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Common cause and special cause (statistics)
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<h2 id="origins-and-concepts">Origins and concepts</h2><p> In 1703, <a href="/facts/Jacob_Bernoulli/rUnwozsy">Jacob Bernoulli</a> wrote to <a href="/facts/Gottfried_Leibniz/cTc2er83">Gottfried Leibniz</a> to discuss their shared interest in applying <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Probability/fgYvMhwb">probability</a> to games of chance. <a href="/facts/Jacob_Bernoulli/rUnwozsy">Bernoulli</a> speculated whether it would be possible to gather <a href="/facts/Mortality_rate/s4gmxyFV">mortality</a> data from gravestones and thereby calculate, by their existing practice, the probability of a man currently aged 20 years outliving a man aged 60 years. <a href="/facts/Gottfried_Leibniz/cTc2er83">Leibniz</a> replied that he doubted this was possible:</p><blockquote><p><i>Nature has established patterns originating in the return of events but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary.</i></p></blockquote> <p>This captures the central idea that some variation is predictable, at least approximately in frequency. This <i>common-cause variation</i> is evident from the experience base. However, new, unanticipated, emergent or previously neglected phenomena (e.g. "new diseases") result in variation outside the historical experience base. <a href="/facts/Walter_A._Shewhart/7rE37orq">Shewhart</a> and <a href="/facts/W._Edwards_Deming/ytaxg6sv">Deming</a> argued that such <i>special-cause variation</i> is fundamentally unpredictable in frequency of occurrence or in severity. </p> <p><a href="/facts/John_Maynard_Keynes/4otHjBRu">John Maynard Keynes</a> emphasised the importance of special-cause variation when he wrote:</p><blockquote><p><i>By "uncertain" knowledge ... I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty ... The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention ... About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know!</i></p></blockquote> <h2 id="definitions">Definitions</h2> <h3>Common-cause variations</h3> <p>Common-cause variation is characterised by: </p> <ul><li>Phenomena constantly active within the system;</li> <li>Variation predictable <a href="/facts/Probability/fgYvMhwb">probabilistically</a>;</li> <li>Irregular variation within a historical experience base; and</li> <li>Lack of significance in individual high or low values.</li></ul> <p>The outcomes of a perfectly balanced <a href="/facts/Roulette/MVKBkyS8">roulette</a> wheel are a good example of common-cause variation. Common-cause variation is the <i>noise</i> within the system. </p><p><a href="/facts/Walter_A._Shewhart/7rE37orq">Walter A. Shewhart</a> originally used the term <i>chance cause</i>.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> The term <i>common cause</i> was coined by <a href="/facts/Harry_Alpert/xweTNXCM">Harry Alpert</a> in 1947. The <a href="/facts/Western_Electric_Company/j15TJJcx">Western Electric Company</a> used the term <i>natural pattern</i>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> Shewhart called a process that features only common-cause variation as being <i>in <a href="/facts/Statistical_control/Qwkqg5d4">statistical control</a></i>. This term is deprecated by some modern statisticians who prefer the phrase <i>stable and predictable</i>. </p> <h3>Special-cause variation</h3> <p>Special-cause variation is characterised by: </p> <ul><li>New, unanticipated, emergent or previously neglected phenomena within the system;</li> <li>Variation inherently unpredictable, even probabilistically;</li> <li>Variation outside the historical experience base; and</li> <li>Evidence of some inherent change in the system or our knowledge of it.</li></ul> <p>Special-cause variation always arrives as a surprise. It is the <i>signal</i> within a system. </p><p>Walter A. Shewhart originally used the term <i>assignable cause</i>.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> The term <i>special-cause</i> was coined by <a href="/facts/W._Edwards_Deming/ytaxg6sv">W. Edwards Deming</a>. The Western Electric Company used the term <i>unnatural pattern</i>.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> </p> <h2 id="examples">Examples</h2> <h3>Common causes</h3> <ul><li>Inappropriate procedures</li> <li>Poor design</li> <li>Poor maintenance of machines</li> <li>Lack of clearly defined <a href="/facts/Standard_operating_procedure/gDkxSoX0">standard operating procedures</a></li> <li>Poor working conditions, e.g. lighting, noise, dirt, temperature, ventilation</li> <li>Substandard raw materials</li> <li><a href="/facts/Measurement/rsLLbn1s">Measurement</a> error</li> <li><a href="/facts/Quality_control/lnXbvqvp">Quality control</a> error</li> <li>Vibration in industrial processes</li> <li>Ambient temperature and humidity</li> <li>Normal <a href="/facts/Wear_and_tear/Jd5HGq7U">wear and tear</a></li> <li>Variability in settings</li> <li>Computer <a href="/facts/Response_time_(technology)/3kQrmztQ">response time</a></li></ul> <h3>Special causes</h3> <ul><li>Faulty adjustment of equipment</li> <li>Operator <a href="/facts/Sleeping_while_on_duty/lMbudqtT">falls asleep</a></li> <li>Defective controllers</li> <li>Machine malfunction</li> <li>Fall of ground</li> <li><a href="/facts/Crash_(computing)/I8yn65yt">Computer crash</a></li> <li>Deficient batch of raw material</li> <li><a href="/facts/Voltage_spike/XYdAJkje">Power surges</a></li> <li>High healthcare demand from elderly people</li> <li>Broken part</li> <li>Insufficient awareness</li> <li>Abnormal traffic (<a href="/facts/Click_fraud/suboHSvE">click fraud</a>) on web ads</li> <li>Extremely long lab testing turnover time due to switching to a new computer system</li> <li>Operator absent<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></li></ul> <h2 id="importance-to-industrial-and-quality-management">Importance to industrial and quality management</h2> <p>A special-cause failure is a failure that can be corrected by changing a component or process, whereas a common-cause failure is equivalent to noise in the system and specific actions cannot be made to prevent the failure. </p> <p><a href="/facts/Harry_Alpert/xweTNXCM">Harry Alpert</a> observed:</p><blockquote><p><i>A riot occurs in a certain prison. Officials and sociologists turn out a detailed report about the prison, with a full explanation of why and how it happened here, ignoring the fact that the causes were common to a majority of prisons, and that the riot could have happened anywhere.</i></p></blockquote><p> Alpert recognises that there is a temptation to react to an extreme outcome and to see it as significant, even where its causes are common to many situations and the distinctive circumstances surrounding its occurrence, the results of mere chance. Such behaviour has many implications within management, often leading to ad hoc interventions that merely increase the level of variation and frequency of undesirable outcomes. </p><p><a href="/facts/W._Edwards_Deming/ytaxg6sv">Deming</a> and <a href="/facts/Walter_A._Shewhart/7rE37orq">Shewhart</a> both advocated the <a href="/facts/Control_chart/mY27mrUe">control chart</a> as a means of managing a <a href="/facts/Business_process/fYH2eREc">business process</a> in an economically efficient manner. </p> <h2 id="importance-to-statistics">Importance to statistics</h2> <h3>Deming and Shewhart</h3> <p>Within the <a href="/facts/Frequency_probability/1f1TjSey">frequency probability</a> framework, there is no process whereby a <a href="/facts/Probability/fgYvMhwb">probability</a> can be attached to the future occurrence of special cause. One might naively ask whether the <a href="/facts/Bayesian_probability/Cvn7WWfG">Bayesian</a> approach does allow such a probability to be specified. The existence of special-cause variation led <a href="/facts/John_Maynard_Keynes/4otHjBRu">Keynes</a> and <a href="/facts/W._Edwards_Deming/ytaxg6sv">Deming</a> to an interest in <a href="/facts/Bayesian_probability/Cvn7WWfG">Bayesian probability</a>, but no formal synthesis emerged from their work. Most statisticians of the Shewhart-Deming school take the view that special causes are not embedded in either experience or in current thinking (that's why they come as a surprise; their prior probability has been neglected—in effect, assigned the value zero) so that any subjective probability is doomed to be hopelessly badly <a href="/facts/Calibration_(probability)/sLeDYpHa">calibrated</a> in practice. </p><p>It is immediately apparent from the <a href="/facts/Gottfried_Leibniz/cTc2er83">Leibniz</a> quote above that there are implications for <a href="/facts/Sampling_(statistics)/kIb01xdL">sampling</a>. Deming observed that in any forecasting activity, the <a href="/facts/Population_(statistics)/KAILs8E3">population</a> is that of future events while the <a href="/facts/Sampling_frame/LhrXV2FS">sampling frame</a> is, inevitably, some <a href="/facts/Subset/SJGERmbA">subset</a> of historical events. Deming held that the disjoint nature of population and sampling frame was inherently problematic once the existence of special-cause variation was admitted, rejecting the general use of probability and conventional statistics in such situations. He articulated the difficulty as the distinction between <a href="/facts/Analytic_and_enumerative_statistical_studies/NgCPewky">analytic and enumerative statistical studies</a>. </p><p><a href="/facts/Walter_A._Shewhart/7rE37orq">Shewhart</a> argued that, as processes subject to special-cause variation were inherently unpredictable, the usual techniques of probability could not be used to separate special-cause from common-cause variation. He developed the <a href="/facts/Control_chart/mY27mrUe">control chart</a> as a statistical <a href="/facts/Heuristic/BcBEkv9c">heuristic</a> to distinguish the two types of variation. Both Deming and <a href="/facts/Walter_A._Shewhart/7rE37orq">Shewhart</a> advocated the control chart as a means of assessing a process's state of <a href="/facts/Statistical_control/Qwkqg5d4">statistical control</a> and as a foundation for forecasting. </p> <h3>Keynes</h3> <p><a href="/facts/John_Maynard_Keynes/4otHjBRu">Keynes</a> identified three domains of probability:<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p> <ul><li><a href="/facts/Frequency/QUSbPaW8">frequency</a> probability;</li> <li>subjective or <a href="/facts/Bayesian_probability/Cvn7WWfG">Bayesian probability</a>; and</li> <li>events lying outside the possibility of any description in terms of probability (special causes)</li></ul> <p>and sought to base a <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> thereon. </p> <h2 id="common-mode-failure-in-engineering">Common mode failure in engineering</h2> <p>Common mode failure has a more specific meaning in engineering. It refers to events which are not <a href="/facts/Statistics/DNPsKGYU">statistically independent</a>. Failures in multiple parts of a system may be caused by a single fault, particularly random failures due to environmental conditions or aging. An example is when all of the pumps for a fire sprinkler system are located in one room. If the room becomes too hot for the pumps to operate, they will all fail at essentially the same time, from one cause (the heat in the room).<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Another example is an electronic system wherein a fault in a power supply injects noise onto a supply line, causing failures in multiple subsystems. </p><p>This is particularly important in safety-critical systems using multiple <a href="/facts/Redundancy_(engineering)/odqzTmIo">redundant</a> channels. If the probability of failure in one subsystem is <i>p</i>, then it would be expected that an <i>N</i> channel system would have a probability of failure of <i>p</i><i>N</i>. However, in practice, the probability of failure is much higher because they are not statistically independent; for example <a href="/facts/Ionizing_radiation/vw0d9GaT">ionizing radiation</a> or <a href="/facts/Electromagnetic_interference/gv3DlKNr">electromagnetic interference</a> (EMI) may affect all the channels.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p><p>The <i>principle of redundancy</i> states that, when events of failure of a component are statistically independent, the probabilities of their joint occurrence multiply.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> Thus, for instance, if the probability of failure of a component of a system is one in one thousand per year, the probability of the joint failure of two of them is one in one million per year, provided that the two events are statistically independent. This principle favors the strategy of the redundancy of components. One place this strategy is implemented is in <a href="/facts/RAID_1/StvCqldY">RAID 1</a>, where two hard disks store a computer's data redundantly. </p><p>But even so, a system can have many common modes of failure. For example, consider the common modes of failure of a RAID1 where two disks are purchased from an online store and installed in a computer: </p> <ul><li>The disks are likely to be from the same manufacturer and of the same model, therefore they share the same design flaws.</li> <li>The disks are likely to have similar serial numbers, thus they may share any manufacturing flaws affecting production of the same batch.</li> <li>The disks are likely to have been shipped at the same time, thus they are likely to have suffered from the same transportation damage.</li> <li>As installed both disks are attached to the same power supply, making them vulnerable to the same power supply issues.</li> <li>As installed both disks are in the same case, making them vulnerable to the same overheating events.</li> <li>They will be both attached to the same card or motherboard, and driven by the same software, which may have the same bugs.</li> <li>Because of the very nature of RAID1, both disks will be subjected to the same workload and very closely similar access patterns, stressing them in the same way.</li></ul> <p>Also, if the events of failure of two components are maximally statistically dependent, the probability of the joint failure of both is identical to the probability of failure of them individually. In such a case, the advantages of redundancy are negated. Strategies for the avoidance of common mode failures include keeping redundant components physically isolated. </p><p>A prime example of redundancy with isolation is a <a href="/facts/Nuclear_power/jzSyvxSn">nuclear power plant</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a><a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> The new <a href="/facts/Advanced_Boiling_Water_Reactor/2lRHFf8V">ABWR</a> has three divisions of <a href="/facts/Emergency_Core_Cooling_System/C1eXQ83x">Emergency Core Cooling Systems</a>, each with its own generators and pumps and each isolated from the others. The new <a href="/facts/European_Pressurized_Reactor/xhc3X98F">European Pressurized Reactor</a> has two <a href="/facts/Containment_building/kIlXYEEK">containment buildings</a>, one inside the other. However, even here it is possible for a common mode failure to occur (for example, in the <a href="/facts/Fukushima_Daiichi_Nuclear_Power_Plant/oEeao1Lz">Fukushima Daiichi Nuclear Power Plant</a>, mains power was severed by the <a href="/facts/2011_T%25C5%258Dhoku_earthquake_and_tsunami/pyIXeVlS">Tōhoku earthquake</a>, then the thirteen backup diesel generators were all simultaneously disabled by the subsequent tsunami that flooded the basements of the turbine halls). </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Corrective_and_preventive_action/bWydduL4">Corrective and preventive action</a> (CAPA)</li> <li><a href="/facts/Nuclear_safety/TtudaSPh">Nuclear safety</a></li> <li><a href="/facts/Probabilistic_risk_assessment/VIkIGuRp">Probabilistic risk assessment</a></li> <li><a href="/facts/Statistical_process_control/Qwkqg5d4">Statistical process control</a></li> <li><a href="/facts/There_are_unknown_unknowns/m68aS2g2">There are unknown unknowns</a></li></ul> <h2 id="bibliography">Bibliography</h2> <ul><li>Deming, W. E. (1975) On probability as a basis for action, <i>The American Statistician</i>, 29(4), pp. 146–152</li> <li>Deming, W. E. (1982) <i>Out of the Crisis: Quality, Productivity and Competitive Position</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-30553-5</li> <li>Keynes, J. M. (1936) <i>The General Theory of Employment, Interest and Money</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 1-57392-139-4</li> <li>Keynes, J. M. (1921)<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a></li> <li>Knight, F. H. (1921) <i>Risk, Uncertainty and Profit</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 1-58798-126-2</li> <li>Shackle, G. L. S. (1972) <i>Epistemics and Economics: A Critique of Economic Doctrines</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 1-56000-558-0</li> <li>Shewhart, W. A. (1931) <i>Economic Control of Quality of Manufactured Product</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-87389-076-0</li> <li>Shewhart, W. A. (1939) <i>Statistical Method from the Viewpoint of Quality Control</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-65232-7</li> <li>Wheeler, D. J. & Chambers, D. S. (1992) <i>Understanding Statistical Process Control</i> <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-945320-13-2</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Shewhart, Walter A. (1931). Economic control of quality of manufactured product. New York City: D. Van Nostrand Company, Inc. p. 7. OCLC 1045408. <a href="/wiki/Walter_A._Shewhart" target="_blank">/wiki/Walter_A._Shewhart</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Western Electric Company (1956). Introduction to Statistical Quality Control handbook (1 ed.). Indianapolis, Indiana: Western Electric Co. pp. 23–24. OCLC 33858387. <a href="/wiki/Western_Electric_Company" target="_blank">/wiki/Western_Electric_Company</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Shewhart, Walter A. (1931). Economic control of quality of manufactured product. New York City: D. Van Nostrand Company, Inc. p. 14. OCLC 1045408. <a href="/wiki/Walter_A._Shewhart" target="_blank">/wiki/Walter_A._Shewhart</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Western Electric Company (1956). Introduction to Statistical Quality Control handbook (1 ed.). Indianapolis, Indiana: Western Electric Co. pp. 23–24. OCLC 33858387. <a href="/wiki/Western_Electric_Company" target="_blank">/wiki/Western_Electric_Company</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"Statistical Inference". Archived from the original on 7 October 2006. Retrieved 13 November 2006. <a href="https://web.archive.org/web/20061007055524/http://www.anu.edu.au/nceph/surfstat/surfstat-home/5-1-2.html" target="_blank">https://web.archive.org/web/20061007055524/http://www.anu.edu.au/nceph/surfstat/surfstat-home/5-1-2.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Keynes, J. M. (1921). A Treatise on Probability. ISBN 0-333-10733-0. {{cite book}}: ISBN / Date incompatibility (help) <a href="0-333-10733-0" target="_blank">0-333-10733-0</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Thomson, Jim (February 2012). "Common-Mode Failure Considerations in High-Integrity C&I Systems" (PDF). Safety in Engineering. Retrieved 21 November 2012. <a href="http://www.safetyinengineering.com/FileUploads/CMF%20in%20high-integrity%20C&I%20systems_1329414280_2.pdf" target="_blank">http://www.safetyinengineering.com/FileUploads/CMF%20in%20high-integrity%20C&I%20systems_1329414280_2.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Randell, Brian Design Fault Tolerance in The Evolution of Fault-Tolerant Computing, Avizienis, A.; Kopetz, H.; Laprie, J.-C. (eds.), pp. 251–270. Springer-Verlag, 1987. ISBN 3-211-81941-X. <a href="/wiki/Brian_Randell" target="_blank">/wiki/Brian_Randell</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>"SEI Framework: Fault Tolerance Mechanisms". Redundancy Management. NIST High Integrity Software Systems Assurance. 30 March 1995. Archived from the original on 24 November 2012. Retrieved 21 November 2012. <a href="https://web.archive.org/web/20121124040539/http://hissa.nist.gov/chissa/SEI_Framework/framework_16.html" target="_blank">https://web.archive.org/web/20121124040539/http://hissa.nist.gov/chissa/SEI_Framework/framework_16.html</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Edwards, G. T.; Watson, I. A. (July 1979). A Study of Common-Mode Failures. UK Atomic Energy Authority: Safety and Reliability Directorate. SRD R146.{{cite book}}: CS1 maint: publisher location (link) <a href="/wiki/Template:Cite_book" target="_blank">/wiki/Template:Cite_book</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Bourne, A. J.; Edwards, G. T.; Hunns, D. M.; Poulter, D. R.; Watson, I. A. (January 1981). Defences against Common-Mode Failures in Redundancy Systems – A Guide for Management, Designers and Operators. UK Atomic Energy Authority: Safety and Reliability Directorate. SRD R196.{{cite book}}: CS1 maint: publisher location (link) <a href="/wiki/Template:Cite_book" target="_blank">/wiki/Template:Cite_book</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Keynes, J. M. (1921). A Treatise on Probability. ISBN 0-333-10733-0. {{cite book}}: ISBN / Date incompatibility (help) <a href="0-333-10733-0" target="_blank">0-333-10733-0</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> </ol>