topology of the saff-sequen 4096x2460@1x















The “Device”

The Industrial Machinery has plenty of Devices, vital to let them operate. Why a team including many thousands of physicists and engineers, participating to Manhattan Project, named “Device” what detonated first time in the New Mexico desert ?  It’ll become more clear in the following. Deeply examining its triggering, we’ll discover a tree-like de Moivre causal structure.


Fusing, considered the Root Cause of whatever explosion, is just one superimposed component of an extremely longer sequence of conditions before and after, greater and smaller, than the Fuzing. Visible the stepped sequence of states of the chemical explosives until implosion of Device's total 126.2 kg of Plutonium and Uranium. An irreversible sequence of states comprised between the firing of 32 detonators and the final nuclear fission, chain reaction and following detonation 


One admitting reversible macroscopic actions, until reaching a certain state.  After that state, the sequence becomes irreversible, admitting nearly (“nearly” meaning >99.999… % ) just a single temporary state visible in the animation above: the device detonation.  Fusing is a sensitive subject and, when describing nuclear weapons' fusing, still more sensitive. What follows had been impossible to write until a few years ago, when some informations reached the public domain. The subjects of fusing and triggering are strictly intertwined with the central idea of Root Cause Analysis, the causal relation. Their deep study allows to understand what is unclear to the majority of the root cause Analysist or Problem Solvers. Say, that the idea of causal relation, as the divide between a Cause and an Effect, is obsolete.  And, closely looking matter and radiation of which all is made, it is a myth. Finally, the exam of the fusing system of the nuclear weapons constitutes a reference of good-practices when Designing a system, Industrial Machinery included, which have to assure its function in the harshest thinkable conditions.



 The triggering procedure of all nuclear weapons is commonly named SAFF-sequence.  It is particularly complex, backed-up by, and interlocked with other systems. Much more conditioned than the conventional bombs adopting chemical high explosives (HE). At the centre of the model visible above the historic implosion A-bomb. All around the central red coloured initiator.  A Beryllium-Polonium neutrons’ source tagged (1), a nucleus of Plutonium-239 weighing 6.2 kg tagged (2) and a neutron reflector of depleted Uranium-238 weighing 120 kg and tagged (4) (  RIA Novosti, 2014)








A tree-like irreversible structure

At the centre of the model visible in the figure above, the historic implosion A-bomb.  All around the Beryllium-Polonium central red coloured neutrons’ source tagged (1), a nucleus of Plutonium-239 weighing 6.2 kg tagged (2) and a neutron reflector of Uranium-238 weighing 120 kg, tagged (4).           

conventional weapon fuze med hr


Its detonation releases an energy of 88 terajoule, equivalent to 21 kiloton of TNT.   The Safing-Arming-Fusing-Firing sequence which lets this Device implode and detonate, is a tree-like irreversible structure.   The effect of some of the Events cannot be reversed.   An electric Trigger cabling ignites the chemical high explosives compressing the fissile material inner hemispheres.  The electric Trigger carries a signal deriving by the superposition of several arming, fuzing and firing conditions related to mechanic, electric, radar and barometric devices.    In our special case the arming and fusing system consisted of: 

  • 2 timers, in parallel, set to 15 seconds for safing and arming plugs, wired in series with a second parallel pair, appeared to satisfy requirements for certainty of operation and safety against inadvertent early arming;
  • 6 barometric switches, connected in parallel; 
  • 4 radars, connected in parallel, with an effective range of only < 800 m, equipped with the Yagi antennas patented a few months before (see figure below), tunable (325-485) MHz;

 

  The modern fuze of a conventional HE weapon is a complex kind of Trigger.  The weapon, non visible in the figure at left side, presents at least five Safeties:  (a) Mechanic, the Fuze on side has to be introduced into the weapon;  (b) Mechanic, insertion of the arming wire;  (c) Mechanic, removal the red coloured tagged metal safety pin;  (d) Electronics, a Safe Time setting;  (e) Electronics, a Burst Height setting.   They are Conditions given in a specific time-ordered sequence where the fifth Event (“Burst Height reached”) plays the role of Root Cause for the firing action.  Finally, detonation’s Root Cause is the last firing action (e) because changes the state of the HE weapon.  HE is a highly exothermal enthropic object, something totally irreversible (  Reutech, 2014) 



The original US Patent, filed Nov. 17, 1944, of the folded dipole Yagi antenna.  In the “Device” four of these elements were installed as part of a redundant Radar system.  When an altitude ~ 1600 m was reached, they triggered the start of the transfer of electricity from the batteries to the electric Capacitors. Capacitors later rapidly discharged in tens of detonators (  USPTO, 2014)  


The Barometric sensors switched at the atmospheric pressure expected to be associated to an altitude of ~1670 m.   Their change of state, triggered the Radar units, as the weapon neared the detonation altitude of ~600 m.   At least 2 of the 4 radars had to agree that the Radar return signal from the ground was compatible with the correct altitude, sending this signal relay back to the fuzing system electronics named Clock Box, visible open in a black and white figure below.   The interconnection of series and parallel was determined by the internal wiring of the “Clock Box”, from where gets out the final firing signal.



Close-up on reversible and irreversible

processes

In the present case, what plays the role of detonation’s Root Cause is the last event (8. firing) in the Time-ordered sequence: 





  1. mechanical arming in the plane, introducing the central Beryllium-Polonium initiator [tagged (1)] and the Plutonium-239 nucleus [tagged (2)] when approaching the target;
  2. mechanical arming in the plane, introducing the missing high-explosive lens [one of them visible above tagged (5)], when approaching the target;
  3. device release at an altitude ranging (10300-10700) m;
  4. electrical arming, when the device starts to fall by the plane. The weapon was released from the bomb bay; Connected to the aircraft by pull-out wires attached to the first set of clock switches, as the bombs left the bomb bay these wires were pulled-out activating the timers;
  5. time arming.  15 seconds after bomb release, when the weapon had fallen 1200 m, the Timer switches closed part of the firing circuit;
  6. barometric arming.  When reached an altitude ~1670 m, the barometric switches closed another part of the firing circuit, allowing flow of electrical current from the batteries in the bomb to: (a) charge electric Capacitors and (b) turn on the Radar fuses;
  7. radar arming.  At an altitude of ~600 m, the emitted Radar signals reflecting from the ground, completed the final part of the firing circuit triggering the detonation signal thru the “Clock Box”;
  8. firing.  Electrons discharge from the Capacitors (see figure below) into the 32 detonators (above tagged (6), firing the High Explosive lenses imploding the Uranium-238 and the Plutonium-239 core with Beryllium initiator inside, until the critical mass starting a chain reaction. 



Root Cause and Conditions


Root Cause is the last step, the  8.  firing when 32 Exploding BridgeWire (EBW) detonators were powered by the discharge of the high voltage in the Capacitors. In the EBW detonators, see figure below, the wire is heated so quickly by the high firing current that the wire vaporizes and explodes due to electric resistance heating. The time precision and consistency of EBWs is less than 25 ns, allowing to synchronise the tens of Detonators’ acting as explosive’ initiator. In the figure above they are tagged (6).    They ignite the chemical high-explosives to detonate until imploding the central masses of radioactive metal, to let them reach the critical mass. This habit to attribute to the last step the role of Root Cause for an Effect of a mind-boggling serie of precedent causes, considering them mere “Conditions”, hides an ambiguity. Ambiguity physically replicated in the many branchings (states) whose information difference is just 1 bit or leaves extremely close to the one at the onset of the Root Cause. 


 The batteries, discharged themselves in the Capacitors when reaching the state 6. of barometric arming at an altitude of 1670 m.  Capacitors discharged to the 32 detonators at the state 8. “firing”.  An electromechanic circuit, including relays, resistors, capacitors, fuses and batteries (  Los Alamos National Laboratory, 2014).   


ebw detonators med

  In the Exploding Bridge-Wire (EBW) detonators a 1-mm long wire is heated so quickly by the high firing current that the wire vaporizes and explodes due to electric resistance heating.  That electrical driven explosion then fires the detonator's initiator explosive (abridged under CC 2.5 by   Timo Halen, 2006) 

The entire sequence of Conditions determines that particular state of an object named Effect. Looking the entire sequence in its correct aspect, a tree-like time-ordered sequence, it is just and only that last action immediately before the Effect, what creates the branch named Effect.  All the precedents causes are named “Conditions” because, on the opposite, by each one of them they may branch-out several effects completely different than what Root Cause Analysis and Actuarial Science define Incident.  Going much deeper, we observe the entire SAFF-sequence (Safing-Arming-Fuzing-Firing) as just few intermediate step before the many followings, until the 2.5 times compression of the inner masses of Plutonium, what really and only releases the energy.   

In other words: 

...the limit on the space-time scale we imposes as boundary for what we want to describe by mean of the classical paradigms of Cause and Effect, defines what is Cause and what is Effect.

The firing, always considered the Root Cause of whatever explosion, is just one superimposed component of an extremely longer sequence of states before and after, greater and smaller, than the Fuzing.   Reducing the Fusing relevance, classically considered decisive to just ...the last condition immediately before an Effect.

thew device at tinian islan med hr




  The “Device” being finally assembled at Tinian Island. Visible the wiring allowing to discharge the high voltage electric energy from the Capacitors to the 32 Exploding Bridge Wire detonators (  Los Alamos National Laboratory, 2014)









The complete story

“Safing-Arming-Fuzing-Firing (SAFF) sequence which let this device implode and detonate, is a tree-like partially irreversible structure”



Refer to the figure below, showing a historical tree-like structure around the point “q” corresponding to the content of the slice (or leaf, or sheet) including the Plutonium-based implosion-Device commonly named “Fat Man”. Imagine to label as “successful” all of the outcomes where the implosion-Device detonates 600 m over the target, the centre of Nagasaki, Japan, on 9 August 1945.  The place where acted the Root Cause named firing (SAFF-phase 8.). In the figure, each one vertex is a new superposed State of the superposition of the electronic components, cables, connectors, etc. included in the SAFF-system aboard “Fat Man”’s.  Each vertex exists in the State Space and cannot be felt in that 4-dimensional useful approximation, named Physical Space, of the higher-dimensional (>9 dimensions) reality. Thus, mapping one-by-one all possible changes intervened before and after the firing.



 Historical tree-like structure around the point “q”  corresponding to the content of the 3-D slice (or leaf, or sheet) including the SAFF-system into the Clock Box aboard the implosion-Device, on August 9, 1945.  The place where acted the Root Cause firing.  As an example of what happened in other Future unsuccessful branches: the relay, controlled by the firing signal, switching the energy accumulated in the Capacitors failed to switch.  Its contacts glued because oxidised by the sparks associated to too many precedent tests at Tinian island.  This unsuccessful outcome  in a multitude of other branches, determining intermediate outcomes, not implying that relay’s failure.  Implying, as an example, that the Device detonated too high over the target, limiting the damages. 

  • Yellow-coloured   subset of all of the initial conditions including the “ Device's” design, construction, testing at Tinian and dropping;
  • Red-coloured   unsuccessful subset of all of the outcomes.  Set of all of the branches where a negative effect arose by the Root Cause;
  • Green-coloured   successful subset of all of the outcomes.  Set of all of the branches where a positive effect arose by the Root Cause
















The graphic before has to be imagined as just a subsection, result of our selection privileging a univoquely defined vertex (q).  Univoquely defined how?  By the sum of its Past branches.  It exists just a single superposition of Past branches originating the interference we name: “q”.   All of the others, many extremely different and some surely similar, are different for not less than 1 bit.   Then, at least in principle, they may be differentiated. The large scale image from which we excerpted the graphic above, resembles the one in the figure below.   Visibly, there are many other interferences close to “q”, corresponding to states similar between themselves and similar to “q”. Also well visible how nor one of them can correspond or may be confused with the state “q”. The entire set of the interferences and superpositions from whom any other derive, is different than any other.   If the amount of Information we are instrumentally equipped to derive by a measurement should be reduced to ~1 bit, then an ambiguity should surely arise.   Arising in the attribution to the last step immediately before the Effect, of the role of its Root Cause. The causes are all the decisions and conditions preceding the Root Cause.   Visibly, vertexes very far one from the other may originate by (then being in the Future of…) exactly the same set of Past states, aka causes.  The ambiguity has a physical parallel in the multitude of branches (or, states) whose information difference is just 1 bit.   As seen by General Relativity's perspective, leaves extremely close to the one at the onset of the Root Cause.  Meaning that they exist many ways, whose difference is so slight we nearly cannot perceive, to go from a Past state at the point “p” to a Future state at the point “q”. The reticular structure below illustrates the deep physical meaning of the word history.


The graphic before has to be imagined as just a subsection, result of our selection privileging a univoquely defined vertex (q). Univoquely defined how ? By the sum of its Past branches. It exists just a single superposition of Past branches originating the interference we name: “q”. All of the others, however similar, are different for not less than 1 bit. Then, at least in principle, they may be differentiated. The large scale image from which we excerpted the graphic above, resembles much more the one in the figure below. Visibly, there are many other interferences close to “q”, corresponding to states similar between themselves and similar to “q”. Also well visible how nor one of them can correspond or may be confused with the state “q”. The entire set of the interferences and superpositions from whom any other derive, is different than any other. The reticular structure below well illustrates the deep physical meaning of the word history. Random variables are points. Each point a projection in the Sample Space of objects’ properties. Objects’ properties having their full existence in the State Space. The function manifests the relation existing between these two spaces. On side are shown in red and blue color two different functions. As an example: red could represent the transfer function of the Energy of a X-ray photon and blue the transfer function of the Polarisation of the same photon. Distinct physical properties of a single object, whose values appear like two random variables when measured by mean of two measurement devices (e.g., a X-ray phototransistor and a X-ray polarimeter), in their own Sample Spaces. Part of the individual points in the Sample Space are simultaneously related to several points in the State Space Reticular structure hinting to the complexity of the state function. Passing from State to Superposition then Interfering and returning a State, then splitting again to a Superposition of States. An ambiguity lies in the attribution to the last step immediately before the Effect, of the role of its Root Cause. The Causes are all the decisions and conditions preceding the Root Cause. Ambiguity physically existing in the multitude of branches (or, states) whose information difference is just 1 bit. Leaves extremely close to the one at the onset of the Root Cause, as seen by General Relativity's perspective. Meaning that they exist many ways, whose difference is so slight we nearly cannot perceive, to go from a Past state at the point p to a Future state at the point q (image credit leafcutterjohn.com, 2014)


 Reticular structure hinting to the complexity of the state function.  Passing from State to Superposition then Interfering and returning a State, then splitting again to a Superposition of States.   An ambiguity lies in the attribution to the last step immediately before the Effect, of the role of its Root Cause.  The Causes are all the decisions and conditions preceding the Root Cause.   Ambiguity physically existing in the multitude of branches (or, states) whose information difference is just 1 bit.  Leaves extremely close to the one at the onset of the Root Cause, as seen by General Relativity's perspective.   Meaning that they exist many ways, whose difference is so slight we nearly cannot perceive, to go from a Past state at the point p to a Future state at the point q (  leafcutterjohn.com, 2014)





“The entire sequence of Conditions determines that particular state of an object named Effect.  

Looking the entire sequence in its correct aspect, a tree-like time-ordered sequence, it is just and only that last action immediately before the Effect, what creates the branch named Effect.    

All the precedents causes are named “Conditions” because, on the opposite, by each one of them may branch-out several effects completely different than what Root Cause Analysis and Actuarial Science define an "Incident”



Measurements’ Redundancy role

The Designer of the SAFF-system sequence, the physicist Robert Bigham Brode, imagined a particularly redundant system including: 

  • 6  Barometric switches, connected in parallel, to limit to an altitude ~1670 m, that causing a flow of electrical current from the batteries in the bomb to:  (a) charge electric Capacitors and (b) to the Radar fuses;
  • 4  Radars, connected in parallel, with an effective range of only < 800 m, to enable the Capacitors’ discharge “precisely” 600 m above the ground.

originating the Effect named firing, Root Cause of the detonation. Redundancy in the Barometric and Radar Detectors, joint with the exclusive Condition preventing Radars’ arming without agreement of at least 2 of the 4 Radars allows to maximise the separation of the subset of the Successful outcomes' states by the Unsuccessful outcomes' states.   In the framework of Signal Theory, redundancy on the amount of Detectors’ making independent measurements of the same property of the same object, acts allowing more precise estimation of the true value of the random variable.   Refer to the figure below.   In the same classic framework, to have an infinite amount of Detectors is the equivalent of the observation of the entire State Space from an infinite amount of Sample Spaces, by mean of the observation of an infinity of random variables.  Thus reconstructing the totality of the fine-details forming what is a physical Property.   True value that in the classic approximation we always know only approximately because: 

  • registering random variables in a reduced amount of Sample Spaces;
  • having available only a limited time to observe and record random values.


 Random variables are points. Each point a projection in the Sample Space of objects’ properties. Objects’ properties having their full existence in the State Space.  The function manifests the relation existing between these two spaces.  On side are shown in red and blue color two different functions.  As an example: red could represent the transfer function of the Energy of a X-ray photon and blue the transfer function of the Polarisation of the same photon.  Distinct physical  properties of a single object, whose values appear like two random variables when measured by mean of two measurement devices (e.g., a X-ray phototransistor and a X-ray polarimeter), in their own Sample Spaces.  Part of the individual points in the Sample Space are simultaneously related to several points in the State Space



Designer's role



modern principle of superpo med hr

Robert Bigham Brode before to design the “Device”’s SAFF-sequence, focused all outcomes he could think.   Those particular Successful and Unsuccessful outcomes were   branched before into his own mind.   Human-mind itself part of the State Space.   The Reader can immediately understand that, thinking those components and relating them with that logic, the Designer:

  1. maximised the amount of branches marked with yellow colour as Conditions, thus occupying a wide Space in the State Space;
  2. minimised the amount of branches marked with red colour as Unsuccessful outcomes, thus forcing them in a small Space in the State Space;
  3. maximised the amount of branches marked with green colour as Successful outcomes, thus occupying a wide Space in the State Space.








“...start to to visualize all possible combinations of failures of these 32 separate and independent wirings.  

You’ll discover immediately the number 4 294 967 296. 

Amount giving Us a clue to the enormous amount of branches where ...Nagasaki never became famous abroad”

From where they get out the Designer's choices maximising the last point 3. Successful outcomes ?    The answer to this question, frankly speaking, probably was given yet over twenty five centuries ago it.   When Greek philosophers conjectured that we only pick up some ideas, floating in the multitude of the pre-existing ideas.    The concept of stateState Space, in the  is in some way reminiscent of that ancient conjecture, when taking in due consideration that in the State Space each state includes all possible future outcomes.    Meaning that at the point q when and where the firing circuit discharged the Capacitors in the 32 Detonators, all possible future outcomes existed in superposition.   However, a kind of existence far from our common sense and perception.   One which can only be fully defined in mathematical terms in an abstract space (Hilbert) where all of the possible outcomes of an action exist before the action.  

   


What no Designer can do

Brode, Designer of the “Device”’s SAFF-sequence, has not really excluded all Unsuccessful outcomes. As an example, it could have been enough to have a mechanical failure at the start of the dropping phase, when the bomb left the plane, affecting just one of the 32 conductors carrying power to the detonators.  All of the following branches of the time-ordered SAFF-sequence would have been fulfilled as thinked by Brode.  But, it had yet been calculated that the missing detonation of just one of the 32 chemical explosives should have prevented the spherical simmetry implosion resulting in the nuclear chain reaction, reducing it to one of 2.4 ton of conventional explosive. 


Let us define the number of degrees of freedom N of the system to be the natural logarithm of the dimension N of its Hilbert space H:

             N  =  ln N  = ln dim( H )


The number of degrees of freedom is equal to the number of bits of information needed to characterize a state. Now, try to visualize all possible combinations of failures of these 32 independent conductors powering the EBW detonators.


 The tree-like historical state structure, has branches tagged as Successful outcomes, corresponding to a detonation of maximum yield, if and only if the 32 concentric HE lenses explode in a highly synchronised way. Each EBW has to feature time precision ~25 ns













The number of degrees of freedom N of the system composed by 32 independent conductors, partially visible above in the photo shot at Tinian, whose dimension in the Hilbert space has  N  =  232 states, is:  


          N   =   4 294 967 296  ln 2   degrees of freedom    


This number gives at least a clue to the enormous amount of branches where ...Nagasaki never became famous abroad. Below an example. In the upper images, a zoom of Nagasaki industrial area at 11:02 a.m of August 9, 1945. Lower images, the state after an aerial reconnassaince flight in the branch following the Successful and Unsuccessful outcome branches. The lower right side frame is the state deriving by the failure of one of the cables powering the 32 detonators. The upper images are the same image and what you front is the visible aspect of a bifurcation at 11:02 a.m of August 9, 1945. Is this a new point of view?  Not really.    

 Frames, like sections of two different branches, zoomed in Nagasaki’s industrial area. Time evolves Up to Down. At left side, the past state of our own branches. At right side, the same past time in another branch. The Reader has to remember that since 1908 Minkowski demonstrated that each one instant of Time corresponds to infinite spaces. These aerial reconnassaince shots are then showing that idea of Relativity in the modern framework of Quantum Mechanics









It is reminiscent of the demonstration given in 1907 by the mathematician Hermann Minkowski, about the coexistence of infinite 3-dimensional spaces, rather than one, referred to each one instant of Time.  By the words of Albert Einstein in 1952: “...there is an infinite number of spaces, which are in motion with respect to each other”.  Finally, start to think the entire “Device”, and not only its wiring from the capacitors to the detonators, as a superposition of many smaller components, and you’ll reach some limits coherent with the smallest and shortest duration “particles”.  State Space encases these Events and many others. Reapply the same logic above to all Device’s components: you’ll front a colossal superposition describing all what the State of the “Device” is, as seen from a superior non-human point of view. Point of view which can be followed in all its details and implications only by mean of a mathematical approach.

Successful Design Outcome. What no Designer can do Brode, Designer of the “Device”’s SAFF-sequence, has not really excluded all Unsuccessful outcomes. As an example, it could have been enough to have a mechanical failure at the start of the dropping phase, when the bomb left the plane, affecting just one of the 32 conductors carrying power to the detonators. All of the following branches of the time-ordered SAFF-sequence would have been fulfilled as thinked by Brode. But, it had yet been calculated that the missing detonation of just one of the 32 chemical explosives should have prevented the spherical simmetry implosion resulting in the nuclear chain reaction, reducing it to one of 2.4 ton of conventional explosive. The number of degrees of freedom N of the system composed by 32 independent conductors, partially visible above in the photo shot at Tinian, whose dimension in the Hilbert space has N = 232 states, is: N = 4 294 967 296 ln 2 degrees of freedom This number gives at least a clue to the enormous amount of branches where ...Nagasaki never became famous abroad. Below an example. In the upper images, a zoom of Nagasaki industrial area at 11:02 a.m of August 9, 1945. Lower images, the state after an aerial reconnassaince flight in the branch following the Successful and Unsuccessful outcome branches. The lower right side frame is the state deriving by the failure of one of the cables powering the 32 detonators. The upper images are the same image and what you front is the visible aspect of a bifurcation at 11:02 a.m of August 9, 1945. Is this a new point of view ? Not really. It is reminiscent of the demonstration given in 1907 by the mathematician Hermann Minkowski, about the coexistence of infinite 3-dimensional spaces, rather than one, referred to each one instant of Time. By the words of Albert Einstein in 1952: “...there is an infinite number of spaces, which are in motion with respect to each other”. Finally, start to think the entire “Device”, and not only its wiring from the capacitors to the detonators, as a superposition of many smaller components, and you’ll reach some limits coherent with the smallest and shortest duration “particles”. State Space encases these Events and many others. Reapply the same logic above to all “Device”’s components and you’ll have in front a colossal superposition describing all what the State of the “Device” is, as seen from a superior non-human point of view. Point of view which can be followed in all its details and implications only by mean of a mathematical approach. Example Megadeaths' SAFF We conclude here this Case Study which examined the Root Cause Analysis of the detonation of the 21 kton implosion-Device, with a practical example of SAFF-sequence, not less real than the precedent. Experiments made after Nagasaki showed to be the ground level and not 600 m the altitude providing the maximum Effects. Also, the Radars on-board the Device could be jammed by Enemies from the ground. Thus, the sequence appearing in the video below presents one additional condition, today applied to nearly all nuclear weapons, the “Impact-condition”, appearing armed in the last 3 minutes of the Oscar-nominated Stanley Kubrick’s “Dr. Strangelove” and makes no more use of the Radars. The SAFF-sequence appears here interrupted by a missing Condition, the interlocked signal “bombs' bay doors open”, when the doors fail to open compelling the Crew to force manually this last step until the Successful outcome.

The “Device” is a superposition of many smaller components. Follow all of them and you’ll reach limits coherent with the smallest and shortest duration “particles”.  Before, along and after a detonation they experience billions of billions of mutual correlations and correlations with the Environment.  State Space encases these Events and many others. Re-apply the same logic before to all the Device’s components: you’ll front a colossal superposition describing all what the State (its wavefunction) of the “Device” is, as seen from a superior non-human point of view


Example  

MegaDeaths' SAFF








We conclude here this Case Study which examined the Root Cause Analysis of the detonation of the 21 kton implosion-Device, with a practical example of SAFF-sequence, not less real than the precedent. Experiments made after Nagasaki showed to be the ground level and not 600 m the altitude providing the maximum Effects.  Also, the Radars on-board the Device could be jammed by Enemies from the ground. Then, the sequence appearing in the video below presents one additional condition, today applied to nearly all nuclear weapons, the “Impact-condition”, appearing armed in the last 3 minutes of the Oscar-nominated Stanley Kubrick’s “Dr. Strangelove” and makes no more use of the Radars. The SAFF-sequence appears here interrupted by a missing Condition, the interlocked signal “bombs' bay doors open”, when the doors fail to open compelling the Crew to force manually this last step until the Successful outcome.

                   Safing-Arming-Fusing-Firing a multi-megaton H-bomb in Stanley Kubrick's film “Dr. Strangelove”


Links to the other Case Studies:

In-the Machine inspectors reduced to Standalone. Introduction “Actions to hide the never commissioned synchronisation of Inspector, Labeller and Conveyor, also implying a permanent impossibility for the Bottler to fulfill the triadic quest for: minimum losses, minimum downtimes, maximum rejection of defects and safety” “...service technicians’ skills are part of the final added-value of the Electronic Inspector, because they are those one who shape the future years of the equipment. World’s most expensive and higher Quality Electronic Inspector, left in the hands of some of the worst technicians, always perform much worse than World’s cheaper and lower Quality Electronic Inspector, left in the hands of some of the average-skilled technicians of the World” In the following, we’ll introduce the study of a pattern observed worldwide after 2004 in the operative reality of around one-hundred Electronic Inspectors sold to be operated in-the-Machine (Labeller, Filler, Capper, Closer or Seamer). Follow us in this Root Cause Analysis Case Study and you’ll discover what really is presently hidden under the surface of that beer. The Electronic Inspectors, whatever their Vendor, are built in two configurations: standalone, in-the-Machine. Standalone configuration Standalone configuration is by far the cheapest. 2-5 times cheaper than the in-the Machine. It does not include any connection, sensors, inspections, detectors nor logic relation with a precedent Labeller-, Filler-, Closer- or Seamer-Machine. Its: tasks are limited to handle a single Shifting-Register, rarely a couple of them; hardware is reduced to the minimum, typically one Trigger sensor over which the unique Shifting-Register is logically built, inspections and a rejector. fitting, wiring, starting and commissioning are accomplished in a limited time and, not being particularly complex tasks, they do not require the typically few available top-skilled service technicians. In systhesis: when configured to operate Standalone, all Inspectors imply an installation task that all of the Optoelectronics' service technicians fulfil. In-the-Machine configuration The Electronic Inspectors with locating positions and/or inspections in-the-Machine (Labeller-, Filler, Closer-, Seamer-Machine) are complex and their: tasks extended to handle several Shifting-Registers, typically two minimum; hardware is maximised, several Trigger sensors (inductive and optic) over which the various Shifting-Registers are logically built, many inspections and frequently more than one Rejector. their complexity is reflected in their pricing, always a factor 2-5 more expensive than the corresponding models operating standalone, years of practice, trainings, deep and true comprehension of the Shifting-Register's concept, are pre-requisite to an accomplished Commissioning. Commissioning honouring the Contract between an OEM or Vendor and a Food and Beverage Bottling and Packaging Company, also respectful of a row of legal requirements imposing, as an example, that the Machine Safeties cannot be left systematically disabled to the unaware Customers. Human-factor does matter Commissionings can only be named and underwritten that way in a worksheet whose siognature is asked you when: honouring the Contract between an OEM or Vendor and a Food and Beverage Bottling and Packaging Company, respectful of a row of legal requirements imposing, as an example, that the Machine Safeties cannot be left systematically disabled to the unaware Customers. We are suggesting the Readers that the service technician’s skills are part of the final added-value of the Electronic Inspector, because they are those one who shape the future years of the equipment. World’s most expensive and higher Quality Electronic Inspector, left in the hands of some of the worst technicians, always perform much worse than World’s cheaper and lower Quality Electronic Inspector, left in the hands of some of the average-skilled technicians of the World. Comparing Standalone & in-the-Machine installations’ pricings How to predict what should be the pricing of an Electronic Inspector’s installation, say its fitting, wiring, start-up, Commissioning and Operators’ Training ? Examing a posteriori many hundredths of different installations of Electronic Inspectors in Beverage Bottling Lines: where the above named installation activities had really been made, and made the only way the laws let them be valid in your country, because conformal to Safety rules and other technical good practices it is possible to see that a relation really exist, in different countries, part of Projects of Bottlers in competition (example, Coca-Cola vs. PepsiCo, AB InBev and SABMiller), whose Quality standards are different, configured with all of the existing spectrum of inspections, processing all existing kinds of containers (glass-, PET-, PRB-bottles, metal cans, crates and cases, etc.), from a wide range of productions, from 8 000 til 92 000 containers-per-hour, regression analysis shows an approximate but straightforward relation deriving be the comparison of the prices of the equipments, when the installation activities are not included. The installation pricing factor has empiric origin, nor we’d imagine what another way could be imagined to observe tendential relations which can only be obtained by linear regression studies a posteriori. As an example, if a Full Bottle Inspector costs 8000 € , ~10000 $ (weighs net 18 kg) is mainly but not only because that amount is proportioned to the sum of the values of its mechanical, pneumatical, optoelectronics, automation and documentation components. Another kind of Full Bottle Inspector of that same Vendor, priced ten times more, i.e., 80000 €, ~100000 $ (weighs 138 kg) shall need installation activities extended approximately to a duration 3.5 times longer than 8000 € model, needing just 3 days. Superior model costs ten times more than the basic: it sports many more functions and optionals to install (Rejectors, Triggers, cables, sensors), fit, wire, start, commission and finally train your staff. Five basic questions submitted to you own critical thinking: an Electronic Inspector needing 10 man*day of activities in your site, has been (strangely) delivered you after just 5 man*day ? What let you feel comfortable with the idea that its configuration is what you paid for ? What techniques you used to test it ? Maybe some test bottles had been passed one hundred times before to decide ? If this is the case, you have to know this is the kind of inspection a cheap Standalone Electronic Inspector does. An expensive in-the-Labeller Machine is paid to do many more additional useful things (like, advanced sampling or inspection in-the-Labeller) than just inspection at-the-Conveyor where the test bottles have been introduced. Would you order a new car, without to be informed before about its configuration, motor and performances ? We don’t think so, then it makes sense the following question: Have you received a precise listing of the functions assured you (Electronic Inspector’s Technical Guarantees) by the OEM or Vendor ? If not, why not ? Why Containers' Triggering is vital To let the Reader of these notes fully understand why all of the Triggering subject has so many pages developed to in this web site, there is to remark that: the identity of whatever object is its most fundamental information. It’d make no sense at all to speak of the “defective status of a container” in presence of ambiguity about “what container” is defective. In other words, containers’ Tracking, is much more important than whatever inspection, say whatever measurement of one of the physical properties of an object; when comparing Food and Beverage Packaging Industry with the Pharmaceutical Packaging Industry, we discover that the former with few exceptions discards as dangerous the rejection over an external Conveyor of the containers detected “defective” in-the-Machine. Following Pharma safety standards and customs, detection and rejection have to happen both in-the-Machine. The rejection has not to happen out of its Shifting-Register, one truly satisfying the requisites of rigidity and impossibility of the containers’ sliding out of the cells them attributed. Pharma Industry refrains to operate like Food and Beverage Packaging Industry operates following the OEMs and Vendors’ design choices; Machine-Conveyors-Inspector synchronisation Whatever the case, then also for relatively slow speed Labellers (<1.0 m/s), it is vital to synchronise the ramp-up and ramp-down phases of the Labeller and of the out feeding Conveyor, so that their speed difference results always <0.1 %. 0.1 % is a value knowingly close to the nonlinearity limit of the commercial Frequency Converters. Say the equipments regulating the speed of the motors in the Labeller and in the Conveyance systems. As an example, 0.1 % of divergence between bottle in-the-Labeller and same bottle at-the-Conveyor, at a speed of 1.5 m/s are 1.5 mm. 1.5 mm may appear a small divergence. But it is the maximum which can be allowed to be, keeping apart the today rare cases where containers’ speed is relatively slow (<0.8 m/s). Containers’ speed, being related to the containers’ kinetic energy following a quadratic law, enhances the slidings’ occurrences and then their negative effects. False Triggers and Data Sheets The Trigger controlling the Rejector, say the last one immediately before the Rejector, shall be exposed to count False Triggers, corresponding to bottles whose identity is unknown because lost. False Triggers which, in your own full interest, have to be absolutely be rejected by the Inspector, also if part of them corresponds to correctly labelled bottles. To let the Reader of these notes fully understand why all of the triggering subject has so many pages referred to in this web site, there is to remark that: the identity of whatever is the most fundamental information; it’d make no sense to speak of the defective status of a container in presence of ambiguity about “what container is defective”. the entire Pharmaceutical Industry discards and avoid as excessively dangerous the rejection of containers detected “defective” in-the-Machine, over an external Conveyor; detection and rejection have to happen in-the-Machine and not out of its Shifting-Register truly satisfying the requisites of rigidity and impossibility of movement of the containers out of the cells there attributed. In brief, Pharma Industry refrains to operate like Food and Beverage Packaging Industry is induced to operate by the choices of the OEMs and Vendors; How many of them has to be expected corresponding to correctly labelled bottles, then False Rejects ? A quite precise answer is given by the Inspector Counter menu for False Triggers, visible below as 0.01 %. Exactly that shall be the portion of the total False Rejects due to Falsely Triggered bottles. The mere existence of the Container Presence sensor shall force this rejection. Do not forget what seen above about the Transfer Point of the Labeller Machine's out feed starwheel.

IntroductionIn the following, we’ll introduce the study of a pattern observed worldwide in the period 2005-2014 in the operative reality of around one-hundred Electronic Inspectors sold to be operated in-the-Machine (Labeller, Filler, Capper, Closer or Seamer). …

Jammed Sampling table. Results of this over-sized Sampling Table were poor because of three independent Root Causes (italics) related to: Installation: the black colour side guide indicated by the arrow below, presents a profile inducing fallen cans due to cans’ anomalous fast deceleration. Fallen cans becomes jams in the end of the Table, where it starts the single way belt devoted to accumulate the orderly row of Filler Machine valves and Seamer heads; Design: the belts chosen are models with high friction coefficients, favouring fallen cans and successive jams; Design: no separate lubrification system existing with the effect that front of many more belts than necessary, no lubricant at all is visible, favouring fallen cans and jams. Incoherences like these are frequently encountered and the list above pin-points what to check first, when Sampling operations results in stopped Bottling or Canning Filler Machines. Results of this over-sized Sampling Table were poor because (Root Causes in italics) of: Installation: the black colour side guide indicated by the arrow below, presents a profile inducing fallen cans due to cans’ anomalous fast deceleration. Fallen cans becomes jams in the end of the Table, where it starts the single way belt devoted to accumulate the orderly row of Filler Machine valves and Seamer heads; Design: the belts chosen are models with high friction coefficients, favouring fallen cans and successive jams; Design: no separate lubrification system existing with the effect that front of many more belts than necessary, no lubricant at all is visible, favouring fallen cans and jams. Incoherences like these are frequently encountered and the list above pin-points what to check first, when Sampling operations results in stopped Bottling or Canning Filler Machines. Cans jammed, blocking the entire Table, after attempting a Filler-, Capper-, Closer- or Seamer-Sampling operation. Root Causes are the superimposed issues numbered above 2. and 3. Cans jammed, blocking the entire Table, after attempting a Filler-, Capper-, Closer- or Seamer-Sampling operation. Root Causes are the superimposed issues numbered above 2. and 3.

Case Study Sampling Table always jammedIntroductionTypical problems in a Food and Beverage Bottling Line derive by missing materials like motors, Frequency Converters, detectors, etc. In the following we’ll briefly study a Case where the “material” was much more than necessary. …

Case Study The Brewery which considered the TechnicalGuarantees part of a Contract to be honoured  ROC-curve of a Fill Level inspection. Imagine to pass 1000 times a test container through one and the same Electronic Inspector equipped with a dual Fill Level Inspection: X-ray and High Frequency (or, Optic with camera). …

IntroductionPowerade® is a famous energy beverage, the first in a row of energy drinks with great success launched in the World, after 1988. In July 2002, The Coca-Cola Company® updated the bottles of the standard Powerade to a new sport-grip bottle. …

Case study 27% rejects stopping all days a Beverage Bottling Line  The rejects' accumulation table of an Electronic Inspector in a Beverage Bottling Line, as it appeared to the eyes of the Operators and Management along 6 consecutive months after the day of the Line startup. …

reynolds numbers and fillin-2

Case study 1 year of Production lost   In the following a case where the Machine blamed by the Bottler never functioned correctly since the first day. 18 months later, and after two different analysis made by elements acting in conditions of …

Milk and milk-based beverages, filled and capped in an aseptic environment, no preservatives. One more time, the cap is their Achilles’ heel, whatever the technology adopted during their filling. A slightly malpositioned cap is enough to clear all of the cares of the Aseptic Filling + Closing process, creating the optimal conditions for an organic contamination

Case study Cap presence control of sensitive beverages in 2001“X” is a great dairy filling and packaging plant. Here were installed, started and commissioned two standalone Full Bottle Inspectors in a new Aseptic Line for PET-bottled dairy products. …

milk aseptic filling med hr

Case study Cap Presence control of sensitive beverages in 2010Introduction “Y” is a great dairy filling and packaging plant. Here it has been installed a standalone Full Bottle Inspector in a new Aseptic filling Line for PET-bottled dairy products. …

99.5 % of the non-labelled bottles to the Market

Case study99.5% of the non-labelled bottles sent to the Market Non labelled and flagging-labelled bottles, manually rejected at the outfeed of a Labeller Machine. Manually rather than automatically rejected by the inspection system, because of a design-error in its configuration, amount of tracking Triggers photocells and Encoders. …

Canning Line's Layout relevance

Case StudyCanning Line’s Layout Relevance   IntroductionNo one of us has X-Ray's radiographic eyes. Because of this obvious reason, the cans’ content cannot be visually verified if, due to any reason, the Full Can Inspector is not active. …

Ampoules Filling and Sealing Machine. Pharmaceutical ampoules’ Filling and Sealing Machine. A container so intrinsically safe, does not need an identification of each one container along its filling, sealing and inspection phases. It can be safely inspected by a standalone Electronic Inspector, with sensors lying in the same Machine Cycle of the Filling-Sealing Machine. When Pharma Industry adopts containers different than ampoules, because having a Cap or Closure like the vials, the Electronic Inspection is always and only in-the-Machine. In-the-Machine at its highest level of safety, with the containers inspected and rejected into the Machine Cycle. Into the Machine Cycle and not over a separate Conveyor Cycle following the Machine Cycle, like in the case of the Food and Beverage Aseptic Packaging (image credit SCHOTT®, 2014)

Case study Electronic inspection of Pharmaceuticalsin-the-Machine-Cycle When speaking of guarantees of asepticity, Pharmaceutical Industry is since many decades what really and only retains the maximum know-how. …

punctured pharmaceutical co med

IntroductionThe Pharmaceutical field is the origin of the technologies adopted today in the Aseptic filling, closing and inspection of beverages without any added preservatives. Are the Food and Beverage Packaging standards competing with the Pharma standards of, as an example 10 years ago ? …

hardware faults 2800x1582@1x

Case HistoryGold-made electronic cardsImagine two huge cases arrived to your store today, filled with the spare parts you ordered and waited for 4-6 months. Electronic cards and other parts urgently needed to let your Machinery produce in Quality and Safety. …

topology of the saff-sequen 4096x2460@1x

The “Device”Fusing, considered the Root Cause of whatever explosion, is just one superimposed component of an extremely longer sequence of conditions before and after, greater and smaller, than the Fuzing. …

human-factor design and nuc-2 4096x2315@1x

What Root Cause Analysis’ names human-factor plays a decisive role. A role made decisive as root cause of the majority (over 50 %) of all of the incidents registered in the productive processes. …

A seismic Incident

False trail to the Root CauseWe’ll brief in the following the incident happened in 2011 in the nuclear power plant at Fukushima Daiichi, Japan, operated by the Tokyo Electric Power Company (TEPCO). …







This website has no affiliation with, endorsement, sponsorship, or support of Heuft Systemtechnik GmbH, MingJia Packaging Inspection Tech Co., Pressco Technology Inc., miho Inspektionsysteme GmbH, Krones AG, KHS GmbH, Bbull Technology, Industrial Dynamics Co., FT System srl, Cognex Co., ICS Inex Inspection Systems, Mettler-Toledo Inc., Logics & Controls srl, Symplex Vision Systems GmbH, Teledyne Dalsa Inc., Microscan Systems Inc., Andor Technology plc, Newton Research Labs Inc., Basler AG, Datalogic SpA, Sidel AG, Matrox Electronics Systems Ltd.  

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