WO2010099170A1 - Method for detecting the impending analytical failure of networked diagnostic clinical analyzers - Google Patents

Method for detecting the impending analytical failure of networked diagnostic clinical analyzers Download PDF

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Publication number
WO2010099170A1
WO2010099170A1 PCT/US2010/025191 US2010025191W WO2010099170A1 WO 2010099170 A1 WO2010099170 A1 WO 2010099170A1 US 2010025191 W US2010025191 W US 2010025191W WO 2010099170 A1 WO2010099170 A1 WO 2010099170A1
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Prior art keywords
analyzer
baseline
operational
column
variables
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English (en)
French (fr)
Inventor
Merrit N. Jacobs
Christopher Thomas Doody
Edwin Craig Bashaw
Joseph Michael Indovina
Owen Altland
Nicholas John Gould
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Ortho Clinical Diagnostics Inc
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Ortho Clinical Diagnostics Inc
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Priority to JP2011552123A priority Critical patent/JP5795268B2/ja
Priority to CN2010800193220A priority patent/CN102428445A/zh
Priority to CA2753571A priority patent/CA2753571A1/en
Priority to US13/203,416 priority patent/US20120042214A1/en
Priority to EP10746746.6A priority patent/EP2401678A4/en
Publication of WO2010099170A1 publication Critical patent/WO2010099170A1/en
Anticipated expiration legal-status Critical
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    • GPHYSICS
    • G06COMPUTING OR CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F11/00Error detection; Error correction; Monitoring
    • G06F11/008Reliability or availability analysis
    • GPHYSICS
    • G16INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16HHEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H10/00ICT specially adapted for the handling or processing of patient-related medical or healthcare data
    • G16H10/40ICT specially adapted for the handling or processing of patient-related medical or healthcare data for data related to laboratory analysis, e.g. patient specimen analysis
    • GPHYSICS
    • G16INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16HHEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H40/00ICT specially adapted for the management or administration of healthcare resources or facilities; ICT specially adapted for the management or operation of medical equipment or devices
    • G16H40/40ICT specially adapted for the management or administration of healthcare resources or facilities; ICT specially adapted for the management or operation of medical equipment or devices for the management of medical equipment or devices, e.g. scheduling maintenance or upgrades

Definitions

  • the invention relates generally to the detection of impending analytical failures in networked diagnostic clinical analyzers.
  • Automated analyzers are a standard fixture in the clinical laboratory. Assays that used to require significant manual human involvement are now handled largely by loading samples into an analyzer, programming the analyzer to conduct the desired tests, and waiting for results. The range of analyzers and methodologies in use is large. Some examples include spectrophotometric absorbance assay such as end-point reaction analysis and rate of reaction analysis, turbidimetric assays, nephelometric assays, radiative energy attenuation assays (such as those described in U.S. Pat. Nos.
  • a plurality of dry chemistry systems and wet chemistry systems can be provided within a contained housing.
  • a plurality of wet chemistry systems can be provided within a contained housing or a plurality of dry chemistry systems can be provided within a contained housing.
  • like systems e.g., wet chemistry systems or dry chemistry systems, can be integrated such that one system can use the resources of another system should it prove to be an operational advantage.
  • each of the above chemistry systems is unique in terms of its operation.
  • known dry chemistry systems typically include a sample supply, a reagent supply that includes a number of dry slide elements, a metering/transport mechanism, and an incubator having a plurality of test read stations.
  • a quantity of sample is aspirated into a metering tip using a proboscis or probe carried by a movable metering truck along a transport rail.
  • a quantity of sample from the tip then is metered (dispensed) onto a dry slide element that is loaded into the incubator.
  • the slide element is incubated, and a measurement such as optical or another read is taken for detecting the presence or concentration of an analyte.
  • a measurement such as optical or another read is taken for detecting the presence or concentration of an analyte.
  • a wet chemistry system utilizes a reaction vessel such as a cuvette, into which quantities of patient sample, at least one reagent fluid, and/or other fluids are combined for conducting an assay.
  • the assay also is incubated and tests are conducted for analyte detection.
  • the wet chemistry system also includes a metering mechanism to transport patient sample fluid from the sample supply to the reaction vessel.
  • sample is generally placed in a sample vessel such as a cup or tube in the analyzer so that aliquots can be dispersed to reaction cuvettes or some other reaction vessel.
  • a probe or proboscis using appropriate fluid handling devices such as pumps, valves, liquid transfer lines such as pipes and tubing, and driven by pressure or vacuum are often used to meter and transfer a predetermined quantity of sample from the sample vessel to the reaction vessel.
  • sample probe or proboscis or a different probe or proboscis is also often required to deliver diluent to the reaction vessel particularly where a relatively large amount of analyte is expected or found in the sample.
  • a wash solution and process are generally needed to clean a non-disposable metering probe.
  • fluid handling devices are necessary to accurately meter and deliver wash solutions and diluents.
  • measurement modules that include some source of stimulation together with some mechanism for detecting the stimulation.
  • These schemes include, for example, monochromatic light sources and calorimeters, reflectometers, polarimeters, and luminometers.
  • Most modern automated analyzers also have sophisticated data processing systems to monitor analyzer operations and report out the data generated either locally or to remote monitoring centers connected via a network or the Internet.
  • Numerous subsystems such as reagent cooler systems, incubators, and sample and reagent conveyor systems are also frequently found within each of the major systems categories already described.
  • An analytical failure occurs when one or more components or modules of a diagnostic clinical analyzer begins to fail.
  • Such failures can be the result of initial manufacturing defects or longer-term wear and deterioration.
  • mechanical failure there are many different kinds of mechanical failure, and they include overload, impact, fatigue, creep, rupture, stress relaxation, stress corrosion cracking, corrosion fatigue and so on.
  • These single component failures can result in an assay result that is believable yet unacceptably inaccurate.
  • These inaccuracies or precision losses can be further enhanced by a large number of factors such as mechanical noise or even inefficient software programming protocols. Most of these are relatively easy to address.
  • sample and reagent manipulation systems require the accurate and precise transport of small volumes of liquids and thus generally incorporate extraordinarily thin tubing and vessels such as those found in sample and reagent probes.
  • Most instruments require the simultaneous and integrated operation of several unique fluid delivery systems, each one of which is dependent on numerous parts of the hardware/software system working correctly. Some parts of these hardware/software systems have failure modes that may occur at a low level of probability.
  • a defect or clog in such a probe can result in wildly erratic and inaccurate results and thus be responsible for analytical failures.
  • a defective washing protocol can lead to carryover errors that give false readings for a large number of assay results involving a large number of samples. This can be caused by adherence of dispensed fluid to the delivery vessel (e.g., probe or proboscis).
  • the vessel contacts reagent or diluent it can lead to over diluted and thus under reported results.
  • Entrainment of air or other fluids to a dispensed fluid can cause the volume of the dispensed fluid to be below specification since a portion of the volume attributed to the dispensed fluid is actually the entrained fluid.
  • Measurements of these variables can be used to detect impending analytical failures as described herein and can also be used to monitor the overall operation of the analyzer as detailed in James O. Westgard and in Carl A. Burtis et al. previously incorporated by reference above.
  • a key issue is which set of variables should be monitored.
  • Error budget calculations are a specialized form of sensitivity analysis. They determine the separate effects of individual error sources, or groups of error sources, which are thought to have potential influence on system accuracy. In essence, the error budget is a catalog of those error sources. Error budgets are a standard fixture in complex electronic systems designs.
  • this application provides a method for predicting the impending analytical failure of a networked diagnostic clinical analyzer in advance of the diagnostic clinical analyzer producing assay results with unacceptable accuracy and precision.
  • This disclosure is not directed to detecting if a failure has already taken place because such determinations are made by other functionalities and circuits in diagnostic analyzers. Further, not all failures affect the reliability of the results generated by a clinical diagnostic analyzer. Instead, this disclosure is concerned with detecting impending failures, and assisting in remedying the same to improve the overall performance of clinical diagnostic analyzers.
  • Another aspect of this application is directed to a methodology for dispatching service representatives to a networked diagnostic clinical analyzer in advance of the analytical failure of the diagnostic clinical analyzer.
  • a preferred method for predicting an impending failure in a diagnostic clinical analyzer includes the steps of monitoring a plurality of variables in a plurality of diagnostic clinical analyzers, screening out outliers from values of monitored variables, deriving a threshold — such as the baseline control chart limit — for each of the monitored variables based on the values of monitored variables screened to remove outliers, normalizing the values of the monitored variables, generating a composite threshold using normalized values of monitored variables, collecting operational data about the monitored variables from a particular diagnostic clinical analyzer and generating an alert if the composite threshold is exceeded by the particular diagnostic clinical analyzer.
  • a threshold such as the baseline control chart limit
  • An outlier value of a variable is a value that is expected to occur, based on the underlying expected or presumed distribution, at a rate selected from the set consisting of no more than 3%, no more than 1 %, no more than 0.1 % and no more than 0.01 %.
  • the threshold for a particular monitored variable is also used to normalize the monitored variable. This implementation choice is not intended to and should not be understood to be a limitation on the scope of the invention unless such is expressly indicated in the claims. Alternative embodiments may normalize monitored variables differently. Normalization ensures that a composite threshold, such as a Baseline Composite Control Chart Limit, reflects appropriately weighted underlying variable values.
  • Normalization enables using parameters as a component of the composite threshold even when the parameter values are numerically different by orders of magnitude.
  • an alert for an impending failure is generated for a particular diagnostic clinical analyzer if the variables monitored for that particular diagnostic clinical analyzer exceed the composite threshold in a prescribed manner, such as once, on two times out of three successive time points, or a present number of times in a specified time interval or period of operation.
  • an impending failure refers to an increased frequency of variations in performance, even when the assay results are well within the bounds of variation specified by the assay or the relevant reagent manufacturer. Such implementation choices are not intended to and should not be understood to limit the scope of the invention unless such is expressly indicated in the claims.
  • FIG. 1 is a diagram of the integrated diagnostic clinical analyzer and general- purpose computer network.
  • a plurality of independently operating diagnostic clinical analyzers 101 , 102, 103, 104, and 105 are connected to a network 106.
  • all diagnostic clinical analyzers 101 , 102, 103, 104, and 105 collect, and subsequently, transfer data to the general-purpose computer 112.
  • additional operational data are collected and transferred to the general- purpose computer 112.
  • FIG. 2 is a diagram of an Assay Predictive Alerts Control Chart showing the robust, statistical control chart limit 201 as derived from baseline data and the value of the statistic computed from operational data reported to the general- purpose computer 112 from a particular diagnostic clinical analyzer for a series of twenty-five daily time periods as indicated by the data points 202. Note that two out of three of the statistic values exceed the control chart limit for days 23, 24, and 25.
  • FIG. 3 is a diagram of the data setup for the computation of the control chart limit using baseline data for Example 1.
  • Column 301 denotes a specific diagnostic clinical analyzer in the population of 862 analyzers.
  • Column 302 denotes the reported percent error codes by analyzer, hereafter known as the baseline errori value.
  • Column 303 denotes the normalized percent error codes value by analyzer, hereafter known as the normalized baseline errori value.
  • Column 304 denotes the reported analog to digital voltage counts by analyzer, hereafter known as the baseline rangel value.
  • Column 305 denotes the normalized analog to digital voltage counts by analyzer, hereafter known as the normalized baseline rangel value.
  • Column 306 denotes the reported ratio of the average value of three validation numbers to the expected value of three signal voltages by analyzer, hereafter known as the baseline ratiol value.
  • Column 307 denotes the normalized ratio of the average value of three validations numbers to the average value of three signal voltages by analyzer, hereafter known as the normalized baseline ratiol value.
  • Column 308 is the average value of the three normalized values in columns 303, 305, and 307, hereafter known as the baseline compositel value.
  • Row 309 is the mean of the values in column 302, column 304, column 306, and column 308, respectively.
  • Row 310 is the standard deviation of the values in column 302, column 304, column 306, and column 308, respectively.
  • Row 311 is the mean of the values remaining in column 302, column 304, column 306, and column 308, respectively, after values not included in the range of the mean plus or minus three standard deviations have been removed.
  • the row 311 means are denoted the trimmed means.
  • Row 312 is the standard deviation of the values remaining in column 302, column 304, column 306, and column 308, respectively, after values not included in the range of the mean plus or minus three standard deviations have been removed.
  • the row 312 standard deviations are denoted the trimmed standard deviations.
  • Row 313 is the individual control chart limit values composed of the trimmed means, in row 311 , plus three times the trimmed standard deviations, in row 312, for column 302, column 304, column 306, and column 308, respectively.
  • the element in row 313 and column 308 is the baseline compositel control chart limit.
  • FIG. 4 is a diagram of the histogram obtained from the analysis of the reported percent error codes obtained from surveying the population of 862 diagnostic clinical analyzers in Example 1 over a specific point in time.
  • FIG. 5 is a diagram of the histogram obtained from the analysis of the reported analog to digital counts obtained from surveying the population of 862 diagnostic clinical analyzers in Example 1 over a specific point in time.
  • FIG. 6 is a diagram of the histogram obtained from the analysis of the reported ratio of average validation numbers to average signal voltages obtained from surveying the population of 862 diagnostic clinical analyzers in Example 1 over a specific point in time.
  • FIG. 7 is a diagram of the data setup for the computation of the compositel value using operational data for Example 1.
  • Column 701 denotes the date that the data was taken.
  • Column 702 denotes the reported percent error codes by analyzer, hereafter known as the operational errori value, for each date respectively.
  • Column 703 denotes the normalized percent error codes value by analyzer, hereafter known as the normalized operational errori value, for each date respectively.
  • Column 704 denotes the reported analog to digital voltage counts by analyzer, hereafter known as the operational rangel value, for each date respectively.
  • Column 705 denotes the normalized analog to digital voltage counts by analyzer, hereafter known as the normalized operational rangel value, for each date respectively.
  • Column 706 denotes the reported ratio of the average value of three validations numbers to the average value of three signal voltages by analyzer, hereafter known as the operational ratiol value, for each date respectively.
  • Column 707 denotes the normalized ratio of the average value of three validations numbers to the average value of three signal voltages by analyzer, hereafter known as the normalized operational ratiol value, for each date respectively.
  • Column 708 is the average value of the three normalized values in columns 703, 705, and 707, hereafter known as the operational compositel value, for each date respectively.
  • FIG. 8 is a diagram of the control chart where the daily value of operational compositel is plotted for Example 1.
  • a line 801 representing the trimmed baseline compositel control chart limit of about 74.332 is shown in the graph.
  • the daily values of the operational compositel are represented by dots 802.
  • FIG. 9 is a diagram of a simple electronic circuit that has four signal inputs: W 901 , X 902, Y 903, and Z 904. These four signals have the characteristics of independent random variables.
  • Signals W 901 and X 902 are combined in an adder 905 resulting in signal A 906.
  • Signal A 906 is combined with signal Y 903 in a multiplier 907 resulting in signal B 908.
  • Signal B 908 is combined with signal Z 904 in an adder 910 resulting in signal C 909.
  • FIG. 10 is a tornado diagram showing the influence of various input variables on the output variance of signal C in the model circuit discussed in the Appendix along with a table of the values in the diagram.
  • FIG. 11 is a diagram of the data setup for the computation of the control chart limit using baseline data for Example 2.
  • Column 1101 denotes a specific diagnostic clinical analyzer in the population of 758 analyzers.
  • Column 1102 denotes the standard deviation of the error in the incubator temperature by analyzer, hereafter known as the baseline inc ⁇ bator2 value.
  • Column 1103 denotes the normalized standard deviation of the incubator temperature by analyzer, hereafter known as the normalized baseline incubator2 value.
  • Column 1104 denotes the standard deviation of the error in the MicroT ⁇ pTM reagent supply temperature by analyzer, hereafter known as the baseline reagent! value.
  • Column 1105 denotes the normalized standard deviation of the error in the MicroT ⁇ pTM reagent supply temperature by analyzer, hereafter known as the normalized baseline reagent2 value.
  • Column 1106 denotes the standard deviation of the ambient temperature by analyzer, hereafter known as the baseline ambient! value.
  • Column 1107 denotes the normalized standard deviation of the ambient temperature by analyzer, hereafter known as the normalized baseline ambient2 value.
  • Column 1108 denotes the percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the baseline codes2 value.
  • Column 1109 denotes the normalized percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the normalized baseline codes2 value.
  • Column 1110 is the average value of the four normalized values in columns 1103, 1105, 1107, and 1109, hereafter known as the baseline composite2 value.
  • Row 1111 is the mean of the values in column 1102, column 1104, column 1106, column 1108, and column 1110, respectively.
  • Row 1112 is the standard deviation of the values in column 1102, column 1104, column 1106, column 1108, and column 1110, respectively.
  • Row 1113 is the mean of the values remaining in column 1102, column 1104, column 1106, column 1108, and column 1110, respectively, after values not in the range of the mean plus or minus three standard deviations have been removed. The row 1113 means are denoted the trimmed means.
  • Row 1114 is the standard deviation of the values remaining in column 1102, column 1104, column 1106, column 1108, and column 1110, respectively, after values not in the range of the mean plus or minus three standard deviations have been removed.
  • the row 1114 standard deviations are denoted the trimmed standard deviations.
  • Row 1115 is the individual control limit values composed of the trimmed mean, in row 1113, plus three trimmed standard deviations, in row 1114, for column 1102, column 1104, column 1106, column 1108, and column 1110, respectively.
  • FIG. 12 is a diagram of the data setup for the computation of the composite2 value using operational data for Example 2.
  • Column 1201 denotes the date that the data was taken.
  • Column 1202 denotes the standard deviation of the incubator temperature by analyzer, hereafter known as the operational inc ⁇ bator2 value, for each date respectively.
  • Column 1203 denotes the normalized standard deviation of the incubator temperature by analyzer, hereafter known as the normalized operational incubator2 value, for each date respectively.
  • Column 1204 denotes the standard deviation of the MicroTipTM reagent supply temperature by analyzer, hereafter known as the operational reagent2 value, for each date respectively.
  • Column 1205 denotes the normalized standard deviation of the MicroTipTM reagent supply temperature by analyzer, hereafter known as the normalized operational reagent2 value, for each date respectively.
  • Column 1206 denotes the standard deviation of the ambient temperature by analyzer, hereafter known as the operational ambient2 value, for each date respectively.
  • Column 1207 denotes the normalized standard deviation of the ambient temperature by analyzer, hereafter known as the normalized operational ambient! value, for each date respectively.
  • Column 1208 denotes the percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the operational codes2 value, for each date respectively.
  • Column 1209 denotes the normalized percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the normalized operational codes2 value, for each date respectively.
  • Column 1210 is the average value of the four normalized values in columns 1203, 1205, 1207, and 1209, hereafter known as the operational composite2 value, for each date respectively.
  • FIG. 13 is a diagram of the control chart where the daily value of operational composite2 is plotted for Example 2.
  • the baseline composite2 control chart limit 1301 is shown to be approximately 89.603 in this graph.
  • the daily values of the operational composite2 are represented by dots 1302.
  • FIG. 14 is a diagram of the data setup for the computation of the composite3 value using operational data for Example 3.
  • Column 1401 denotes the date that the data was taken.
  • Column 1402 denotes the standard deviation of the incubator temperature by analyzer, hereafter known as the operational incubatort value, for each date respectively.
  • Column 1403 denotes the normalized standard deviation of the incubator temperature by analyzer, hereafter known as the normalized operational inc ⁇ bator3 value, for each date respectively.
  • Column 1404 denotes the standard deviation of the MicroTipTM reagent supply temperature by analyzer hereafter known as the operational reagent3 value, for each date respectively.
  • Column 1405 denotes the normalized standard deviation of the MicroTipTM reagent supply temperature by analyzer, hereafter known as the normalized operational reagent3 value, for each date respectively.
  • Column 1406 denotes the standard deviation of the ambient temperature by analyzer, hereafter known as the operational ambient3 value, for each date respectively.
  • Column 1407 denotes the normalized standard deviation of the ambient temperature by analyzer, hereafter known as the normalized operational ambient3 value, for each date respectively.
  • Column 1408 denotes the percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the operational codes3 value, for each date respectively.
  • Column 1409 denotes the normalized percent condition codes of the combined secondary metering and three read delta check codes by analyzer, hereafter known as the normalized operational codes3 value, for each date respectively.
  • Column 1410 is the average value of the four normalized values in columns 1403, 1405, 1407, and 1409, hereafter known as the operational composite3 value, for each date respectively.
  • FIG. 15 is a diagram of the control chart where the daily value of operational composite3 value is plotted for Example 3.
  • the baseline composite3 control chart limit 1501 is shown to be approximately 89.603 in this graph.
  • the daily values of the operational composite3 are represented by dots 1502.
  • FIG. 16 is a flowchart of the software used to compute the baseline composite control chart limit and operational data points. Processing begins at the START ellipse 1601 after which the number of analyzers 1602 for which data is available is input. After baseline data for one analyzer is read 1603, a check is made 1604, to see if data for additional analyzers remains to be input. If yes, control is returned to the 1603 block, otherwise the baseline mean and standard deviation is computed for each input variable 1605 over the cross-section of all analyzers. Now, all data with values not in the range of the mean plus or minus at least three standard deviations is removed from the computational data set 1606, a process known as trimming, and the trimmed mean and standard deviation is computed for each variable 1607.
  • the baseline control chart limit value for each variable is computed 1607A, and the baseline composite control chart limit is computed 1608 using the trimmed means and standard deviations.
  • the input of operational data for a specific period 1609 for a particular analyzer begins.
  • a check is made to determine if additional periods of data are available. If, yes, control is returned to block 1609, otherwise, each variable's input values are divided by the variable's baseline control chart value normalizing each variable 1611.
  • the operational composite value is computed 1612. Subsequently, these operational values are stored in computer memory 1613 and compared to the baseline composite control limit previously computed 1614.
  • control limit is exceeded for a specified number of times over a defined time horizon, the Remote Monitoring Center is notified of an impending analyzer analytical failure 1615, otherwise, control is returned to block 1610 to await the input of another period of operational data from the particular analyzer.
  • FIG. 17 is a schematic of an exemplary display of information about monitored variables on different time points and of their respective thresholds.
  • the shaded boxes draw attention to the monitored variables exceeding their respective thresholds to aid in troubleshooting or improving the performance of an analyzer.
  • the display aids in troubleshooting an impending failure by directing attention to suspect subsystems.
  • the benefits of the techniques discussed within are detecting the impending analytical failure in advance of the actual event and servicing (determining and ameliorating the cause of the impending analytical failure) the remotely located diagnostic clinical analyzer at a time that is convenient for both the commercial entity employing the analyzer and the service provider.
  • the term "parameter” refers herein to a characteristic of a process or population. For example, for a defined process or population probability density function, the mean, a parameter of the population, has a fixed, but perhaps, unknown value ⁇ .
  • variable refers herein to a characteristic of a process or population that varies as an input or an output of the process or population. For example, the observed error of the incubator temperature from its desired setpoint is +0.5° C at present represents an output.
  • statistic refers herein to a function of one or more random variables.
  • a “statistic” based upon a sample from a population can be used to estimate the unknown value of a population parameter.
  • trimmed mean refers herein to a statistic that is an estimation of location where the data used to compute the statistic has been analyzed and restructured such that data values with unusually small or large magnitudes have been eliminated.
  • trimmed statistic refers herein to a statistic, of which the trimmed mean is a simple example, which seeks to outperform classical statistical methods in the presence of outliers, or, more generally, when underlying parametric assumptions are not quite correct.
  • cross-sectional refers herein to data or statistics generated in a specific time period across a number of different diagnostic clinical analyzers.
  • time series refers herein to data or statistics generated in a number of time periods for a specific diagnostic clinical analyzer.
  • time period refers herein to a length of time over which data is accumulated and individual statistics generated. For example, data accumulated over twenty-four hours and used to generate a statistic would result in a statistical value based upon a "time period" of a day. Furthermore, data accumulated over sixty minutes and used to generate a statistic would result in a statistical value based upon a "time period” of an hour.
  • time horizon refers herein to a length of time over which some issue is considered. A “time horizon" may contain a number of "time periods.”
  • baseline period refers herein to the length of time over which data from the population of diagnostic clinical analyzers on the network is collected, e.g., data might be collected daily for 24 hours.
  • operation period refers herein to the length of time over which data from a particular diagnostic clinical analyzer is collected, e.g., data might be collected once an hour over an operational period of 24 hours resulting in 24 observations or data points.
  • Variables associated with a particular design of a diagnostic clinical analyzer are selected for monitoring based upon their individual ability to identify abnormally elevated contributions to the overall error budget of the analyzer.
  • the diagnostic clinical analyzer must be capable of measuring these variables.
  • the decision as to how many of these variables to monitor is an engineering decision and depends upon the assay method being employed, i.e., MicroSlideTM, MicroTipTM, or MicroWellTM in Ortho-Clinical Diagnostics® analyzers, and the diagnostic clinical analyzer instrument itself, i.e., Vitros® 5,1 FS; Vitros® ECiQ; Vitros® 350; Vitros® DT60 II; Vitros® 3600; or Vitros® 5600.
  • the baseline data is collected from a plurality of diagnostic clinical analyzers 101 , 102, 103, 104, and 105 in normal commercial operation over a specified first time period, normally during the Monday to Friday workweek.
  • Baseline data accumulation over the specified first time period results in one data set per diagnostic clinical analyzer that is sent over the network 106 and is cumulatively represented by the data flow 107.
  • the general-purpose computer 112 receives this baseline data from the plurality of diagnostic clinical analyzers on the network 106.
  • the baseline data from a plurality of diagnostic clinical analyzers are then merged by the general-purpose computer 112 producing multiple cross-sectional observations, over a specified first time period, composed of three variables as follows: (1 ) the percentage of micro-slide assays resulting in a non-zero condition or error code, referred to as baseline error, (2) a measure of the variation in the primary voltage circuit, referred to as baseline range, and (3) the ratio of the average value of three validation numbers to the average value of three signal voltages, referred to as baseline ratio. To further transform this information, the mean and standard deviation of each of the three variables is computed and individual observations not included in the range of the mean plus or minus at least three standard deviations are eliminated from the collective data. This operation is known as trimming.
  • the trimmed mean is an example of a robust statistic in that it is resistant to data outliers and contains all the information available in the trimmed data set. It should be noted that alternative preferred embodiments may use statistics that are not robust, but are based upon incomplete or fragmentary information.
  • a new trimmed mean and trimmed standard deviation is calculated based upon the observations remaining in the data set.
  • the trimmed mean and trimmed standard deviation are used to compute a baseline control chart limit consisting of the trimmed mean plus at least three times the trimmed standard deviation for each of the three variables. Multiplying each variable by 100 and by dividing each variable by its baseline control chart limit, respectively, normalizes the individual baseline error, baseline range, and baseline ratio values.
  • an average of the three normalized values is computed, referred to as the baseline composite value.
  • the mean and standard deviation of the baseline composite values are computed.
  • baseline composite values not included in the range of the baseline composite mean plus or minus at least three times the baseline composite standard deviation are removed, and a trimmed baseline composite mean and trimmed baseline composite standard deviation are computed.
  • a trimmed baseline composite control chart limit 201 is then computed as the trimmed baseline composite mean plus at least three times the trimmed baseline composite standard deviation.
  • the trimmed baseline composite control chart limit 201 is a robust statistic completely derived from the remote diagnostic clinical analyzer baseline data. It should be noted that alternative preferred embodiments may use statistics that are not robust, but are based upon incomplete or fragmentary information. A detailed flowchart of baseline computations above and operational computations below are presented in FIG. 16.
  • baseline statistics may also be used to individually monitor the remote clinical analyzer at the remote setting to determine changes in the operation of the analyzer relative to adequacy of calibration or the need for the adjustment of parameter values when changing lots of reagents or detection devices such as MicroSlidesTM.
  • Monitoring Center the same or alternative statistics can be calculated and downloaded to the remote site either upon demand or at prescheduled intervals.
  • the numerical values of these statistics can subsequently be used as baseline values for Shewhart charts, Levey-Jennings charts, or Westgard rules. Such methodology is described in both James O. Westgard and in Carl A. Burtis et al. previously incorporated by reference above.
  • operational data is collected for a particular diagnostic clinical analyzer over a specified sequence of second time periods and is sent over the network 113 to the general-purpose computer 112 at the end of each time period, denoted by network data flows 108, 109, 110, and 111.
  • the data consists of numerous second time period values for operational error, operational range, and operational ratio.
  • the values are normalized by multiplying by 100 and dividing by the associated baseline control chart limit for that variable which was calculated previously.
  • the general-purpose computer 112 is programmed to calculate the average value of these three normalized operational variables for to obtain the operational composite value for a sequence of second time periods.
  • These values of the operational composite computed over a sequence of second time periods represent a time-series of observations.
  • the operational composite value, the second statistic computed is a statistic whose magnitude is indicative of the overall fluctuation in a particular diagnostic clinical analyzer's error budget. It should be noted that alternative preferred embodiments may use statistics that are not robust, but are based upon incomplete or fragmentary information.
  • the general-purpose computer 112 stores and tracks these values, as indicated by the values 202 plotted in FIG. 2, and when the value of the operational composite is greater than the trimmed baseline composite control chart limit 201 , as determined from the baseline data, for a predetermined number of second time periods over a predetermined time horizon, the Remote Monitoring Center is notified that there is an impending analytical failure of that particular analyzer.
  • FIG. 16 A detailed flowchart of the above baseline and operational computations is presented in FIG. 16.
  • the criteria stated above for determining when to alert for an impending analytical failure is significantly stricter than traditional statistical process control criteria. Specifically, the criteria being used in this methodology is when the value of the operational composite exceeds the trimmed baseline composite control chart limit 201 for two out of three consecutive observations. This is equivalent to exceeding the trimmed mean plus three times the trimmed standard deviation. As pointed out by John S.
  • the usual criteria for alerting that a process is out of control when using an individuals or run control chart is (1 ) an observation of the critical variable greater than the mean plus three standard deviations, (2) two out of three consecutive observations of the critical variable that exceed the mean plus two standard deviations, or (3) eight consecutive observations of the critical variable that either always exceed the mean or always are less than the mean.
  • the criterion used in this methodology is much stricter, i.e., much less likely to occur, than the criteria normally employed.
  • Operational statistics may also be used to individually monitor the remote clinical analyzer at the remote setting to determine changes in the operation of the analyzer relative to adequacy of calibration or the need for the adjustment of parameter values when changing lots of reagents or detection devices such as MicroSlidesTM.
  • the statistics can be calculated and downloaded to the remote site either upon demand or at prescheduled intervals.
  • the numerical values of these statistics can subsequently be analyzed using Shewhart charts, Levey- Jennings charts, or Westgard rules as data is received. Such methodology is described in both James O. Westgard and in Carl A. Burtis et al. previously incorporated by reference above.
  • the Remote Monitoring Center upon notice that at least one remote diagnostic clinical analyzer has an impending analytical failure, must decide the appropriate follow up course of action to be employed.
  • the techniques discussed herein allow the transformation of the gathered data and subsequently calculated statistics into an ordered series of actions by the Remote Monitoring Center management.
  • the value of the second statistic available for each remote diagnostic clinical analyzer where an impending analytical failure has been predicted, can be used to prioritize which remote analyzer should be serviced first as the relative magnitude of the second statistic is indicative of overall potential for failure for that analyzer. The higher the value of the second statistic, the greater the chance that an impending failure will occur. This is of significant value when the service resources are limited and it is desirable to make the most of such resources.
  • an on- site service call may take up to several hours. Part of this time is devoted to travel to the site (and return) plus the amount of time it takes to identify and replace one or more components of the diagnostic clinical analyzer that are starting to fail. Furthermore, if the notice of an impending failure is very timely, it may be possible to schedule an on-site service call to coincide with already scheduled downtime for the analyzer thereby preventing a disruption of analyzer uptime to the commercial entity employing the analyzer. For example, some hospitals collect patient samples so that many are analyzed from about 7:00 AM to 10:00 PM during the working day. It is most convenient for such hospitals to have the diagnostic clinical analyzers down from 10:00 PM to 7:00 AM. In addition, for the service site location, it is better to schedule service calls during routine working hours and certainly in advance of major holidays and other events.
  • Preferred embodiments for wet chemistries employing either cuvettes or microtitre plates is similar to the preferred embodiment above for thin-film slides except that a different set of variables is required to be monitored.
  • the overall transformation of the baseline information to a first, robust statistic and the transformation of the operational data to a second statistic remains the same, as does the operation of the control chart. Exemplary examples of the implementation of this disclosure are described below.
  • This example deals with the detection of impending analytical failure in dry chemistry MicroSlideTM diagnostic clinical analyzers using ion-specific electrodes as the assay-measuring device.
  • the first variable is the percentage of all sodium, potassium, and chloride assays that resulted in non-zero error codes or conditions.
  • the second variable is the average of the three voltage signal levels taken during the ion-specific electrode readout for all potassium assays.
  • the third variable is the standard deviation of the ratio of the average signal analog-to-digital count to the average validation analog-to-digital count for all potassium assays.
  • the signal analog-to-digital count is the voltage of the slide measured by the electrometer and the validation analog-to-digital count is the voltage of the slide taken with the internal reference voltage applied to the slide in series.
  • baseline and operational data values are obtained as double precision floating point values as defined by the IEEE Floating Point Standard 754. As such, these values, while represented internally in a computer using 8 digital bytes, have approximately 15 decimal digits of precision. This degree of precision is maintained throughout the sequence of numerical computations; however, such precision is impractical to maintain in textual references and in figures. For the purpose of this exposition, all floatingpoint numbers referenced in the text or in figures will be displayed to three decimal places rounded up or down to the nearest digit in the third decimal place without regard to the number of significant decimal digits present.
  • 123.456781234567 will be displayed as 123.457, and 0.00123456781234567 will be displayed as 0.001.
  • This display mechanism has the effect of potentially yielding incorrect arithmetic if numerical quantities as displayed are used for computation. For example, multiplying the two 15 decimal digit numbers above yields 0.152415768327997 to 15 decimal digits of precision; however, if the two displayed representations of the two numbers are multiplied, then 0.123456 to 6 decimal digits is obtained. Clearly, the two values thus obtained are significantly different.
  • FIG. 3 contains the data setup for the computation of the control chart limit using the above baseline data.
  • Column 301 denotes a specific diagnostic clinical analyzer in the population of 862 analyzers.
  • Column 302 denotes the reported percent error codes by analyzer, i.e., baseline errori.
  • Column 304 denotes the reported average of three voltage signal levels by analyzer, i.e., baseline rangel.
  • Column 306 denotes the reported ratio of the average value of the signal analog- to-digital count numbers to the average of the signal analog-to-digital count by analyzer, i.e., baseline ratioi.
  • FIG. 4, FIG. 5, and FIG. 6 show a histogram of the reported baseline errori values, the reported baseline rangel values, and the reported baseline ratiol values for all the 862 reporting diagnostic clinical analyzers, respectively.
  • all baseline errori values in column 302 not included in the range of the baseline errori mean value of 0.257 plus or minus three times the baseline errori standard deviation value of 1.136 are then removed.
  • Trimmed baseline errori mean values, shown in row 311 , and trimmed baseline errori standard deviation values, shown in row 312, are computed from the values remaining in column 302 after trimming. Similar trimming computations are performed for the baseline rangel and baseline ratiol values.
  • the resulting baseline errori control chart limit value, baseline rangel control chart limit value, and baseline rangel control chart limit value, shown as the first three elements of row 313, are computed as the trimmed mean plus three times the trimmed standard deviation.
  • Each data value of baseline errori, in column 302 is then multiplied by 100 and divided by the baseline errori control chart limit (the first element in row 313) to yield the normalized baseline errori as shown in column 303.
  • Elements of column 308 not included in the range of the baseline compositel mean plus or minus three baseline compositel standard deviations are removed via trimming. Subsequently, the trimmed baseline compositel mean, element four in row 311 of column 308, is computed using the baseline compositel values remaining in column 308 after trimming. In addition, the trimmed baseline compositel standard deviation, element four in row 312 of column 308, is computed using the baseline compositel values remaining in column 308 after trimming. The trimmed baseline compositel control chart limit value, the first statistic calculated, is then computed as the trimmed baseline compositel mean plus three times the trimmed baseline compositel standard deviation, the result being shown as element four in row 313 of column 308.
  • FIG. 7 contains the data setup for the daily operational data reports from the 647 analyzer displayed as rows of data.
  • Column 701 denotes the date on which the data was taken.
  • Columns 702, 704, and 706 denote reported values of operational errori, operational rangel, and operational ratiol, respectively.
  • Columns 703, 705, and 707 are the computed normalized values of operational errori, operational rangel, and operational ratiol, respectively, obtained by multiplying columns 702, 704, and 706 by 100 and then dividing by the trimmed baseline errori mean value, trimmed baseline rangel mean value, and trimmed baseline ratiol mean value, respectively.
  • Column 708 contains values of the operational compositel value, the second statistic calculated, obtained by averaging the values in columns 703, 705, and 707.
  • FIG. 8 contains the 647 diagnostic clinical analyzer control chart where each value of the operational compositel in column 708 is plotted as dots 802.
  • the line 801 represents the trimmed baseline compositel control chart limit value of 74.332.
  • the daily operational compositel value starts out near the control chart limit value and then exceeds it for three days but subsequently drops below the control limit value. This would be the first indication of an impending analytical failure by the diagnostic clinical analyzer. After several more days, the operational compositel value once again exceeds the control chart limit for two days out of three. While still showing no outward signs of operational problems, a service technician was dispatched to the analyzer site and, after careful analysis, the electrometer was found to be slowly failing. The electrometer was replaced on September 28 th . Subsequently, for the duration of this test data, values of operational compositel remained below the control chart limit.
  • This example deals with the detection of impending analytical failure in wet chemistry MicroTipTM diagnostic clinical analyzers using a photometer to measure the absorbance through the sample as the assay-measuring device.
  • the first variable is the standard deviation of the error in the incubator temperature, defined as the baseline incubator! value, as measured hourly.
  • the second variable is the standard deviation of the error in the MicroT ⁇ pTM reagent supply temperature, defined as the baseline reagent2 value, as measured hourly.
  • the third variable is the standard deviation of the ambient temperature, defined as the baseline ambient! value, as measured hourly.
  • the fourth variable is the percent condition codes of the combined secondary metering and three read delta check codes, defined as the codes2 value.
  • the trimmed baseline composite2 control chart limit value for this example is computed in the same manner as was employed to compute the trimmed baseline compositel control chart limit value in Example 1.
  • the data structure is shown in FIG. 11 where column 1101 denotes the analyzer providing the baseline data, columns 1102, 1104, 1106, and 1108 are values of baseline incubator2, baseline reagent!, baseline ambient2, and baseline codes2, respectively. Normalized values of the input values of baseline incubator2, baseline reagent2, baseline ambient2, and baseline codes2 are shown in columns 1103, 1105, 1107, and 1109, respectively. Rows 1111 and 1112 contain the mean and standard deviation, respectively, of columns 1102, 1104, 1106, and 1108, respectively.
  • Rows 1113 and 1114 contain the trimmed mean and trimmed standard deviation of columns 1103, 1105, 1107, and 1109, respectively.
  • Element 5 in row 1115 of column 1110 is the value of the trimmed baseline composite2 control chart limit value, the first statistic calculated, specifically 89.603.
  • FIG. 12 contains the data setup for the daily operational data reports from the 267 analyzer displayed as rows of data.
  • Column 1201 contains the date on which the data was taken.
  • Column 1202, 1204, 1206, and 1208 contain the reported daily values of the operational incubator2, operational reagent2, operational ambient2, and operational codes2 values, respectively.
  • 1207, and 1209 are normalized values of the four values of operational incubator2, operational reagent2, operational ambient2, and operational codes2, respectively, obtained in the same manner as values of operational values were in Example 1.
  • Column 1210 contains values of the daily operational composite2 value, the second statistic calculated.
  • FIG. 13 contains the 267 diagnostic clinical analyzer control chart where each value of the operational composite2 in column 1210 is plotted as dots 1302.
  • the trimmed baseline composite2 control chart limit value of 89.603 is represented by the line 1301. Note that the daily operational composite2 value starts out at a low value for 7 days then jumps up to exceed the control limit for 3 days. After returning to a low value for eight more days, the operational composite2 value once again exceeds the control chart limit for two days out of three. Both of the above events would result in an alert regarding an impending analytical failure. Subsequently, for the duration of this test data, values of daily operational composite2 remained below the control chart limit.
  • This example deals with the detection of impending analytical failure in wet chemistry MicroTipTM diagnostic clinical analyzers using a photometer to measure the absorbance through the sample as the assay-measuring device.
  • Example 2 baseline data obtained on November 13, 2008 operational data for the 406 analyzer were obtained on a daily basis from October 24, 2008 to December 2, 2008 as shown in FIG. 14.
  • Column 1401 contains the date on which the data was taken.
  • Column 1402, 1404, 1406, and 1408 contain the reported daily values of the operational incubatort, operational reagent3, operational ambient3, and operational codes3, respectively.
  • Columns 1403, 1405, 1407, and 1409 are normalized values of the four values of operational incubatort, operational reagent3, operational ambient3, and operational codes3, respectively, obtained in the same manner as values of operational variables were in Example 1.
  • Column 1410 contains values of the daily operational composite3 value, the second statistic calculated.
  • FIG. 15 contains the 406 diagnostic clinical analyzer control chart where each value of the operational composite3 in column 1410 is plotted as dots 1502.
  • the trimmed baseline composite3 control chart limit value of 89.603 is represented by the line 1501. Note that the daily operational composite3 value starts out at a low value for many days then jumps up to exceed the control limit for two out of three days on November 20, 2008. After returning to a low value for a couple more days, the operational composite3 value once again exceeds the control chart limit for two days out of three. Both of the above events would result in an alert regarding an impending analytical failure. Subsequently, for the duration of this test data, values of daily operational composite3 remained below the control chart limit.
  • This example demonstrates the higher imprecision in the results generated by MicroTipTM diagnostic clinical analyzers that more frequently flag an impending failure.
  • the detection of impending failures not only makes fixing failures faster, it also allows for better performance in the assays by flagging analyzers most likely to have less than perfect assay performance. Such improvements are otherwise difficult to make because often an assay result examined in isolation appears to meet the formal tolerances set for the assay. Detecting that the variance in the assay results reflect increased imprecision allows measures to be taken to reduce the variance and, as a result, increase the reliability of the assay results.
  • the baseline data were processed as represented in Fig. 16 to calculate the mean and standard deviation for each of the above variables followed by trimming to remove values that were more than three standard deviations away from the mean by dropping such entries.
  • the remaining variable entries were processed to compute a trimmed mean and trimmed standard deviation for each of the eight variables.
  • the sum of the mean and three standard deviations of the trimmed variable was used to normalize the variable values as described earlier. This implementation choice is not intended to and should not be understood to be a limitation on the scope of the invention unless such is expressly indicated in the claims.
  • the normalization factor, sum of the mean and three standard deviations of the trimmed variables is used as a threshold for the variable to flag unusual changes in operational data and assist in trouble shooting and servicing clinical diagnostic analyzers.
  • Example data for the Calcium ( 1 Ca') assay in TABLE 2 show the identifiers for five 'bad' diagnostic clinical analyzers, the number of times Quality
  • Control reagents were measured on each of them, the mean, the Standard Deviation, and the Coefficient of Variation followed by similar numbers for five 'good' clinical diagnostic analyzers.
  • Analyzers were selected based on similar QC. Since customers run QC fluids from various QC manufacturers, analyzers were identified that had similar means (indicating the same manufacturer) for QC reagents for multiple assays. It is useful to appreciate that the term 'impending failure' does not require similarly degraded performance for different assays. While ALB (for albumin) assays on Analyzer 1 may run the same QC reagents for ALB as Analyzer 2, Analyzer 1 may be using a different QC fluid for Ca assays and thus may differ from Analyzer 2. Therefore, at least five (5) (out of the twelve(12)) analyzers were identified that ran QC with a similar mean (manufacturer or comparable performance) for each assay.
  • analyzers identified as the five 'bad' or the five 'good' analyzers were not the same for all assays.
  • the worst analyzer for Fe assays may not be the worst for Mg assays based on the frequency of triggering alerts.
  • EXAMPLE 5 Assay Yield affected by impending failures This example uses the analyzers and data described in Example 4. Another examined measure in those analyzers was the First Time Yield (FTY), which refers to the number of acceptable assays as a fraction of all of the assays run on the analytical analyzer in a time period.
  • FY First Time Yield
  • the FTY measure examines the performance of actual assays on clinical diagnostic analyzers.
  • a low FTY value indicates that many assay results are being rejected by assay failure detection systems and procedures — as opposed to the detection of an impending failure of the system rather than a particular assay — which often requires repeating the assay and reduces the throughput.
  • an FTY value of 90% or better, and typically better than 94% is expected for diagnostic clinical analyzers.
  • FTY was also compared for 5 "good” (with the highest FTY) and 5 "bad” (with the lowest FTY) systems with the "bad” systems experiencing a lower FTY.
  • Example data in TABLE 3 below show the identifiers for five 'Bad' diagnostic clinical analyzers, the number of assays run on each of them, the respective first time yields followed by similar numbers for 'Good' clinical diagnostic analyzers.
  • This example uses the analyzers and data described in Example 4. Using operational data, for selected colorimetric assays ten (10) clinical diagnostic analyzer systems were identified that exhibited high average Alert Values (which is compared to the Baseline Composite Control Chart Limit to generate an Alert) and compared to twelve (12) clinical diagnostic analyzer systems that had a low average Alert Value. For this analysis the Alert Value for an analyzer triggering the Alert was not counted — in other words, the triggering value was discounted — when comparing the assay performance on known Quality Control ( 1 QC) reagents. Systems triggering the alert can have a small number of triggered values that can be very large and artificially elevate the average. For this method the alert values when the Alert was triggered were discounted to identify systems that had an elevated mean value. This is very similar to Example 4, but includes some systems that had an elevated mean Alert Value but would not have triggered the alert for all of the elevated Alert Values.
  • This example also uses an analyzer similar to those described in Example 4. QC reagents based data was evaluated for all CM assays on a single system. The analyzer performance in a time period when the system was exceeding the Alert limit was compared to the analyzer performance during a time period when it was not exceeding the Alert limit. Such a comparison ensures similar environment, operator protocol, and reagents and allows evaluation of the utility of the detection of impending failures. This method provides a gauge to measure performance differences in assay results (i.e. QC results).
  • An analyzer that is consistently about the Baseline Composite Control Chart Limit may be selected for proactive repair or the information associated with the assay predictive alert can be used in a reactive mode when a customer calls about assay performance concerns. If the composite alert is above the threshold, which indicates that one or more of the underlying variables are abnormal, a preferred process to identify a cause is to look at the individual variables. For instance, in Example 4 there are eight individual variables that make up the Alert Value (which is compared to the Baseline Composite Control Chart Limit). Each of these variables has a threshold, which in a preferred embodiment was used to both trim data and to normalize the values of the variables.
  • the schematic shows a listing of various monitored variables, their respective thresholds and the values on various time points.
  • the individual thresholds are exceeded (not necessarily resulting in triggering an alert for an impending failure)
  • the variable is flagged.
  • different colors, flashing values and other techniques may be used as is well known to those having ordinary skill in the art.
  • FIG. 9 displays a simple electronic circuit that has four input signals each having the characteristic of an independent random variable with known mean and known variance.
  • the explicit characteristics of each signal is as follows:
  • E() denotes the expected value
  • V() denotes the variance
  • the characteristics of signal A can be computed using known relationships for the expected value and variance of sums and products of independent random variables as found in H. D. Brunk, An Introduction to Mathematical Statistics, 2 nd Edition, Blaisdell Publishing Company, 1965, which is hereby incorporated by reference, and in Alexander McFarlane Mood, Franklin A. Graybill, and Duane C. Boes, Introduction to the Theory of Statistics, 3 rd Edition, McGraw-Hill, 1974, which is hereby incorporated by reference. Specifically,
  • the characteristics of signal C can be determined as follows:
  • Tornado tables or diagrams are obtained by specifying a range of values over which the input signal characteristic is to be varied while monitoring the change in the output signal C variance. Doing this results in the tornado table as presented in FIG. 10.
  • the variance of signal Y has the greatest influence on the variance of signal C by an overwhelming margin. In descending order of influence is the expected value of W, the expected value of X, the expected value of Y, the variance of Z, the variance of X, and the variance of W. For this particular circuit, small variations in the variance of Y will have a significant impact on the variance of signal C.
  • FIG. 10 also contains a tornado diagram of the information in the tornado table graphically pointing out the significant influence of the variance of Y.

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US20120042214A1 (en) 2012-02-16
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