Sunday 3 May 2015

A STUDY ON LUFTHANSA GERMANWINGS AIRBUS CRASH



A STUDY ON LUFTHANSA GERMANWINGS AIRBUS CRASH
     (Updated on June 4 2015)

Dr. Sohei Matsuno1), MS. Asmadi2)
1) Prof. 2) Lecturer, at Faculty of Eng.
IBA University PLG, RI
E-mail: sohei_matsuno@yahoo.com
ABSTRACT

The Writers (of this paper) predicted in their earlier report on the AirAsia Airbus crash that a similar event would happen at about 5-yr interval. Really, the Lufthansa Germanwings Airbus crash has come but much sooner than they assumed, only 86 days later. For this event, there have been a variety of causal speculations. However, few make an analogy between the two events despite their resemblance. Unlike AirAsia event, it was fine when this event happened. Hence, the favorite weather/pilot-error hypothesis isn’t applicable to this event. Given a criterion, a co-pilot-suicide hypothesis has appeared. Black-box-data analyses are going with this hypothesis. The purpose of this report is to forward a bulkhead-fatigue-rupture Hypothesis that shall replace the co-pilot-suicide hypothesis for a right solution to this event.
To realize the purpose, this report proceeds in the following steps: (i) defining two logical terms, induction and deduction, clarifying a background to which the events happened, making an analogy between the two events, identifying the behavior of the plane on its last problematic timeline, (ii) learning the ongoing causation study, (iii) showing the Writer’s Bulkhead-fatigue rupture Hypothesis, and (iv) summarizing its conclusions.

Keywords: Lufthansa / AirAsia crashes, Airbus / Budget airline, analogy between plane crashes

INTRODUCTION

Purposes of this report
The direct purpose of this report is to present the bulkhead-fatigue-rupture Hypothesis for the Lufthansa Germanwings Airbus crash event as it was so done for the AirAsia Airbus crash event, REFERENCE [1]. On the way, this report tends to think convincing the societies concerned of the methodology (methods, principles and rules) of a causation study. In this way, this report works to salvage a causation study that’s currently in disarray. This is the indirect purpose of this report.
Definitions of logical terms
(1) Induction
This is a logical process of any form of reasoning in which a hypothesis, though supported by premises, does not follow from them necessarily. The one that survives this process is the hypothesis that gives a genuine conclusion. A conclusion reached by this process is also called an induction.
(2) Deduction
This is a logical process of reasoning in which a conclusion follows necessarily from the premises. A conclusion reached by this process is also called a deduction.
Note 1: As to definitions of technical terms, ‘cause’ and ‘fatigue’, cf. [1] and [18] respectively.
Note 2: As to abbreviations in this report, cf. GLOSSARY (shown at the end of this report).
[Explanations]
The above expressions of the definitions are abstract. Hence, for the sake of readers’ better understanding, they’re to be concretely explained as follows.
The first step of induction is to gather as many relevant premises as possible. The premises are such as status of the consequence, its behavior on space-time dimensions, techno-socio-cultural circumstantial evidence, analogy to past events etc. Next is to assume a plural hypothesis for a conclusion.
As premises accumulate, the degree to which the premises come to support a hypothesis, as measured by the logic, should tend to indicate that false hypotheses are probably false and that true hypotheses are probably true. In this way, among the assumed hypotheses, the one that follows from the premises without a contradiction is found. It’s a genuine hypothesis.
Induction precedes deduction, unless an event has vis-á-vis happened and been red-handedly evidenced on the spot, since the event can be reached directly by deduction without induction.
In deduction, the premises are given as material evidence, e.g., black box data. A conclusion necessarily follows from the premises. Deduction is to be guided by induction with exceptions mentioned above. Deduction proves induction.
In this context, it’s clear that induction is more strategic / complex by nature, and needs wider, deeper and stronger intelligence, experience and inspiration (not imagination) than deduction (often forensic technicians’ job) needs. A misjudge in induction leads a study to a wrong conclusion unless deduction checks induction properly.
There’re two things that the Writers call readers’ attention in this concern. That is;
(1) The material data are not necessarily such that those lead to an absolute truth independently. For instance, the black-box data are often opaque that can be interpreted into a plural way, and how to interpret them is black-box-data analyzers’ prerogative. If they’ve been given a hypothesis composed by their superior body (in an inner circle), they tend to interpret the data so as to meet the given hypothesis, regardless of its reasonability. An example seen in the A-event is shown herewith.
There was about 5 minutes after an emergency happened till the plane plunged into the sea. During this time, pilots had no contact with ATC Center, could do nothing to recover plane’s balance, gave no voice to CVR and didn’t send a distress signal. For these material data, the weather/pilot-error hypotheses judges; ‘If there’s mechanical failure, pilots must inform of it. No message is a good message, as it means no mechanical trouble is. For pilots, sending a distress signal is a second priority at the time of emergency. A supreme priority is to solve the facing problem. The distress signal is to be sent after everything has been settled. In the A-event, pilots’ efforts were in vain until the last moment; hence, there was no distress signal. Pilots were concentrating their efforts tacitly on the problem, or their voices vanished into screaming warnings. That is, according to the hypothesis, no communication, no plane’s balance recovery, no recorded voice and no distress signal are all the evidence of pilots’ and control system’s good physical statuses during the event. Contrarily, the Writer’s Hypothesis judges that no contact, no voice etc are the evidence of pilots’ and control system’s physical defunct. You see? For the same material data, there’re two interpretations that are of completely opposite directions, [1].
(2) If a black-box investigation goes without a hypothesis, it can reach nowhere. Suppose, at a crime site, fingerprints and DNA of a culprit have been found as material evidence. Can the material evidence single the culprit out from a population of people? No, it’s practically impossible, unless otherwise given a small finite number of inductively-identified suspects. Remember! A black-box data analysis without a hypothesis is tantamount to a kite with a cut string. It must be guided by a correctly defined hypothesis.
If there’d be any discrepancy between induction and deduction, either of them is wrong. The study must be reviewed and restructured. If a hypothesis has been faultily set up, both are wrong even if they agree to each other. It can happen by interpreting the black-box data so as to meet the hypothesis given by a superior position to the black-box-data-investigation technicians. In the worst case, forging data, or even substituting secretly a false black-box for an original one happens. It really happened in the Airbus A320 crash event, Habsheim, France in 1988.
Background of L-event
A- and L- events are, from a macro view point, results of a disproportionately rapid development of airline automation, having left basic intelligence, which the development should accompany, behind. The events are not isolated phenomena. They’ve appeared in a global automation drive that commenced in 1950s. It’s been ceaselessly pursuing to substitute automatic devices for humans. The automation is driven in the belief that humans commit errors but high-fidelity automatic devices do not. It’s in effect contributed to reduce the number of workers and, at the same time, to marginalize them to auxiliary keyboard punchers who know nothing about basic principles of the matters they’re engaged in. It’s prevailed in all sectors, including education and research. Really, current graduates’ basic intelligence deficiency is unpardonable. It is further waxed by due computerized practices. They can manage everything so far as the things are going as programmed. But once something beyond the programs happens, they’re painfully impotent to manage them. It has passed two-generations since a computerization drive began. Hence, all the current societies are, from the president to the rank and file, occupied by ABIDS patients. The aviation industry is a typical example among all the societies.
The above is the background against which a cause or a to-be cause is not found or is overlooked after or before the plane crash, and the same event repeats again and again.
Three generations ago, people in all sectors had controlled everything with their own brains. As they had been bred in this way throughout their education and practices, they were able to manage problems in that way too. Regrettably, those who witnessed the automation era are, at youngest, 85 years old if still arrive. Hence, they’re in their dotage. Suppose there’d be someone who is miraculously capable as he was 60 years ago, God’s willing, what role would he play in a plane crash causation study? May it be of the heroic outlaw Robin Hood, the ingenious gentleman Don Quixote, the original (but absurd) solution maker Mr. Bean, or anyone else? Readers shall see it.
Plane’s behavior in last 15-min. timeline
It is shown in Fig. 1.
The Writers call readers’ attention to three significant characters in the altitude chart; viz. (i) after the plane had reached a 11400-m cruising altitude, it was still climbing at a slight rate of 75 (m/min.). After 4 minutes, it reached 11700-m altitude, (ii) immediately after the above ascent, the plane descended with a steep but constant rate of 1070 (m/min.) down to 2000-m altitude in 9 minutes, (iii) at the end of the descent, the plane had level flight of a constant 2000-m altitude and 710-km/hr speed for 1.3 minutes until it collided the mountainside. The behavior in speed is also shown in Fig. 1.
Note: ft: feet (1 foot = 0.3048 m), kts: knots (1 knot = 1.852 km/hr)
Time (hr.min.)
  Barcelona (Spain)                              the Mediterranean Sea                             the French Alps
Fig. 1 Altitude / speed chart of Germanwings Flight 4U9525 (Source: Flightradar24)
During the 15-min. period, the plane had no communication with ATC Center, no voice recorded in CVR and no distress signal to ATC Center as stated earlier.
Any induction (hypothesis) that explains the above plane behavior without contradiction to the given premises, including material evidence from black-box data, is the hypothesis that gives a genuine cause of the L-event.

ONGOING CAUSATION STUDY

Co-pilot-suicide hypothesis
General
In this and next Sects, every quotation doesn’t show its origin to avoid criticism by name. If readers are interested in them, it is found in websites, e.g., mentioned in [2] ~ [6]. All the quotations are written in Italic letters.
A-event is a typical case to which the weather/pilot-error hypothesis is comfortably applied. There was a storm on the course of the crashed Airbus. But five other planes were concurrently traveling the same stormy zone, and had passed the zone without trouble. cf. Fig. 2. As the weather alone cannot be an enough cause, there must be one more factor with which a compound cause is to be composed. As the additional factor, conveniently chosen is a dead pilot’s error. Attributing a cause to dead pilot's error is the safest way in the causation hypothesis composition, since the pilot can no longer speak for his cause. This is the background against which the weather/pilot-error hypothesis appears. Its logic is usually, ‘Pilot’s efforts to avoid the bad weather caused the mishap.’
However, L-event happened when it was fine. The worldly hypotheses’ favorite compound cause is inapplicable to lt. Hence, the hypothesis is forced to attribute the consequence totally to a pilot only. Further, pilot’s error is difficult to assume under the fine weather. That is, there’s no way for the hypothesis other than to impose particular nature of either (or both) ideological or (and) mental matter on one pilot (not two pilots as it’s scarcely probable). This is the background against which the co-pilot-suicide hypothesis has appeared.
Fig. 2 Planes flying over the Java Sea concurrently with AirAsia 8501
(Source: Jason Rabinowitz @AirlineFlyer)
Episode
For the sake of readers’ better understanding in this regard, the Writers herewith forward an episode before readers:
It was early 1980s when one of the Writers (then professor at Niigata University in Japan) was visited at his office by his dear reporter (then Chief of Niigata Branch Office of xx-Newspaper, one of the four leading dailies in Japan). The reporter informed him that the Niigata Prefectural Police HQs regarded him as a communist, as one of the detectives attended a police-media joint meeting had spoken. The reporter, who knew him be by far different from a communist through his publications, added, ‘I immediately convinced them of their wrong concept.’ He asked the reporter, ‘Why do they regard me as a communist?’ The reporter replied, ‘No reason. It’s their nature. For them, any theories or persons of unfamiliar originality or personality are all communism and communists.’ Nowadays, it may be converted into Islamism and Islamists. The Writer possesses the Koran. His computer saves data of the Islamic State. These are to reinforce his basic intelligence. He wanders one day he might be arrested as a radical Islamist.
In SSR, it went in a different manner. A secret service used to regard those people of unfamiliar personality (of course, not as communists but) as mentally deranged who only fit for a lunatic asylum where they had to undergo brain-wash therapy. It was often kindly penetrating a prick into their front brain to make them be persons of few works.
Keep the above in mind; let’s enter the following articles to discuss the real matters.
Induction in co-pilot-suicide hypothesis
In short, it is practically not a hypothesis to solve the event reasonably with maximum socio-techno-scientific efforts but hypocrisy to settle the matter as quick as possible with a minimum socio-economic impact. It is inducted by wishful imaginations and improper discards.
It assumes Islamic and/or mental motivation for the co-pilot. However, if the co-pilot’s act was from an Islamic motive, why didn’t he target the Eiffel Tower but the French Alps, as 9/11 plane hijackers’ didn’t target the American Rockies but the WTC Twin Tower? In this context, An Islamic motivation doesn’t make sense with the cause of L-event. Then, how about a depression cause? First, to involve population is an inevitable consequence of a suicide bombing (a drone bombing as well). Second, a person of depression does not necessarily commit suicide. According to a study on Afghanistan / Iraq war veterans, the probability of persons of depression commit suicide is 0.03 %. Any study on an important subject such as this event shall not be grounded on such a low probability as this. If dare do it, the authenticity of the hypothesis itself is 0.03 %. That is, the co-pilot-suicide hypothesis hardly conforms to the cause of L-event.
The hypothesis originally began with an allegation that says, ‘the captain left the cockpit and couldn’t get back to the cockpit as it was locked from the inside.’ It is said that the captain knocked at the door lightly first and strongly later, but no response from the co-pilot. Finally, the captain frantically tried to smash his way into ‘Flight 4U9525's cockpit as he shouted at killer co-pilot: "For God's sake, open the door,” but in vain. This story made a military-police-prosecutor group be possessed by the co-pilot-suicide hypothesis, having interpreted the story, ‘the co-pilot locked the door from the inside and silently rejected to open it despite the knocking calls from the outside.’ This interpretation is a product of wishful thinking and improper discards as elaborated in the next article. cf. a quotation below.
‘Mr. Robin said Lubitz (co-pilot) 'voluntarily' refused to open the door, adding that his breathing was normal throughout the final minutes of the flight.’
Problematic imaginations and discards
First, did the captain really left the cockpit? In A-event, the same was consistently advocated based on the CVR data. But it was finally denied by the fact that the body of the captain was found in his cockpit seat. Unfortunately, in L-event, it’s impossible neither to confirm nor to deny the allegation in this way, as the fuselage had been wholly smashed to pieces. Remember! The absence of the captain in the cockpit is an indispensable necessary condition of the co-pilot-suicide hypothesis.
Second, the cockpit door was really locked from inside? The door couldn’t be unlocked from the outside even if it was not locked from the inside. That is, if the door (airtight) was pressed from the outside by cabin air pressure, the door couldn’t be unlocked. This is easily proven by a simple domestic test. Stand inside a door that opens outside. Confirm first that it can be easily locked and unlocked with a key. Then, lock it. Next, pushing the door forward you, try to unlock it, and you’ll realize it be difficult. It is because of frictional resistance between the lock bar and the door sash. The phenomenon happens regardless of the type of the lock and if it is manual or automatic, as their basic mechanism is the same. The cockpit door was pushed by air pressure of the passenger cabin that was caused by greater air pressure in the cabin than the one in the cockpit. It was due to decompression in the cockpit. Frictional force on the lock bar due to air pressure may have reached a few ton-f vs. the force by manpower is a few kg-f.
Third, was the so-called cockpit-door-knocking sounds recorded in CVR have been compared to the results of tests with other A320-200 Airbus cockpit door knocking? Can it be recorded by CVR? Are they confirmed by means of Fourier analysis (one of computer’s favorite subjects) to confirm if the recorded sound is really of the cockpit door knocking? The Writers can do it if the digital sound record is given. The sound recorded in CVR is analogue data, but still the same comparison is possible by physical analogues, though its results are less objective than the former’s.
The Writers are skeptical, from the beginning, if the recorded sound is really of the captain’s knocking at the door. They suspect it is the sound of the developing cockpit bulkhead crack and rupture. In the first place, it is dubious if the door’s sound waves generated by light knocking at the sound-proof-door from outside can be recorded by CVR.
Last, if the captain really tried to force his way into the cockpit, it’s not a heroic but a helpless effort, since the door is so designed as to bear any conceivable terror attack, and the captain himself must have known it. It was an effort of ‘kicks against the pricks.’ The captain must have had no way other than praying to God for opening door. But, God’s willing, the door didn’t open. cf. a quotation below:
‘In a desperate attempt to stop the fatal crash, Mr. Sondenheimer (captain) spent up to five minutes attempting to smash his way into the cockpit using an axe.’
An axe is strictly prohibited to bring in a cabin. How could the captain find it easily? Anything that can be used to break a cockpit door, a crowbar (allegedly the captain asked to bring) as well, are all not allowed bringing in a cabin.
First discard that allowed all other discards to follow
The co-pilot-suicide hypothesis committed a fatal discard in its first stage when it neglected a fact, ‘the plane crashed 12 hrs after it’d undergone repairs,’ as a minor matter.’ It allowed, in effect, all other hopeful-imaginations and miss-discards to follow. cf. a quotation below:
‘Lufthansa said the 24-year-old plane had just on Monday had repairs to the hatch through which the nose wheel descends for landing. A spokeswoman said that was not a safety issue but that repairs had been made to reduce noise.’
For a person who has basic intelligence in a theory of ‘wave motion and vibration,’ the noise is a safety issue that should be carefully examined. A noise (sound) is a wave motion being generated by a vibrating body. And the vibration is a No. 1 cause of the fatigue. If there was an extraordinary noise, there could be extraordinary vibrations. The reason why Lufthansa discarded the matter was likely due to a lack of basic intelligence among the staffers in charge.
As the noise (vibration) might have been while the plane was flying. Was it reported by pilots? How loud / high (low) pitched the sound was and how long had the part been subjected to the vibration until it underwent the repairs? What were the irregularities? What kind of repairs was made (allegedly within several hours)? Were there no relevant irregularities around the problematic part?  Was it confirmed that there was no noise after the repairs? How was it confirmed? Clear answers to these questions are needed.
A mechanism how the vibration of a part attached to a fuselage accelerates and triggers the bulkhead fatigue and rupture is as follows:
Any component (hatches, doors, windows, windscreens, and other devices) that is rigidly fixed to a fuselage vibrates at the same frequency of but at less amplitude than the exciting force, because the exciting force’s frequency (engines’ RPM) is much higher than the natural frequency of the fuselage. It’s called forced vibration. If the fixing rigidity lowers to elastic-plasticity, the component starts vibrating at its natural frequency. It is called natural vibration. Its frequency is less and amplitude is greater than the exciting force’s. The resultant vibration is called free vibration in which the forced and natural vibrations coexist. If the component is structurally inhomogeneous, it generates natural vibrations of various frequencies and amplitudes. These vibrations play a role of exciting force to the adjacent sections of the fuselage. Of course the vibrating component itself causes trouble around its fixed points. There’s another problem that is more serious than it. There’re many devices attached to a cockpit fuselage. Each of them forms an auxiliary mass-spring vibration system consisting of the mass of each device and its supporting fuselage as a spring. If one of their natural frequencies coincides to one of the exciting forces’ frequencies, it causes resonance involving the device-fuselage (mass – spring) vibration system. Take note that the attached remote control device might be the one involved in the phenomena.
In this context, it is highly probable that the overlooked flaws at the nose wheel accommodation hutch under the cockpit had accelerated and triggered the fatigue and rupture of the cockpit bulkhead. This assumption can be denied if, only if, the repairs had been done long time (e.g., 20 years) before the crash. Really, JAL F123 aft pressure bulkhead’s fatigue rupture occurred 7 years after the improper repairs. In L-event, there was only a 12-hr time lag between the repairs and the crash. The plane had no flight between the repairs and the crash flight. Practically, the crash happened immediately after the repairs. There’s no reason to discard the repairs from the consideration.
It is reiterated in the next Sect. in which the Writer’s bulkhead-fatigue-rupture Hypothesis is studied in analogy with the BEA’s co-pilot-suicide hypothesis.
Comment-1: In a budget system, it is prohibited for stuffers to do anything that’s not included in budget items. This is a factor in the budget system discouraging staffers to find out and to grapple with problems, [1].
Comment-2: The event has led to an upsurge of hero-seeking sentiment. If the event has only a bad character, the event is not dramatic. From a circulation point of view, the event is to be dramatic. Let it be so, the scenario must have a good character as well. cf. quotations below:
The flight data recorder (FDR) revealed Mr. Sondenheimer's heroics on the plane.’
FDR never reveals such a thing. Media do it to play to the gallery. L-event has neither good nor bad character. Those 150 on board are all victims of the bulkhead fatigue rupture from a scientific view point. cf. a quotation below,
‘A social media campaign has been running for more than a week to memorialize Mr. Sondenheimer's efforts to save those on board.
To produce hero has a negative effect on a correct solution to the event.
Black-box data analysis
The examiners of CVR firstly regarded the co-pilot-suicide hypothesis as a speculation.
cf. a quotation below.
‘A Lufthansa spokesman said the carrier was aware of the Times story (co-pilot-suicide hypothesis), adding: "We have no information from the authorities (BEA black-box data investigators) that confirms this report and we are seeking more information. We will not take part in speculation on the causes of the crash.’
That is; in effect, they tried to find their conclusion without a hypothesis. As stated earlier, it is an uneasy job for them to accomplish studies without hypothesis, much more, in the case of L-event where FDR missed its essential part, a memory card. cf. Quotations below and Fig. 3.
‘BEA said it was “optimistic” the second black box, the flight data recorder, would be found and the mystery of the crash solved.’
Comment: It implies that if FDR is not found, the L-event is to be mystery forever.
FDR’s memory card containing data on the plane’s altitude, speed, location and condition was not inside, apparently having been thrown loose or destroyed by the impact.
Comment: Black-box investigations can neither confirm nor deny any hypotheses decisively without the memory card, unless otherwise mobilize bold imaginations and discards.
  
                        CVR                                                FDR
Fig. 3 Black boxes damaged by shock (origin: www.pilotman.net, www.bea.aero)
It’s right when the black-box-data investigators say, ‘Nobody knows if the determined result is correct until we see the result.’ Similarly, it is right when drone bomb attack operators say, ‘Nobody knows if the target is correct until we see the result (a group of enemy fighters or a party of wedding ceremony participants).’
It takes so long time until the investigators reach the goal, if they do without a hypothesis at best or it is impossible at worst. cf. a quotation below.
‘Jouty expected the first basic analysis in "a matter of days" but warned this read-out could be object to errors and that more work would be needed for a full interpretation.
Now the co-pilot-suicide hypothesis has been given. One of the investigators was quoted as saying, ‘The CVR data support the hypothesis.’ Does it represent BEA as a whole? Let’s learn.
A Summary of the Transcript from the CVR Recording (provided by BEA, obtained by the German newspaper Bild, translated by US. New York Times, reported by CNN and slightly rearranged for a reasonable order by the Writers) gives the timeline of L-event as follows:
(1) After reaching cruising altitude, Sondenheimer asked Lubitz to prepare the landing. There is the sound of a seat being pushed backward after which the captain says, "You can take over."
(2) Sondenheimer begs Lubitz to let him in. Next comes the banging.
(3) Passengers then begin to scream. For God's sake, open the door!" Capt. Patrick Sondenheimer screamed as he banged on the cockpit door, pleading with the co-pilot. "Open the damn door!" the pilot says.
(4) At 10:29 a.m., air traffic radar detects that the plane is starting to descend.
(5) Three minutes later, air traffic controllers try to contact the plane and receive no answer -- shortly after which an alarm goes off in the cockpit, warning of the "sink rate,"
(6) Another three minutes pass. A loud metallic bang is heard at 7,000 meters (almost 23,000 feet).
(7) It is 10:38, and the plane is at 4,000 meters (about 13,000 feet). Lubitz's breathing can still be heard on the voice recorder, according to Bild's report.
(8) Two minutes later, investigators think they hear the plane's right wing scrape a mountaintop.
(9) A minute and half later and 2,000 meters (about 6,500 feet) lower to the ground, an alarm says "Terrain -- pull up!"
    The plane slammed into the French Alps.
Note: It uses a local standard time.
There can be seen three untimely time-settings in this timeline, viz. (i) (10:38 – 10:29 =) 9 minutes after the beginning of descent, the plane was still at 4000-m high. It doesn’t meet the reality. 9 minutes after the descent began, the plane was at 2000-m high. (ii) After the above stated 9 min. the plane flew 3.5 more minutes. Really, 1.3 minutes after 9-min. descent, the plane had already smashed to pieces. (iii) As to the statement ‘Two minutes later, investigators think they hear …..,’ 2 minutes after a 9-min decent is time-wise at odd with the reality. Further, it may be the sound from the last fatigue-rupture at the cockpit bulkhead, if not an illusory hearing. Note: The problematic time settings are, the Writers suppose, not BEA made but media group made during their editorial processing.
Anyhow, as the Writers start with a timeline of the event, BEA did the same at first. Readers can make analogy between the Writers’ and BEA’s timeline in the next Sect. In this Sect., the Writers firstly call readers’ attention that BEA’s timeline mentions particular individuals’ names but this report’s timeline doesn’t. This indicates the intention of each report, i.e., to support a human-cause (BEA) and an engineering-cause (the Writers). cf. following quotations.
 Jean Pierre Michel, lead investigator for the French inquiry, said on Saturday that investigators are not ruling out any scenario with respect to the crash out at this point,’
This statement is of BEA’s open stance.
But French authorities have said that Lubitz appeared to have crashed Germanwings Flight 9525 deliberately into the Alps.’
The sounds recorded on one of the "black boxes" recovered from downed Germanwings Flight 9525 firms up investigators' theory that the co-pilot locked the captain out of the cockpit and then crashed the plane (CNN),
‘Referring to Lubitz, Mr. Robin said: 'He did this for a reason which we don't know why, but we can only deduct that he destroyed this plane.
These statements represent BEA’s real intention.
A person in charge ruled out a midair explosion and expressed his reluctance to link the crash to decompression. cf. quotations below.
‘While stressing it was too early to form a clear picture, he ruled out a mid-air explosion and said the crash scenario did not appear to be linked to depressurization.’
‘Jouty said it was too early to give details of the cockpit recording. However, he said the information investigators had put together suggested the plane had not exploded and did not suffer a “classic decompression situation”.’
What does he mean by “classic decompression situation”? If it means the bulkhead material (that governs the behavior of fatigue rupture and decompression) is modern, it’s OK. Really, the material is not classic aluminum. But if it means the decompression itself is modern, it’s a queer story. There’s neither modern nor classic decompression, as there’s neither modern nor classic temperature.
Given the setting as the above, if BEA won’t support the co-pilot-suicide hypothesis in due studies, BEA investigators’ mental stability itself must be on the agenda. Of course, the Writers will support the bulkhead-fatigue-rupture Hypothesis (explained in the next Sect.) without fail.

BULKHEAD-FATIGUE-RUPTURE HYPOTHESIS

Analogy between A- and L- events
There’s a resemblance between the two events as follows:
(1) The planes involved in the two events are both Airbus A320-200 of budget flights.
(2)  Both the planes were more or less in a climbing tendency while they were cruising before their final death descent.
(3) After the plane entered emergency status, there was no communication between ATC Center and the plane, no pilot voice recorded in CVR, no act to save the plane and no distress signal sent from the plane.
(4) In both the events, it is (was) said that the captains were not in the cockpit when the plane crashed.
(5) The crashes are both high altitude events that are rare statistically.
The two events have differences as well. They’re as follows:
(1)   A-event’s descent was of an uncontrolled free fall until the plane hit the seawater, while L-event’s was of controlled and had a post-descent level flight until the plane hit the mountain.

(2)   L-event’s plane was 25 years old, while A-event’s was 6 years.
(3) The L-event’s plane underwent repairs at a nose wheel accommodation hatches (existing below the cockpit) to eliminate noise. It was 12 hrs before the event. A-event’s plane did not undergo such repairs.
(4) The captains’ absence in the cockpits was denied when his body was found in the cockpit in A-event. In L-event, it can be neither confirmed nor denied in the same manner as A-event.
(5) In L-event, the plane hit steep solid mountainside with 710-km/hr flight speed and its fuselage was smashed to pieces. While in A-event, the plane hit flat liquid seawater with 200-km/hr falling speed and the fuselage split in three big parts.
(5) The bulkhead fatigue rupture in the cockpit (the Writers assume it’s a common cause for both the events) seems to have developed slowly ~ rapidly in L-event, while in A-event explosively. Hence, the primary consequence, decompression, developed slowly ~ rapidly in L-event though it did explosively in A-event.
(6) Consequently, one of the two secondary consequences, physical defunct of the co-pilot, progressed rather slowly in L-event than instantly of the pilots in A-event. Similarly, another secondary consequence, mechanical defunct of the plane’s remote control system, was total involving engines and helms in A-event, while in L-event it was insignificant.
(7) It was fine when L-event happened, while A-event occurred under the stormy weather.

If something of rare event happens with a short time lag and high resemblance each other in their feature, there’s no reason to discard an analogy between them. BEA has yet to do it up to now. They should do it in their due diligent studies.
Plane’s behavior for last 15 minutes
General
The following arguments are done with captain’s absence in the cockpit, because of four reasons; viz. (i) The Writers can’t deny its possibility. (ii) They understand why BEA investigators adhere to it. It is because their co-pilots-suicide hypothesis can’t stand without it. (iii) Contrarily, the Writers’ bulkhead-fatigue-rupture Hypothesis can go with it. (iv) Then, to avoid being engaged in such an unessential subject, the arguments shall go with it.
After the plane reached cruising (pre-descent) level flight, it had showed a slight but not ignorable ascent before a sudden descant. This period is a prelude to the crash event. After the pre-descent level flight, the plane descended a steep but stable decent. After the descent, the plane had short but not ignorable (post-descent) level flight until it smashed against the mountainside. That is, the last problematic minutes begins at the time when the auto-pilot was set on a cruising flight position. It is Time 0-min. It terminated at Time 15-min. when the plane crashed into the mountainside. That is, it consists of pre-descent level flight (5 min.), descent (9- min.) and post-descent level flight (1+ min.).
Note: In the following explanations, refer to the plane’s behavior on the timelines of the Hypothesis and the hypothesis shown respectively in the previous Sects.
Identifications
The Hypothesis identifies the plane’s behavior in its last 15 minutes as follows:
(1)   After having set auto-pilot on a cruising position at Tim 0-min., the captain unlocked and opened the cockpit door and went out the cockpit at about Time 1-min. The cockpit door was closed and automatically locked. There was no difficulty to unlock and lock the door at this Time.

(2)   Despite the cruising level flight setting, the plane showed a tendency of ascent. An uncontrolled ascent in high altitude cruising level flight before a sudden descent was a common behavior in F-event in 2009, A-event in 2014 and L-event in 2015. The Writers have yet to be able to explain the cause of this uncontrolled ascent. However, they assume the wireless hydraulic control unit attached to the cockpit panel might have started being affected by the early-stage development of the bulkhead fatigue rupture. In any case, it’s an undeniable fact that the Airbus’ uncontrolled ascent in cruising altitude had preceded the decent in all the three events.

(3)   The co-pilot probably tried to balance the ascent by fractional manual descents several times. Slow decompression must have been developing during the cruising, and the co-pilot had suffered from difficult hearing.

(4)   The captain wanted to reenter the cockpit at around Time 3-min, but found it was impossible to unlock the cockpit door. He asked the co-pilot to unlock it from the cockpit side. Alas, the co-pilot couldn’t hear it, hence, didn’t answer. Though he couldn’t hear captain’s plea, provably, he might have tried himself to open the door, but it was unable to unlock too. There was only one chance in the early stage of decompression to unlock the door, i.e., while had the door pushed from the cockpit side toward the cabin side by the co-pilot and the captain unlocked it from the cabin side, as the co-pilot’s push could balance the push by air pressure in the cabin, having released the lock bar from constraint due to Coulomb friction. The Coulomb Friction theory is high school level intelligence. cf. a quotation below:
French prosecutor Brice Robin sensationally reveals that the co-pilot of the doomed Germanwings Airbus A320 locked his captain out of the cockpit before deliberately crashing into a mountain to 'destroy the plane.’

(5)   As decompression had developed to an unbearable degree, the co-pilot reflexively (deliberately, voluntarily, abruptly aren’t suitable adverbs) set the auto-pilot on steep descent position down to 2000-m altitude as regularly trained by exercises and instructed in the Airbus Flight Manual that pilots are given. It was Time 5-min. cf. the following quotations.
‘Here are some of the factors that could have caused the pilots to make an emergency descent. These are all speculative at this point, given the paucity of information about the situation the Germanwings pilots faced.’
‘The most common reason for an airliner diverting from its cruising altitude and making a steep but controlled descent is to respond to a problem with the plane's pressurization system. Aircraft like the A320 are pressurized to about 10,000 feet while flying at cruising altitude, but a problem with this system would force passengers to wear oxygen masks while the pilot brought the plane to a lower altitude where outside air contains higher levels of oxygen.’
‘This is a relatively common occurrence for which flight crews are regularly trained, and typically pilots are able to make a distress call followed by an emergency landing, depending on the nature of the problem.’
Comment: The co-pilot never set the auto-pilot on descent down to 100-ft (30.48-m) altitude as popularly speculated but at 2000-m as per a rule. It is clearly evidenced by the existence of post-descent level flight of 2000-m altitude. The co-pilot set so, having hoped that, at the designated altitude, he could manage the matter, e.g., turning to right with a circular flight for an alighting emergency land on the Mediterranean Sea. When the plane descended to 2000-m altitude, it had still 15-km distant to the mountainside. It was enough distant for him to do so. cf. quotations below:
At 10.40.47, a French radar picked up Flight 4U9525 for the last time. It was flying steadily at a height of 6,175ft (1882.14-m) – almost exactly the altitude (of 2000-m) at which the debris that is now all that remains of the Airbus lies scattered on the mountainside.
‘(Based on) satellite data, he said it had found evidence the autopilot was abruptly switched from cruising altitude to just 100 feet, the lowest possible setting.
Among the new details, he said the airliner had flown in a straight line directly into the mountain, but would not say whether that seemed to be at the hand of a pilot or auto-pilot.
(6)   During the descent, the fatigue crack and rupture developed from slowly to rapidly and ended up in a stable deformation. Following the development, it generated metallic sounds first lightly (crack developing), next strongly (rupture developing) and last violently (Bulkhead flattering at the rupture section). The fluctuation in sounds was popularly regarded as captain’s knocking at door (first lightly, second heavily) and (third frantically) by axing at the cockpit door. The crack-rupture development lasted from Time 3-min. to Time 8-min.
BEA says, ’The co-pilot was breathing when the plane descended down to 2000-m altitude,’ suggesting he was still good enough to have saved the plane but purposely he didn’t.
What on earth are two, viz. (i) Even after brain death, human’s lungs breathe, heart beats, (ii) It is dubious if CVR can record human breaths. It should be tested with other A320-200 and compare it to the L-event record by means of the Fourier analysis. The recorded sound was, more possibly, wind breaths (much louder than human breaths) generated by flowing air across the fatigue crack. The simplst way is to make an analogy with A-event’s CVR record.
(7) After the descent, it entered the post-descent level flight that began at Time 14-min. The plane was in 2000-m altitude and 15-km distant before the mountainside. The co-pilot’s intention, at the time when he set the auto-pilot, was, ‘after the plane descent to the designated altitude, make the plane turn to the right for alighting emergency land on the Mediterranean Seawater.’ Alas, he couldn’t do it as he’d been physically defunct. At Time-15-min. the plane smashed to the mountainside by the auto-pilot as had been so set and had no further command.

The Hypothesis and its induction
The Writers induct their Hypothesis that the cause of L-event is the bulkhead fatigue rupture in the cockpit. It caused slow-to-rapid decompression in the cockpit. It’s a primary consequence of the cause, ‘bulkhead fatigue crack-rapture.’ It made the cockpit door be unable to unlock. So the captain couldn’t reenter the cockpit. The co-pilot lost his auditory sense as it’s the first symptom of the slow decompression. He reflexively set the auto-pilot on a steep descent position down to 2000-m altitude as so trained and instructed. It was his last effort to save the plane.
He had fallen into physical defunct before the plane began level flight as soset. As the co-pilot gave the auto-pilot no further command, the plane faithfully kept its course to crash. They’re the secondary, tertiary to the last consequence of the cause, ‘bulkhead fatigue rupture.’
The Hypothesis thus set up has no contradiction with all the premises. And there can be found no other hypothesis that is fully compatible to the premises. In this way, the induction has reached a conclusion, and the Hypothesis has been established.
L-event quite likely has been accelerated and triggered by nose wheel accommodation hutch’s improper repairs implemented 12 hrs before the event. For the time being, it’s unknown what role did the repairs and its consequential matters play in the event. It can be proven by scrutinizing all the pieces of the cockpit and identifying the existence of fatigue marks and their positions. It is to be reinforced by the symptoms of decompression with co-pilot’s body. If the fatigue marks would be found on its cut sections, the co-pilot-suicide hypothesis should have Gone with El Plane Pasa.
An insertion
There’s an insertion that assumes windscreen cracks. cf. a quotation below:
‘In a separate development, experts claimed the Germanwings plane may have crashed because the windscreen cracked; causing a sudden drop in oxygen levels that rendered the pilots unconscious. Reports circulating on professional pilot forums suggested the black box on the Airbus A320 had been analyzed and revealed that a 'structural failure' was responsible for the disaster.’
The Writers appreciate the insertion as a movement to get rid of the hypothesis’ logical impasse. However, they’d like to express their opinion that the windscreen cracks won’t lower oxygen and air pressure in the cockpit to a meaningful degree in any case.
A wind pressure of Mach number < 0.8 (subsonic resume) to which commercial airliners pertain is a postgraduate level theme. It needs sophisticated wind-tunnel tests and analyses. This report herewith briefly introduces only its basic matters.
Total pressure (Ptotal) on an effective perspective unit area perpendicular to a wind direction is:
Ptotal = Pw + Pa  = 0.5 * r* v2 * CD + Pa  -- - - -  (1),                 where;
Pw: Wind pressure (kg/m2), Pa: Atmospheric pressure at any altitude (kg/m2), r: Air density at any altitude (kg*sec2/m4), v: Wind velocity (m/sec), CD: Drag coefficient (dimensionless).
CD (defined by wind-tunnel tests, is assumed) = 1. Other data at any altitude can be found in reference books. Substituting them into Formula (1), Ptotal is determined. For instance, at 10000-ft altitude, r, v and Pa are 0.093, 200 and 7120. From them, Ptotal is 9000. Usual air pressure in a cabin is 9400~9600 > Ptotal. Hence, cockpit air may blow out at 10000-ft altitude. But ‘A320 are pressurized to about 10,000 feet (7120 < Ptotal = 9000) while flying at cruising altitude.’ cf. a quotation in page 13~14. In this context, outside air still blows in at 10000-ft altitude. At 35000-ft altitude, Ptotal = 3670 < 7120, hence, cockpit air blows out. The pressure difference between inside and outside cockpit is 7120 – 3670 = 3450 (kg/m2). If a crack happens at a surrounding bulkhead where atmospheric air flows parallel to a bulkhead (no wind pressure). In this case, Ptotal = - 0.5 * r* v2 + Pa -------- (2). From Formulae (1) and (2), it is clear that Ptotal of a side bulkhead is 2 * 0.5 * r* v2 less than the one of a windscreen. The pressure difference is 7120 – 1190 = 5930 (kg/m2). Referring to the fact that in- and out-side cockpit air has an equal potential head (h), and a velocity head of air inside cockpit (hv) is 0, the above can be easily proven by Bernoulli’s theory, hv + h +hp = constant for both in- and out-side cockpit,
Unlike fatigue cracks in a bulkhead, the scope and scale of crack development in a windscreen is limited, Hence, A320’s pressure keeping system likely overpowers a pressure decrease due to windscreen cracks. That is, oxygen in a cockpit won’t problematically decrease at any condition.

ISSUES BEYOND ENGINEERING

Legal issue
The setting of co-pilot-suicide hypothesis up to now may be an accidental act. However, would it last even after this report without reasonable explanations, it’s to be an intentional act that should be prosecuted. However, this is not an engineering issue but a judicial one with which the Writers have no business.
Disproportionate automation
As discussed earlier, A- and L- events (probably many others as well) are inevitable results of the over-automation shored up by the belief in computer-almighty. It results in society’s weakness, i.e., a lack of ability to deal with problems emerging beyond programs. An accident and a disaster are two typical examples that happen beyond programs.  It is the reason why the causation studies on them aren’t easily solved in general. The air crashes are a part of these general issues. As discussed already, it’s the background against which an effective solution to the problem is difficult. However, in this issue, there’s still a chance to reach a correct solution, if the matter is handled from a long-run point of view. This report is written for this chance.
Trend of totalitarianism
There’s another issue of more formidable nature. It’s totalitarianism. It’s as follows: A stalemate in over-automation is appearing not only in the technical but in many other sectors, e.g., political, economic, cultural etc. The best example is a war policy. In unconventional wars against so-called terrorists whose warfare is shored up by the belief in God-almighty. Fighters use IED, suicide car bomb, martyr attack, kidnapping and selective killing (beheading). All are manual, hence, can’t go without people’s support (contrarily, air strikes, drone bombing are all computerized that can go without people’s support). Terrorists’ strategy and tactics are all beyond programs. It is no wander all the wars have yet to be conclusive. The Writers wonder all the wars are unwinnable. Nonetheless, the war policy is consistent (no exit), because wars are allegedly in the interest of nations.
Now, bring the topic back to L-event, The co-pilot-suicide hypothesis is consistent, no exit unless it’d end up in collapse per se. The hypothesis is a computer-aided (black-box reliant) product; hence, It’ll go without people’s knowledge. Really, the things are going in this way.
The hypothesis is, in effect, a practice of a thought, ‘an individual may be sacrificed for general interest.’ This ideology is the very totalitarianism to which National Socialism and Communism representatively pertain. Under this regime, the police regard theories or persons of unfamiliar originality or personality as communism, Islamism, jargon and communists, Islamists, lunatics. The Writers’ works are of unfamiliar originality. Readers who do not understand or do not like the works will agree with the police. The readers of the works are to be suspected of sympathizers. The Writers are no longer able to write their works as they’re doing now.
How to meet the issues of beyond programs
To solve the issue fundamentally is very difficult and not engineers’ business but politicians, who has charismatic great leadership. Such a politician has yet to emerge on the stage. However, engineers can do and must do something to deal with the issue. There’re two keynotes on this way, viz. (i) to see the matter from a long-range point of view, and (ii) to seek a solution to problems coming back to a foundation ground. There must be potential talent in societies to meet these needs. Make all carriers open to the talent, and the things naturally move to a good direction. To respond this report is the first step of this movement.
If L-event could be settled with the co-pilot-suicide hypothesis, it works out cheap, as it needs only a minor change in the cockpit rule. It also causes less damage to the fame of Airbus and Lufthansa. Contrarily, to settle the matter with the bulkhead-fatigue-rupture Hypothesis is expensive. It also brings about more image-down to their reputation than the hypothesis does. It’s true the former is more bankable in the short term. Remember F-, A-, and L- events, in fact, carry a common cause. However, the cause of the first F-event was wrongly defined as a combined cause of minor mechanical failure (Pitot tube freeze) and pilots’ erroneous elevator handling (instead of nose down the plane, pilot nose it up). If F-event would have been handled rightly, the second and the third events, A- and L- events, that happened 6 years later, could be avoided. It implies that the correct disposal of the event pays even in the medium term. Much more, in the long term. The Writers encourage BEA investigators to respond this report in any form (con or pro) as a first step to put the matter back on a right track.
The Writers have made the same call in their past causation study reports on construction / structural accidents (bridge collapse, FNPP failure et al) and disasters (JKT flood, 2011 Japan Quake et al) for institutions (HU, HT, WB, OECD, JICA, BEA, JCEA, Scott-Ciwem et al), some by name, [7] ~ [18]. However, there’s been no response from nowhere. They may presume not to respond is less dangerous than to respond. May the Writers expect it in L-event?

CONCLUSIONS

This report gives its conclusions as follows:
(1) The Writers’ Hypothesis assumes that the cause of L-event is the bulkhead fatigue rupture in the cockpit. It has been confirmed: (i) this assumption has no contradiction to all the given premises, (ii) there’s no alternative hypothesis that fully satisfies the premises. Thus, the bulkhead-fatigue-rupture Hypothesis has been set up.
(2) The co-pilot-suicide hypothesis’ wishful imagination is seen throughout its logic. But the most imaginary one is to imagine that co-pilot’s breaths are recorded in CVR and to regard it as evidence that proves his good physical function until the last moment. The sounds are not co-pilot’s breaths but wind breaths at a crack-rupture opening. It can be confirmed by in-situ tests with other A320-200 and Fourier analyses, and in analogy with CVR data of A-event.
(3) The improper discards are also in many occasions. But the most fatal two are: (i) The neglect of the repairs that the plane had undergone 12 hrs before the event happened, and (ii) the omission of an analogy between A-event and L-event.
(4) After the captain left the cockpit, the cockpit door was automatically locked. When he wanted to reenter, he couldn’t unlock the door. It was not caused by being locked from the cockpit side but the friction between the lock bar and the door sash caused by the cabin side air pressure that pushed the door. The cabin side air pressure was caused by the decompression in the cockpit. The decompression was caused by the bulkhead fatigue rupture in the cockpit.
(5) When the decompression developed to an unbearable degree, the Co-pilot reflexively set the auto-pilot on a deep descent position down to 2000-m altitude as he had been so trained and instructed. He’d become physically defunct before the plane descended down to the designated altitude, hence, couldn’t give the auto-pilot further commands. The auto-pilot executed the given command, having had no further command until the plane crashed.
(6) There’s a high possibility that the repairs, which the plane had undergone 12 hrs before the event accelerated the development of fatigue cracks and triggered rupture.
(7) To the Writers’ regret, the Writers’ Hypothesis is not proven by black box data, since FDR missed its essential component, a data-memory card. However, it’d be proven by identifying fatigue marks in the cockpit debris and/or finding symptoms of decompression in the co-pilot’s remains (be the Writers highest condolences on him).
(8) As the event is deeply tangled in politico-socio-cultural-monetary settings, its techno-scientific disposal is not easy. To fundamentally solve this issue, it needs ultra-powerful-charismatic leadership that will appear on the last stage of the current too-stretched automation, but such leadership has yet to be in sight.
(9) For the time being, what the people concerned can do and should do is to handle each problem in a right way. The two keynotes on this way are (i) to see a problem in a long term and (ii) to think a problem coming back to foundation ground. To respond this report is the first step of it.

GLOSSARY

RI: The Republic of Indonesia, US: The United States of America, SSR: Soviet Socialist Republic, JKT: Jakarta, PLG: Palembang,
WB: the World Bank (the International Bank for Reconstruction and Development),
OECD: Organization for Economic Cooperation and Development, JICA: Japan International Cooperation Agency, BEA: Bureau d'Enquêtes Accident (Accident Enquiry Bureau), Paris,
ATC Center: Air Traffic Control Center, FNPP: Fukusima Nuclear Power Plant, JCEA: Japan Civil Engineering Association,
UIBA: IBA University, HU: Harvard University, UT: University of Tokyo,
L-event: Lufthansa Germanwings Airbus crash event, A-event: AirAsia Airbus crash event,
F-event: Air France Flight 447 Airbus A330-220 crash event,
CVR: Cockpit Voice Recorder (a "Black Box"), FDR: Flight Data Recorder (a "Black Box"),
IED: Improvised Explosive Device, ABIDS: Acquired Basic-Intelligence Deficiency Syndrome, RPM: Round per Minute, DNA: Deoxyribonucleic Acid
REFERENCES

[1] Sohei Matsuno, ‘SEA LEVEL RISE AND COASTAL FLOODING (JAKARTA),’

      www.iba.ac.id/

[3] World News, ‘Asia AirAsia flight QZ8501 missing: Q&A - what is known about ...

      www.independent.co.uk/
[5] The Guardian, ‘Germanwings flight 4U9525’ www.theguardian.com, Mar 26, 2015
[6] news/article-3011235, ‘Germanwings-pilots-REFUSE-fly-s-revealed-doomed-jet,’ www.dailymail.co.uk/
      www.iba.ac.id/ Jan 6, 2012

[8] Sohei Matsuno, ‘a sequel to uiba's 1st report on kukar bridge collapse,’

      www.iba.ac.id/  Dec 2, 2011

[9] Sohei Matsuno, “uiba's and happy pontist's kukar bridge collapse theory,iba.ac.id/

[10] Sohei Matsuno,jakarta flood prevention project with a true cause,”
         www.iba.ac.id/ 8 Mar 2013
      www.lba.ac.id/, 30 Apr.2013

[12] Sohei Matsuno, JAKARTA-FLOOD PREVENTION BY TRAINING DIKE vs. GIANT SEA WALL,www.iba.ac.id/

[13] Sohei Matsuno, “CAUSE & PREVENTION OF COASTAL FLOOFING, JAKAETA FLOODING AS A CASE,“ www.iba.ac.id/

[14] Sohei Matsuno, ‘uiba's and happy pontist's kukar bridge collapse theory,’

        iba.ac.id/documents/

[15] Sohei Matsuno, “CAUSE & PREVENTION OF COASTAL FLOOFING, JAKAETA FLOODING AS A CASE,“ www.iba.ac.id/

[16] Sohei Matsuno,2011 JAPAN QUAKE OVERPOWERS PLATE TECTONICS,’

        www.iba.ac.id/, 11 Mar. 2011, at 14 hr. 46 min 30 ...
[17] Sohei Matsuno,2011 JAPAN QUAKE OVERPOWERed PLATE TECTONICS,’ soheimatsuno.blogspot.com/, Jun 19 2013

[18] Sohei Matsuno et al,A CAUSAL STUDY ON THE AIRASIA AIRBUS CRASH EVENT,’

         www.iba.ac.id/,  2015


Completed on April 24 2015

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