil attributes manifest a number of variance structures in addition to the normal distribution. Count or enumeration data, such as worm counts, follow the Poisson distribution. Rates, such as hydrauUc conductivity, are often best described as lognormal. Example 3 has been chosen to illustrate the c-chart of count data. We generated a count data set consisting of 30 independent Poisson (mean 2 = 1 0 ) variates. These data have a mean c = 8.76667 and a standard deviation = 2.96086 and are plotted in the control chart in Figure 9.3a. The control limits were determined as UCL = 17.6492 and LCL = 0. All data points plot within the control chart, but when subjected to Rule 4 for charting (Table 9.2), a signal occurs at point 15, the end point of a set of five counts with four points beyond one standard deviation. This is a "false positive" in this example, since we know from the method of data generation that the process is "in control". We generated a second set of count data consisting of 100 independent Poisson variates, the first 50 generated from a Poisson A = 10 and the second 50 from Poisson X = 20. These data are plotted in the control chart in Figure 9.3b using the mean and control limits from Figure 9.3a. For the first 50 data points, the process is "in control" by design. However, a "false positive" is present in data-point 43 since it is beyond the upper control limit. For the second 50 points, the process is "out of control" as, by design, there is a shift in the mean. The first empirical indication of the shift is found in point 53, which is beyond the upper control limit. Additionally, a number of run-tests (Table 9.2) were significant soon after the shift. Thus, the control chart clearly detected the shift in the mean soon after the shift occurred. The operating characteristics of the rules in Table 9.2 are somewhat diff'erent for ccharts than for x-charts. The Poisson distribution is not symmetric, and the tail probabilities are different from those of the normal distribution. For the Poisson distribution with mean A = 10, the lower 3-sigma tail has a probability of 0.000045, the lower 2-sigma tail has a probabihty of 0.0103, and the lower 1-sigma tail has a probability of 0.1301. The corresponding upper tail probabilities are 0.0035, 0.0270, and 0.1355. For the normal distribution they are 0.00135, 0.0228, and 0.1587. The
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UCL
LCL
Sample # UCL
3 O
O LCL
Sample # Fig. 9.3 Control charts of (a) count data for 30 independent variables from a Poisson A = 10 and (b) for 100 independent variables, the first 50 from a Poisson A = 10 and the second 50 from a Poisson X = 20.
probability of falling below the mean for the Poisson (A = 10) is 0.4579 compared to 0.5000 for the normal distribution. Ryan (1989, Chapter 5) discusses the use of probability-based control limits as alternatives to the Shewhart limits when charting. 4. Example 4: Real data for a count process We monitored seed drop from each of six planter units on a John Deere 7200 corn planter using a standard seed monitoring unit connected to a data logger (Pierce, unpubHshed data). A number of variables were monitored in alternating seconds for six passes of the corn planter, including the total number of skips per second across all six planter units. A skip was defined as the failure of a seed to drop within a time tolerance corresponding to the desired seed spacing (calculated from seed drop per unit time and speed). The counts of the number of skips per second in the first three passes are plotted in Figure 9.4a (299 measurements). The average count is c = 5.27 with the UCL = 12.16 and the LCL = 0. The action rules of Table 9.2 indicate out of control at time 223, which concludes a run of nine counts above the center line (6, 8, 7, 7, 7, 8, 7, 9). This is not, however, an indication of a serious departure from control for this application. The c-chart control limits above were used as standards for the remaining three passes of the corn planter plotted in Figure 9.4b. The Shewhart 3-sigma UCL was exceeded at times 337, 341, 342, 347, 380, and 403, which concludes a run of 9, 10, 4, 10, 11. Action Rule 5 produces signals at counts 342, 343, 344, 371, 372, and 373. Thus, there is a strong indication that in the fourth pass, the corn planter was out of
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O
UCL
a o o
4) CO
*>*
LCL
CO
e«
50
3 xn
100
150
200
250
300
350
Time (seconds)
I o
UCL
-l
250
300
350
1
1
400
450
• I
500
1
550
•!
600
tLCL
650
Time (seconds) Fig. 9.4 C-control charts of (a) measurements of seed drop skips per second obtained from three passes of a six-row corn planter and (b) for a second set of three passes of the same corn planter (Pierce, unpublished data). Control limits in (a) were calculated from the count data and used in (b) to evaluate system stability.
control for the period from count 337 through count 347 and again in the period from time 371 through time 380. The signal at count 403 comes from the number of skips, 13, exceeding the UCL 12.16. These out-of-control periods should be investigated for special causes of variation within the planter units so as to adjust the planter units to an in-control condition. 5. Example 5: Real data on soil bulk density This example illustrates the use of control charts to monitor selected soil quaUty parameters. Larson and Pierce (1991) proposed the use of a minimum data set (MDS) of soil attributes to monitor soil quaUty. The emphasis is to assess whether soil quality is changing and how it is changing (recall that monitoring does not affect soil quahty). Bulk density has been proposed as one component of a soil quahty MDS (Larson and Pierce, 1991; Doran and Parkin, 1994), and we will use it to illustrate the use of control charts for monitoring soil quality. Figure 9.5 presents x\ and Si control charts for the bulk density measurements of 20 subgroups {n = 5) obtained from the 0 to 8 cm depth of a fine sandy loam soil in
214
F J . PIERCE and D.C. GILLILAND 1.6 1.5 -I
. No-tillage. UCL
1.4 4 ix"
1.3-^ 1.2 -I 1.1
LCL
UCL
E
LCL Pbw
1.5 A 3 CQ IK"
Plowed
1.4 J 1.3 A
UCL X
1.2 -] 1.1
LCL UCL
0.16 A ^' 0.10 -j
jf-^
0.05 -f 0.00 200
400
600
800
1000
LCL
1200
Time (days) Fig. 9.5 Mean, x\, and standard deviation, 5,, control charts for surface bulk density measurements for a fine sandy loam soil in Prince Edward Island, Canada managed under (a) no-tillage and (b) moldboard plowing (from Carter, 1988, 1995).
Prince Edward Island, Canada, for no-tillage and moldboard-plowed experimental treatments (Carter, 1988; 1995). The bulk density measurements were obtained over a three-year period, 1 June, 1983 to 6 May, 1986. For no-tillage, x\ was generally stable, ranging from 1.32 to 1.46 Mg m"^ and a ^ = 1.39 Mgm"^, with no apparent special causes of variation, i.e., all x\ falling within the control limits determined from the data (Fig. 9.5a). The S[ for bulk density under no-tillage was quite variable, ranging from 0.01 to 0.11 Mg m~^. None of the St values plotted outside the control limits, but the pattern in ^i was rather cyclic, with lower ^i occurring in the fall months than in the spring and early summer. Bulk density in the plowed soil was lower (1=: 1.27Mgm~^) and more variable (1.14 to 1.35 Mg m~^) than under notillage, with broader control limits. This would be expected in response to disturbance by tillage and reconsolidation. The ^i for bulk density under plowing was similar to no-tillage in mean, range, and cyclic pattern of temporal variation. The bulk density created under each tillage system was different, but the higher bulk density under no-tillage was not necessarily indicative of soil degradation. The fact that bulk density under no-tillage was stable over time indicates that some sort of
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equilibrium level of bulk density is reached under no-tillage, and that this level is predictable within limits. In some cases, therefore, it may not be reasonable to apply the control limits of a soil quaUty parameter under one management system to limits created under another system if system dynamics are quite different, as they are in no-tillage. Interestingly, if the control limits of the plowed soil are applied to the notillage soil, only one point, the bulk density at day 81, plots outside the control limits. On the other hand, since the LCL under no-tillage is near the mean for plowed soil, bulk densities under plowing below the mean exceed the LCL under no-tillage. This phenomenon appears to hold for other bulk density data sets. Control charts of the means Xi and standard deviations Si of bulk density measurements for 15 subgroup (n = 3) obtained over the period from April 1987 to April 1989 from the 0 to 7.6 cm depth of a soil formed in glacial outwash in south central Michigan (data from a single experimental plot; Reinert and Pierce, unpublished data) are given in Figure 9.6. Like data from P.E.L, bulk density under no-tillage is stable
1.7 1.6 H 1.5 1 1.4 1.3
. NortUlage
^^V
^
UCL
X
"^i^
LCL
0.10 H UCL
E LCL
C 0)
o
1.7 1.6 H 1.5 1.4 1.3
Plowed UCL
X LCL
0.10 H 0.05 H 0.00
UCL
^v•v^A T
0
1
r
LCL
100 200 300 400 500 600 700 800 900 Time (Days)
Fig. 9.6 Mean, Xi, and standard deviation, Si, control charts for soil bulk density measured from single experimental plots from a sandy loam soil in south central Michigan, U.S.A. managed under (a) no-tillage and (b) moldboard plowing (Reinert and Pierce, unpubUshed data).
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F.J. PIERCE and D.C. GILLILAND
(x = 1.53 Mgm~^), but the ^i is not as variable nor as cyclic (Fig. 9.6a). Under plowing, the bulk density is highly variable, with a lower mean value (f = 1.37 Mgm~^) than under no-tillage (Fig. 9.6b). The ^-i under plowing is similar to that under no-tillage and not subject to the wide variation as xi. There are six points outside the control limits on the x-chart for bulk density under plowing (Fig. 9.6b), whereas none of the P.E.I, data (Fig. 9.5b) plot outside the control limits. The control charts in Figures 9.5 and 9.6, however, demonstrate the value of charting soil quahty variables and clearly point out the need for repeated measures to assess the dynamics of soil quality. It is important to evaluate intrinsic cycles and trends associated with the spatial and temporal variability of a property, and these can be identified with the control charts (Montgomery, 1985; Ryan, 1989). As indicated earlier, a single measurement in space and time is difficult to evaluate. Using traditional SPC charts alone can be of questionable value. A proper analysis of bulk density and its variability over growing seasons should include estimates for cyclic components. Then charts should be made for the adjusted time series or for the separate periods of the growing seasons. Clearly, there are not enough data here to support such analyses. III. USING STATISTICAL QUALITY CONTROL TO REGULATE SOIL QUALITY There are two applications of SQC to soil quality. One is its use in monitoring programs where a set of soil attributes, a soil quality MDS, is charted over time. The control limits for each quality parameter would be based on the charted values or on values determined by experts or from previous experiments. The goal, for example, could be to maintain or enhance soil organic matter content at some level (in control). We envision that each parameter constituting a soil quahty MDS would be charted independently, as in Figures 9.5 and 9.6, with appropriate rules (e.g.. Table 9.2) or tests applied to the interpretation of each chart. Each parameter's control chart would be interpreted separately or in light of information on other parameters, because each chart provides different but possible correlated information about the state of soil quality. This procedure would allow a simple, easy-to-use, yet quantitative evaluation of the impact of a particular land use or soil management practice on soil quality. The problem is that, although these charts may detect a change in soil quality, it tells nothing about the process that created the change. The other, perhaps more important, application of SQC lies in the process-control domain of soil quality, which is generally called engineering control (e.g., example 4). In this application, the goal is still soil quality, but the approach focuses on the process that regulates quality rather than simply monitoring a set of soil quality parameters. Consider soil organic matter, but this time think in terms of the processes that regulate organic matter content in soil. Recall that SQC involves design and process control as major components. Thus, the first matter of concern is whether or not the design of the management practice can even produce the desired level of organic matter. If the design is wrong, the desired output can never be achieved. If the system design is correct, then the important questions relate to
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whether operational components of the system are working within the design specifications and tolerances. If the processes that create the outcome are not in control, then the desired output may not be achieved. In SQC, if the design is correct and the manufacturing process is stable (in control), then the quality of the product is good. Thus, for a properly designed management system, the key to good soil quaUty is process control. The objective of engineering control is to identify the key variables controlUng the process and to chart those variables as in Figure 9.1. In the case of soil organic matter, the key variables relate to the amount and quahty of organic matter returned to the soil, the rate and degree of decomposition, and the amount lost by erosion or gained by deposition. Some set of these variables would be chosen to be monitored over time and space. Further, some control limits would be selected that, if the process was in control, would achieve the desired soil organic matter content. If the control charts for these key variables are out of control, then the process would be adjusted according to design criteria. In another example, the goal might be to achieve a specific amount of crop cover or crop residue cover on the soil surface after tillage. The key control variables would Hkely be associated with the tillage tool components that regulate how much crop residue is buried (e.g., operating depth, speed, implement angle or number). As posed by Pierce and Larson (1993), simply informing the farmer after planting that crop residue cover on the field doesn't meet erosion control guidelines is too late to affect the process that created that condition. Adequate residue cover could be achieved if the key variables were charted and adjustments were made to bring the process back into control during the tillage operation (as in the seeding rate. Example 4). An important aspect of this approach is that it places the responsibihty for soil quality in the hands of the land manager, which is the only way to really cause a change in soil quality. It may seem that system design and engineering control are not practical in agricultural management systems. However, emerging technologies associated with site-specific management and precision agriculture are, in fact, capable of achieving this level of design and control. Technologies include very accurate location control (e.g., global positioning systems, GPS), variable rate application equipment, and sensors for both control and performance evaluation (e.g., yield sensors). These technologies are now readily available (Larson and Robert, 1991; Schueller, 1992; Robert et al., 1993, 1995). The potential for real-time control is rapidly emerging and may be the best means of achieving good soil quality. While monitoring will continue to be a focus in soil quality assessment, it is soil quality control that will affect the soil resource base. IV. CONCLUSIONS The analogy of soil quality control to quaUty control in product manufacturing is presented as a model to achieve soil quahty. The analogy is not perfect, but the use of SQC is intuitively appealing given the goals of sustained or improved soil quality. This chapter merely introduces the topic and the concepts involve in SQC. As SQC is
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applied to soil quality, considerable refinement of the concepts and procedures in SQC to this application will emerge.
REFERENCES Acton, D.F. and Gregorich, L.J. 1995, eds. The health of our soils—toward sustainable agriculture in Canada. Centre for Land and Biological Resources Research, Research Branch, Agriculture and Agri-Food Canada, Ottawa, Ont., Canada. Acton, D.F. and Padbury, G.A. 1993. A conceptual framework for soil quality assessment and monitoring. Pages 2-1-2-10 in D.F. Action, ed. A program to assess and monitor soil quality in Canada: soil quality evaluation program summary. Research Branch, Agriculture Canada, Ottawa, Ont., Canada. American Association of Testing Materials (ASTM). 1992. Manual on presentation of data and control chart analysis, 6th ed. ASTM Manual Series MNL 7. ASTM, Philadelphia, Penn., U.S.A. Carter, M.R. 1988. Temporal variability of soil macroporosity in a fine sandy loam under mouldboard ploughing and direct drilling. Soil Till. Res. 12:37-51. Carter, M.R. 1995. Spatial variability of soil porosity under reduced tillage in a Humo-Ferric Podzol. Can. J. Soil Sci. 75:149-152. Campbell, C.L., Bay, J., Franks, C.C, Hallkamp, A.S., Helzer, N.P., Munster, M.J., Heher, D., Olson, G.L., Peck, S.L., Rawlings, J.O., Schumacher, B. and Tooley, M.B. 1994. Environmental monitoring and assessment program—Agroecosystem Pilot Field Program Plan, 1993. EPA/620/R-93/014. U.S. Environmental Protection Agency, Washington, D . C , U.S.A. Deming, W.E. 1986. Out of the crisis. Center for Advanced Study, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A. Doran, J.W. and Parkin, T.B. 1994. Defining and assessing soil quality. Pages 3-21 in J.W. Doran, D.C. Coleman, D.F. Bezdicek, and B.A. Stewart, eds. Defining soil quality for a sustainable environment. Special Pub. 35, Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Hatfield, J.L. and Stewart, B.A., eds. 1993. Soil biology: effects on soil quality. Lewis Publ., Ann Arbor, Mich., U.S.A. Isaaks, E.H. and Srivastava, R.M. 1989. Applied geostatistics. Oxford University Press, New York, N.Y., U.S.A. Larson, W.E. and Pierce, F.J. 1991. Conservation and enhancement of soil quality. Pages 175203 in Evaluation for sustainable land management in the developing world, Vol. 2: Technical Papers. International Board for Soil Research and Management Proc. 12(2). Bangkok, Thailand. Larson, W.E. and Pierce, F.J. 1994. The dynamics of soil quality as a measure of sustainable management. Pages 37-51 in J.W. Doran, D.C. Coleman, D.F. Bezdicek, and B.A. Stewart, eds. Defining soil quality for a sustainable environment. Special Pub. 35, Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Larson, W.E. and Robert, P.C. 1991. Farming by soil. Pages 103-112 in R. Lai and F.J. Pierce, eds. Soil management for sustainability. Soil Water Conserv. Soc, Ankeny, Iowa, U.S.A. Mausbach, M.J. and Wilding, L.P., eds. 1991. Spatial variabilities of soils and landforms. Special Pub. 28. Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Montgomery, D.C. 1985. Introduction to statistical quahty control. John Wiley and Sons, New York, N.Y., U.S.A.
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Pierce, F.J. and Larson, W.E. 1993. Developing criteria to evaluate sustainable land management. Pages 7-14 in J.M. Kimble, ed. Proceedings of the Eighth International Soil Management Workshop: Utilization of Soil Survey Information for Sustainable Land Use, May 3, 1993. USDA Soil Conservation Service, National Soil Survey Center. Robert, P.C, Rust, R.H. and Larson, W.E., eds. 1993. Proceedings of soil specific crop management: A workshop on research and development issues. Am. Soc. Agron., Crop Sci. Soc. Am., and Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Robert, P.C, Rust, R.H. and Larson, W.E., eds. 1995. Proceedings of site-specific management for agricultural systems. Second International Conference. Am. Soc. Agron., Crop Sci. Soc. Am., and Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Ryan, T.P. 1989. Statistical methods for quality control. John Wiley and Sons, New York, N.Y., U.S.A. Schueller, J.K. 1992. A review and integrating analysis of spatially-variable control of crop production. Pert. Res. 33:1-34. Shumway, R.H. 1988. AppHed statistical time series analysis. Prentice Hall, Englewood CUffs, N.J., U.S.A. Webster, R. and Oliver, M.A. 1990. Statistical methods in soil and land resource survey. Oxford University Press, New York, N.Y., U.S.A.
SOIL QUALITY CONTROL F.J. PIERCE and D.C. GILLILAND
I. Introduction II. The Case for Statistical Quality Control in Soil Quality A. An overview B. Application to soil quality C. Basics of statistical process control D. Examples of control charts III. Potential for Statistical Quality Control to Regulate Soil QuaHty IV. Conclusions References
203 204 204 206 207 209 216 217 218
I. INTRODUCTION The search is on for acceptable methods to quantify soil quality and its change in response to land management practices (Larson and Pierce, 1991, 1994; Acton and Gregorich, 1995; Hatfield and Stewart, 1993; Doran and Parkin, 1994). This chapter proposes methodology for soil quality control based on an analogy with the quaUty control of manufactured products using statistical quality control (SQC) concepts and procedures. It introduces the fundamental principles and concepts of SQC in an effort to provide a basis for applying these principles to the task of sustaining and improving the quality of soils. A thorough discussion of SQC is not given, because SQC procedures are described in other readily available sources (Montgomery, 1985; Ryan, 1989; ASTM, 1992). We recognize that other techniques are available to assess soil quahty, including procedures to analyze spatial and temporal variation in soils (Shumway, 1988; Isaaks and Srivastava, 1989; Webster and Oliver, 1990; Mausbach and Wilding, 1991); these are discussed by Wendroth et al. (this volume). Quality control involves both monitoring and control. Monitoring is the regular surveillance of the condition of something, whereas control means to influence or regulate. Monitoring keeps track of quality but it does not change it, whereas the main objective of SQC is to change quahty. It does this by controlling the processes that determine product quality, systematically reducing variabiHty in the characteristics that define a good-quality product so that it meets the specifications and tolerances of the design (Montgomery, 1985). Because one goal of sustainable land management should be to achieve good soil quahty, it is necessary to go beyond simply monitoring and to focus on quahty management. For the purpose of this discussion, soil quahty means fitness for use, analogous to product quahty in
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manufacturing (Pierce and Larson, 1993). The analogy between product quality and soil quality is practical, because it allows the use of an extensive set of techniques in the field of SQC (ibid.). Thus, soil quahty control involves the three major components of SQC: experimental design, process monitoring and control, and continuous improvement. In terms of SQC, soil quaUty can be described as follows: for a given land use, soil quahty will be sustained or improved if the management system is well designed relative to the intended goals (quahty of design) and if the components of the system conform to specifications and tolerances that the design requires (quality of conformance) (ibid.). II. THE CASE FOR STATISTICAL QUALITY CONTROL IN SOIL QUALITY The use of SQC for soil quality evaluation was first proposed by Pierce and Larson (1993) as a means of developing criteria to evaluate sustainable land management. They recognized that although natural resource assessment programs, such as the National Resources Inventory and the Environmental Monitoring and Assessment Program in the U.S. (Campbell et al., 1994) and the Soil Quality Evaluation Program in Canada (Acton and Padbury, 1993), use monitoring as the primary assessment tool, monitoring itself does nothing to affect the condition of the target resource. They concluded that ''monitoring soil quality does not affect land (soil) quality unless this information is used to identify and implement opportunities for improvement.'' In the field of SQC, experimental design and process control are used to build quahty into the process to the point that quality assurance sampling (monitoring) of the product is minimized (Pierce and Larson, 1993). The focus shifts from monitoring to a goal of quality control or quality improvement. Thus, soil quality control must include the design of management systems that do not degrade soil quality (i.e., are inherently sustainable) and the development of process-control procedures that ensure that the processes within the management systems conform to the specifications and tolerances of that design. Soil quality is exactly analogous to SQC and is intuitively appealing. Also, SQC places control primarily in the hands of the manager and the operator, who alone can effect change in the operation of the management system. Compare SQC to traditional monitoring programs, which are generally institutional, costly, and designed for a specific purpose under a limited budget and thus hmited in scope, and which produce data that are often difficult to interpret. Our discussion focuses on the components of process control. A list of pertinent symbols and abbreviations is given in Table 9.1. A. An overview Statistical quahty control is a method to help control processes. It uses simple control charts, produced by sampling a quahty parameter over time, to determine if a specific process operates within the range of "natural variation". Natural variation is the cumulative effect of many uncontrollable causes. In SQC, a process is
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TABLE 9.1 List of symbols and abbreviations used to describe statistical quality control Symbol/Abbreviation
Description mean of distribution standard deviation of distribution sample average (for subgroup i) sample standard deviation (for subgroup i) average of sample averages average of sample standard deviations count at time i average of counts constant mean of Poisson distribution Statistical Quality Control Statistical Process Control Average Run Length Upper Control Limit Lower Control Limit
G
X
's C\
c C4
X SQC SPC ARL UCL LCL
considered to be "in statistical control" if it operates within the range of natural variation and is considered to be "out of control" if other variations resulting from "specific causes" are present in the process. Sample means and standard deviations of a quahty control parameter are plotted over time on a control chart (Fig. 9.1). The upper control limit (UCL) and lower control limit (LCL) are set based on estimated
UCL
.-
1 H
c
o4
IX
CO
0)
-1 H LCL
UCL
Sample # Fig. 9.1 Mean, x, and standard deviation, 5, control charts for 30 subgroups {n — 4) from a set of 120 independent normally distributed random variables.
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means and variances or are known through some other means (Pierce and Larson, 1993). Montgomery (1985) described the use of SQC in the product-manufacturing process. The design phase in product manufacturing determines the specifications and tolerances desired in the product and designs the manufacturing process that will produce that product. ''The manufacturing process transforms inputs into a finished product that has several parameters that describe its quality or fitness for use'' (Montgomery, 1985). Some of the inputs are controllable, others are not. The primary output is the product, but measures of process quahty can also be output as part of the manufacturing process. Designed experiments, in conjunction with regression and time series analysis techniques, are used to identify the key variables influencing the quality characteristics of interest in the product and to determine the levels of the controllable variables that optimize the process performance. These key variables are then monitored and the process inputs adjusted as required to bring the process back to an in-control state using models that determine the nature and magnitude of the adjustments required. In dealing with a process, the stabihty of the process should be of primary concern; generally, little can be done to improve or manipulate a process until it is brought into control. B. Application to soil quality In this discussion, soil quality is denoted as Q and defined functionally as a set of soil attributes, q^ (Larson and Pierce, 1991). It is desirable to precisely define Q since the quality of two or more soils can then be compared. If Q is quantifiable, then the change in Q over time is a measure of the change in soil quality in response to management or land use. However, Q cannot be precisely defined, but some subset of q^s can be used to develop an estimate of Q, called Q'. If we view some subset of q[S as key characteristics or attributes of soil quality and define soil quahty as fitness for use, then SQC concepts and procedures can be applied to soil quality control. There are several aspects of SQC that apply to soil quality control. The first deals with the use of control charts to monitor each ^j and assess if soil quality is stable in response to the current management system. This statistical process-control approach indicates only that the process is either in control or not but does not in itself indicate how to bring the process back to an in-control state. If the control chart indicates that special causes of variation are present, then they should be identified and removed (if possible) to bring the process into control. Problemsolving skills, intimate knowledge of the process, and the gathering of relevant information help in identifying special causes. A second aspect of SQC applicable to soil quahty control concerns the identification of key variables influencing each qi of interest through research on the fundamental mechanisms of the process. Research involving designed experiments and computer simulation models can contribute to this basic understanding. A third aspect is the charting of the key variables and their control and adjustment to make desired changes in the q^, which is analogous to the engineering control of a chemical process through the monitoring and adjustment of critical variables.
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In the next section, we present some basics of statistical process control with examples using simulated and real data. Of course, in a given application the nature and number of variables to monitor with control charts will be determined by the nature of the application, the level of technical skills available, funding and the monitoring time frame. Our focus is on variation and whether soil quality is stable in response to management; we do not discuss experimental design and engineering control. C. Basics of statistical process control Soil properties and processes vary over time and space. A single measurement or set of measurements at a given time and place may carry Httle information about a soil property or the processes affecting it. Only by measuring a property over time and space can its nature be understood. The charting of measurements is a standard tool in Statistical Process Control (SPC). Charts provide a history of measured aspects of the process. Charts show variation and sometimes trends and cycles as well. Processes that have erratic behavior are unpredictable; they are called unstable or out of control. Processes that have regular behavior are predictable (within limits); they are called stable or in control. Action rules applied to control charts can operationally define whether the process is in control or not. Statistical process control encompasses a large set of techniques and ideas for dealing with data that vary in time. One technique involves plotting of means and standard deviations of a quantitative variable over time. Typically, the measurements come in subgroups that are close (local) in time, and it is the means, Xi, and standard deviations, ^i, of the subgroups that are plotted. These statistics provide local estimates of the mean and standard deviation of the variable being driven by the process. The action rules that determine whether the process is in control or not are functions applied to the data in these charts. The general model for a control chart as given by Montgomery (1985) is repeated here using terminology relative to soil quaUty, as follows. Let q^ be a soil quaHty attribute of interest, and let the mean of q{ be /iqj and the standard deviation of q^ be o-qi. Then the center fine, the upper control limit (UCL) and the lower control limit (LCL) become: UCL = /Iqi + A:(Tqi
(1)
Center line = /iqj LCL = jUqi - A:(Tqi (2) where k is the "distance" of the control limits from the center Une, expressed in standard deviation units. These hmits are commonly used today and may be referred to as the Shewhart limits (Deming, 1986). Although the general form of the Shewhart control limits is as given above, the equations for the center line and the control limits depend on the type of data being
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generated and plotted, and on the estimates. For sample means, x, and standard deviations, s, of subgroups of n measurements on a continuous variable, the Shewhart control limits for k = 3 are: jc-chart: UCL=f+3^/(c4V«)
(3)
Center line = ^ LCL=^-3s/{c4y/n)
(4)
^-chart: UCL = s + 3^{l-cl){s/c4)
(5)
Center line = s LCL = s-3^{\-cl){s/c4)
.
(6)
where x is the average of the subgroup means Xj, 5 is the average of the subgroup standard deviations ^i, and C4 is a constant that depends on the sample size n and adjusts for bias (see Ryan, 1989, Chapter 5). For « = 4, C4 = 0.9213. The estimates x and s/c4 are, respectively, unbiased estimated of the mean, /i, and the standard deviation, a, of the process if the process variable is normally distributed and the subgroup measurements are random samples of size n from the distribution. The Poisson distribution, in which the mean and the variance are equal, often describes the distribution of count data. If counts Cj are charted, the Shewhart k = 3 limits take the form, c-chart: VCL = fi^3{y/c)
(7)
Center line = c LCL = c-3{y/c) . (8) For the ^-chart and c-chart, the quantities being charted (.^i and q) are non-negative. If the LCL is negative, then it is usually stated as zero, and the chart effectively has no lower control limit. In some applications, it may be desirable to control within a specific level, that is, to specify standard values for the mean and standard deviation of soil quaUty attributes or indicators and to use these standards to establish the control charts. In this case, fi and a are given, and the control limits of the x chart are UCL = /i-h3(T/v'«
(9)
Center hne — fi LCL = fi-3a/y/n
.
(10)
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The selection of standards is important in soil quality control, since standards in measurement and for control limits will assist in the detection of real change in soil quality. D. Examples of control charts 1. Example 1: Generated data for in-control process To illustrate the use of control charts, we generated a data set of 120 independent normally distributed random variables and placed them in 30 subgroups {n = A). Envision these 30 subgroups to represent samples of a soil quality parameter, ^i, taken over a period of time. These subgroups have a mean, x = 0.0646952, and an average standard deviation, ^ = 0.9848. The subgroup means and standard deviations were plotted in control charts (as per Fig. 9.1). The upper and lower control limits for the x-chart were 1.66805 and -1.53866, respectively, and were 2.2316 and 0.0, respectively, for the ^--chart. The control charts in Figure 9.1 indicate that the process is "in control", because the variation of both the mean and standard deviation of the subgroup samples are within the range expected (within the control limits), and there are no apparent trends in the data (i.e., the variation is random and not dependent on the process). The appearance of trends in a soil quality data set should be evaluated, as they can occur even though the data fall within the control limits and are important in exposing a change in the process or system. There are a number of tests or action rules available to identify trends in control charts. Some commonly used tests are given in Table 9.2. The data in Figure 9.1 were subjected to these tests, and neither the mean nor the standard deviation charts exhibited any detectable trends. In Example 1, the data were generated as a stable process and the action rules indicated that the process was in control. In using control charts, there is a danger of over-analysis in the search for out-ofcontrol indications. Assume that points 3 through 7 were examined as part of a soil quality evaluation study. It would appear from these data that both the mean and standard deviation were decHning over time. In examining only these data, there would likely be a strong inclination to conclude that the process was changing in a TABLE 9.2 Some action rules for Statistical Process Control charts Test #
Description
1 2 3 4
Any point beyond the control limits Runs above or below the center line longer than 8 Runs up or down of length 7 or greater Sets of 5 consecutive points with 4 beyond 1 standard deviation in the same direction Sets of 3 consecutive points with 2 beyond 2 standard deviations in the same direction
5
F.J. PIERCE and D.C. GILLILAND
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significant manner and that an adjustment in the system was needed. This conclusion would of course be incorrect, given the full data set in Figure 9.1. Any action to adjust the system would be detrimental, because tampering with a stable system will often make the system less stable (Deming, 1986). Thus it is necessary to know how measured quality variables vary over time (and space), so that real changes and special causes are detected. It is also necessary to stay with predetermined action rules rather than to selectively inspect the data and make intuitive decisions on an ad hoc basis. 2. Example 2: Generated data for a shifted process To further illustrate the use of control charts, we generated a second data set of 400 normal random variables to create 100 subgroups (« = 4). The first 200 variables were generated from a normal distribution with a mean of 0 and a standard deviation of 1. The second 200 variables were generated from a normal distribution with a mean of 0.5 and a standard deviation of 1 to simulate a change in the system. These data are plotted in the control charts in Figure 9.2. Note that the standard deviation remains stable, as expected, since the population variance was not altered. The shift in the mean is visually evident soon after the data from the shifted distribution are encountered. However, the subgroup means fall within the control limits until sample 77 and remain within the control limits for the remaining samples. Two of the other tests in Table 9.2 for detecting trends did reveal the shift in the
UCL
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LCL
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0)
^
UCL
2
S
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0
\ 0
r 20
"T
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40^J 60
T
80
100
120
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Sample # Fig. 9.2 Mean, x, and standard deviation, s, control charts for 100 subgroups (n = 4) from a set of 400 independent normally distributed random variables, with the first 200 variables generated from a normal distribution with a mean 0 and standard deviation 1 and the second 200 variables from a normal distribution with a mean 0.5 and standard deviation 1.
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mean, but not until sample 77. Thus, a shift in the process was not detected for some time after the change had occurred. In SPC, the expected or average run length (ARL) until an action rule signals an out-of-control situation is a measure of the power of a rule to detect the change. Rules based on accumulated deviations from the center Hne in one direction or the other are known to have smaller ALRs than Action Rule 1 (Table 9.2) in the presence of small shifts of mean (see Ryan, 1989, Chapter 5). Of course, a shift would be detected much earlier by rules 1, 4, and 5 if the control limits were reduced. Thus, questions as to what should be the control limits relate in part to the level of change that must be detected and the cost of responding to false positives. In some cases, this change in the mean may be inconsequential and of limited importance to the quahty goals of the design, while in others, a change of this magnitude is important and must be detected early. Thus, standards for soil quality evaluation are critical to both the monitoring and interpretation of soil quaUty parameters. 3. Example 3: Generated data for a shifted count process Soil attributes manifest a number of variance structures in addition to the normal distribution. Count or enumeration data, such as worm counts, follow the Poisson distribution. Rates, such as hydrauUc conductivity, are often best described as lognormal. Example 3 has been chosen to illustrate the c-chart of count data. We generated a count data set consisting of 30 independent Poisson (mean 2 = 1 0 ) variates. These data have a mean c = 8.76667 and a standard deviation = 2.96086 and are plotted in the control chart in Figure 9.3a. The control limits were determined as UCL = 17.6492 and LCL = 0. All data points plot within the control chart, but when subjected to Rule 4 for charting (Table 9.2), a signal occurs at point 15, the end point of a set of five counts with four points beyond one standard deviation. This is a "false positive" in this example, since we know from the method of data generation that the process is "in control". We generated a second set of count data consisting of 100 independent Poisson variates, the first 50 generated from a Poisson A = 10 and the second 50 from Poisson X = 20. These data are plotted in the control chart in Figure 9.3b using the mean and control limits from Figure 9.3a. For the first 50 data points, the process is "in control" by design. However, a "false positive" is present in data-point 43 since it is beyond the upper control limit. For the second 50 points, the process is "out of control" as, by design, there is a shift in the mean. The first empirical indication of the shift is found in point 53, which is beyond the upper control limit. Additionally, a number of run-tests (Table 9.2) were significant soon after the shift. Thus, the control chart clearly detected the shift in the mean soon after the shift occurred. The operating characteristics of the rules in Table 9.2 are somewhat diff'erent for ccharts than for x-charts. The Poisson distribution is not symmetric, and the tail probabilities are different from those of the normal distribution. For the Poisson distribution with mean A = 10, the lower 3-sigma tail has a probability of 0.000045, the lower 2-sigma tail has a probabihty of 0.0103, and the lower 1-sigma tail has a probability of 0.1301. The corresponding upper tail probabilities are 0.0035, 0.0270, and 0.1355. For the normal distribution they are 0.00135, 0.0228, and 0.1587. The
212
F J . PIERCE and D.C. GILLILAND
UCL
LCL
Sample # UCL
3 O
O LCL
Sample # Fig. 9.3 Control charts of (a) count data for 30 independent variables from a Poisson A = 10 and (b) for 100 independent variables, the first 50 from a Poisson A = 10 and the second 50 from a Poisson X = 20.
probability of falling below the mean for the Poisson (A = 10) is 0.4579 compared to 0.5000 for the normal distribution. Ryan (1989, Chapter 5) discusses the use of probability-based control limits as alternatives to the Shewhart limits when charting. 4. Example 4: Real data for a count process We monitored seed drop from each of six planter units on a John Deere 7200 corn planter using a standard seed monitoring unit connected to a data logger (Pierce, unpubHshed data). A number of variables were monitored in alternating seconds for six passes of the corn planter, including the total number of skips per second across all six planter units. A skip was defined as the failure of a seed to drop within a time tolerance corresponding to the desired seed spacing (calculated from seed drop per unit time and speed). The counts of the number of skips per second in the first three passes are plotted in Figure 9.4a (299 measurements). The average count is c = 5.27 with the UCL = 12.16 and the LCL = 0. The action rules of Table 9.2 indicate out of control at time 223, which concludes a run of nine counts above the center line (6, 8, 7, 7, 7, 8, 7, 9). This is not, however, an indication of a serious departure from control for this application. The c-chart control limits above were used as standards for the remaining three passes of the corn planter plotted in Figure 9.4b. The Shewhart 3-sigma UCL was exceeded at times 337, 341, 342, 347, 380, and 403, which concludes a run of 9, 10, 4, 10, 11. Action Rule 5 produces signals at counts 342, 343, 344, 371, 372, and 373. Thus, there is a strong indication that in the fourth pass, the corn planter was out of
SOIL QUALITY CONTROL
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O
UCL
a o o
4) CO
*>*
LCL
CO
e«
50
3 xn
100
150
200
250
300
350
Time (seconds)
I o
UCL
-l
250
300
350
1
1
400
450
• I
500
1
550
•!
600
tLCL
650
Time (seconds) Fig. 9.4 C-control charts of (a) measurements of seed drop skips per second obtained from three passes of a six-row corn planter and (b) for a second set of three passes of the same corn planter (Pierce, unpublished data). Control limits in (a) were calculated from the count data and used in (b) to evaluate system stability.
control for the period from count 337 through count 347 and again in the period from time 371 through time 380. The signal at count 403 comes from the number of skips, 13, exceeding the UCL 12.16. These out-of-control periods should be investigated for special causes of variation within the planter units so as to adjust the planter units to an in-control condition. 5. Example 5: Real data on soil bulk density This example illustrates the use of control charts to monitor selected soil quaUty parameters. Larson and Pierce (1991) proposed the use of a minimum data set (MDS) of soil attributes to monitor soil quaUty. The emphasis is to assess whether soil quality is changing and how it is changing (recall that monitoring does not affect soil quahty). Bulk density has been proposed as one component of a soil quahty MDS (Larson and Pierce, 1991; Doran and Parkin, 1994), and we will use it to illustrate the use of control charts for monitoring soil quality. Figure 9.5 presents x\ and Si control charts for the bulk density measurements of 20 subgroups {n = 5) obtained from the 0 to 8 cm depth of a fine sandy loam soil in
214
F J . PIERCE and D.C. GILLILAND 1.6 1.5 -I
. No-tillage. UCL
1.4 4 ix"
1.3-^ 1.2 -I 1.1
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UCL
E
LCL Pbw
1.5 A 3 CQ IK"
Plowed
1.4 J 1.3 A
UCL X
1.2 -] 1.1
LCL UCL
0.16 A ^' 0.10 -j
jf-^
0.05 -f 0.00 200
400
600
800
1000
LCL
1200
Time (days) Fig. 9.5 Mean, x\, and standard deviation, 5,, control charts for surface bulk density measurements for a fine sandy loam soil in Prince Edward Island, Canada managed under (a) no-tillage and (b) moldboard plowing (from Carter, 1988, 1995).
Prince Edward Island, Canada, for no-tillage and moldboard-plowed experimental treatments (Carter, 1988; 1995). The bulk density measurements were obtained over a three-year period, 1 June, 1983 to 6 May, 1986. For no-tillage, x\ was generally stable, ranging from 1.32 to 1.46 Mg m"^ and a ^ = 1.39 Mgm"^, with no apparent special causes of variation, i.e., all x\ falling within the control limits determined from the data (Fig. 9.5a). The S[ for bulk density under no-tillage was quite variable, ranging from 0.01 to 0.11 Mg m~^. None of the St values plotted outside the control limits, but the pattern in ^i was rather cyclic, with lower ^i occurring in the fall months than in the spring and early summer. Bulk density in the plowed soil was lower (1=: 1.27Mgm~^) and more variable (1.14 to 1.35 Mg m~^) than under notillage, with broader control limits. This would be expected in response to disturbance by tillage and reconsolidation. The ^i for bulk density under plowing was similar to no-tillage in mean, range, and cyclic pattern of temporal variation. The bulk density created under each tillage system was different, but the higher bulk density under no-tillage was not necessarily indicative of soil degradation. The fact that bulk density under no-tillage was stable over time indicates that some sort of
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equilibrium level of bulk density is reached under no-tillage, and that this level is predictable within limits. In some cases, therefore, it may not be reasonable to apply the control limits of a soil quaUty parameter under one management system to limits created under another system if system dynamics are quite different, as they are in no-tillage. Interestingly, if the control limits of the plowed soil are applied to the notillage soil, only one point, the bulk density at day 81, plots outside the control limits. On the other hand, since the LCL under no-tillage is near the mean for plowed soil, bulk densities under plowing below the mean exceed the LCL under no-tillage. This phenomenon appears to hold for other bulk density data sets. Control charts of the means Xi and standard deviations Si of bulk density measurements for 15 subgroup (n = 3) obtained over the period from April 1987 to April 1989 from the 0 to 7.6 cm depth of a soil formed in glacial outwash in south central Michigan (data from a single experimental plot; Reinert and Pierce, unpublished data) are given in Figure 9.6. Like data from P.E.L, bulk density under no-tillage is stable
1.7 1.6 H 1.5 1 1.4 1.3
. NortUlage
^^V
^
UCL
X
"^i^
LCL
0.10 H UCL
E LCL
C 0)
o
1.7 1.6 H 1.5 1.4 1.3
Plowed UCL
X LCL
0.10 H 0.05 H 0.00
UCL
^v•v^A T
0
1
r
LCL
100 200 300 400 500 600 700 800 900 Time (Days)
Fig. 9.6 Mean, Xi, and standard deviation, Si, control charts for soil bulk density measured from single experimental plots from a sandy loam soil in south central Michigan, U.S.A. managed under (a) no-tillage and (b) moldboard plowing (Reinert and Pierce, unpubUshed data).
216
F.J. PIERCE and D.C. GILLILAND
(x = 1.53 Mgm~^), but the ^i is not as variable nor as cyclic (Fig. 9.6a). Under plowing, the bulk density is highly variable, with a lower mean value (f = 1.37 Mgm~^) than under no-tillage (Fig. 9.6b). The ^-i under plowing is similar to that under no-tillage and not subject to the wide variation as xi. There are six points outside the control limits on the x-chart for bulk density under plowing (Fig. 9.6b), whereas none of the P.E.I, data (Fig. 9.5b) plot outside the control limits. The control charts in Figures 9.5 and 9.6, however, demonstrate the value of charting soil quahty variables and clearly point out the need for repeated measures to assess the dynamics of soil quality. It is important to evaluate intrinsic cycles and trends associated with the spatial and temporal variability of a property, and these can be identified with the control charts (Montgomery, 1985; Ryan, 1989). As indicated earlier, a single measurement in space and time is difficult to evaluate. Using traditional SPC charts alone can be of questionable value. A proper analysis of bulk density and its variability over growing seasons should include estimates for cyclic components. Then charts should be made for the adjusted time series or for the separate periods of the growing seasons. Clearly, there are not enough data here to support such analyses. III. USING STATISTICAL QUALITY CONTROL TO REGULATE SOIL QUALITY There are two applications of SQC to soil quality. One is its use in monitoring programs where a set of soil attributes, a soil quality MDS, is charted over time. The control limits for each quality parameter would be based on the charted values or on values determined by experts or from previous experiments. The goal, for example, could be to maintain or enhance soil organic matter content at some level (in control). We envision that each parameter constituting a soil quahty MDS would be charted independently, as in Figures 9.5 and 9.6, with appropriate rules (e.g.. Table 9.2) or tests applied to the interpretation of each chart. Each parameter's control chart would be interpreted separately or in light of information on other parameters, because each chart provides different but possible correlated information about the state of soil quality. This procedure would allow a simple, easy-to-use, yet quantitative evaluation of the impact of a particular land use or soil management practice on soil quality. The problem is that, although these charts may detect a change in soil quality, it tells nothing about the process that created the change. The other, perhaps more important, application of SQC lies in the process-control domain of soil quality, which is generally called engineering control (e.g., example 4). In this application, the goal is still soil quality, but the approach focuses on the process that regulates quality rather than simply monitoring a set of soil quality parameters. Consider soil organic matter, but this time think in terms of the processes that regulate organic matter content in soil. Recall that SQC involves design and process control as major components. Thus, the first matter of concern is whether or not the design of the management practice can even produce the desired level of organic matter. If the design is wrong, the desired output can never be achieved. If the system design is correct, then the important questions relate to
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whether operational components of the system are working within the design specifications and tolerances. If the processes that create the outcome are not in control, then the desired output may not be achieved. In SQC, if the design is correct and the manufacturing process is stable (in control), then the quality of the product is good. Thus, for a properly designed management system, the key to good soil quaUty is process control. The objective of engineering control is to identify the key variables controlUng the process and to chart those variables as in Figure 9.1. In the case of soil organic matter, the key variables relate to the amount and quahty of organic matter returned to the soil, the rate and degree of decomposition, and the amount lost by erosion or gained by deposition. Some set of these variables would be chosen to be monitored over time and space. Further, some control limits would be selected that, if the process was in control, would achieve the desired soil organic matter content. If the control charts for these key variables are out of control, then the process would be adjusted according to design criteria. In another example, the goal might be to achieve a specific amount of crop cover or crop residue cover on the soil surface after tillage. The key control variables would Hkely be associated with the tillage tool components that regulate how much crop residue is buried (e.g., operating depth, speed, implement angle or number). As posed by Pierce and Larson (1993), simply informing the farmer after planting that crop residue cover on the field doesn't meet erosion control guidelines is too late to affect the process that created that condition. Adequate residue cover could be achieved if the key variables were charted and adjustments were made to bring the process back into control during the tillage operation (as in the seeding rate. Example 4). An important aspect of this approach is that it places the responsibihty for soil quality in the hands of the land manager, which is the only way to really cause a change in soil quality. It may seem that system design and engineering control are not practical in agricultural management systems. However, emerging technologies associated with site-specific management and precision agriculture are, in fact, capable of achieving this level of design and control. Technologies include very accurate location control (e.g., global positioning systems, GPS), variable rate application equipment, and sensors for both control and performance evaluation (e.g., yield sensors). These technologies are now readily available (Larson and Robert, 1991; Schueller, 1992; Robert et al., 1993, 1995). The potential for real-time control is rapidly emerging and may be the best means of achieving good soil quality. While monitoring will continue to be a focus in soil quality assessment, it is soil quality control that will affect the soil resource base. IV. CONCLUSIONS The analogy of soil quality control to quaUty control in product manufacturing is presented as a model to achieve soil quahty. The analogy is not perfect, but the use of SQC is intuitively appealing given the goals of sustained or improved soil quality. This chapter merely introduces the topic and the concepts involve in SQC. As SQC is
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applied to soil quality, considerable refinement of the concepts and procedures in SQC to this application will emerge.
REFERENCES Acton, D.F. and Gregorich, L.J. 1995, eds. The health of our soils—toward sustainable agriculture in Canada. Centre for Land and Biological Resources Research, Research Branch, Agriculture and Agri-Food Canada, Ottawa, Ont., Canada. Acton, D.F. and Padbury, G.A. 1993. A conceptual framework for soil quality assessment and monitoring. Pages 2-1-2-10 in D.F. Action, ed. A program to assess and monitor soil quality in Canada: soil quality evaluation program summary. Research Branch, Agriculture Canada, Ottawa, Ont., Canada. American Association of Testing Materials (ASTM). 1992. Manual on presentation of data and control chart analysis, 6th ed. ASTM Manual Series MNL 7. ASTM, Philadelphia, Penn., U.S.A. Carter, M.R. 1988. Temporal variability of soil macroporosity in a fine sandy loam under mouldboard ploughing and direct drilling. Soil Till. Res. 12:37-51. Carter, M.R. 1995. Spatial variability of soil porosity under reduced tillage in a Humo-Ferric Podzol. Can. J. Soil Sci. 75:149-152. Campbell, C.L., Bay, J., Franks, C.C, Hallkamp, A.S., Helzer, N.P., Munster, M.J., Heher, D., Olson, G.L., Peck, S.L., Rawlings, J.O., Schumacher, B. and Tooley, M.B. 1994. Environmental monitoring and assessment program—Agroecosystem Pilot Field Program Plan, 1993. EPA/620/R-93/014. U.S. Environmental Protection Agency, Washington, D . C , U.S.A. Deming, W.E. 1986. Out of the crisis. Center for Advanced Study, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A. Doran, J.W. and Parkin, T.B. 1994. Defining and assessing soil quality. Pages 3-21 in J.W. Doran, D.C. Coleman, D.F. Bezdicek, and B.A. Stewart, eds. Defining soil quality for a sustainable environment. Special Pub. 35, Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Hatfield, J.L. and Stewart, B.A., eds. 1993. Soil biology: effects on soil quality. Lewis Publ., Ann Arbor, Mich., U.S.A. Isaaks, E.H. and Srivastava, R.M. 1989. Applied geostatistics. Oxford University Press, New York, N.Y., U.S.A. Larson, W.E. and Pierce, F.J. 1991. Conservation and enhancement of soil quality. Pages 175203 in Evaluation for sustainable land management in the developing world, Vol. 2: Technical Papers. International Board for Soil Research and Management Proc. 12(2). Bangkok, Thailand. Larson, W.E. and Pierce, F.J. 1994. The dynamics of soil quality as a measure of sustainable management. Pages 37-51 in J.W. Doran, D.C. Coleman, D.F. Bezdicek, and B.A. Stewart, eds. Defining soil quality for a sustainable environment. Special Pub. 35, Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Larson, W.E. and Robert, P.C. 1991. Farming by soil. Pages 103-112 in R. Lai and F.J. Pierce, eds. Soil management for sustainability. Soil Water Conserv. Soc, Ankeny, Iowa, U.S.A. Mausbach, M.J. and Wilding, L.P., eds. 1991. Spatial variabilities of soils and landforms. Special Pub. 28. Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Montgomery, D.C. 1985. Introduction to statistical quahty control. John Wiley and Sons, New York, N.Y., U.S.A.
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Pierce, F.J. and Larson, W.E. 1993. Developing criteria to evaluate sustainable land management. Pages 7-14 in J.M. Kimble, ed. Proceedings of the Eighth International Soil Management Workshop: Utilization of Soil Survey Information for Sustainable Land Use, May 3, 1993. USDA Soil Conservation Service, National Soil Survey Center. Robert, P.C, Rust, R.H. and Larson, W.E., eds. 1993. Proceedings of soil specific crop management: A workshop on research and development issues. Am. Soc. Agron., Crop Sci. Soc. Am., and Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Robert, P.C, Rust, R.H. and Larson, W.E., eds. 1995. Proceedings of site-specific management for agricultural systems. Second International Conference. Am. Soc. Agron., Crop Sci. Soc. Am., and Soil Sci. Soc. Am. Inc., Madison, Wise, U.S.A. Ryan, T.P. 1989. Statistical methods for quality control. John Wiley and Sons, New York, N.Y., U.S.A. Schueller, J.K. 1992. A review and integrating analysis of spatially-variable control of crop production. Pert. Res. 33:1-34. Shumway, R.H. 1988. AppHed statistical time series analysis. Prentice Hall, Englewood CUffs, N.J., U.S.A. Webster, R. and Oliver, M.A. 1990. Statistical methods in soil and land resource survey. Oxford University Press, New York, N.Y., U.S.A.