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Formalism Helps in Describing Accidents

Peter B. Ladkin

Research Report RVS-RR-96-12

I analyse the 'probable cause' of the 1979 Chicago DC-10 accident using a minimal formalism, and find an omission. The omission is contained in the body of the report. McDonnell Douglas's statement barely addresses the point contained in the omission. I conclude that formalism helps in accident reporting by enabling simple consistency and omission checks.

Accident reports in aviation present careful reasoned conclusions about causes and causal factors contributing to the accident, as well as providing pro forma details which may be useful in other contexts, say for statistical investigations of accident types.

The reasoning in accident reports is informal. Could it help to formalise this reasoning? I'll consider one famous example in detail. First, the statement of 'probable cause' of the Chicago-O'Hare 1979 DC-10 accident (1):

The National Transportation Safety Board determines that the probable cause of this accident was the asymmetrical stall and the ensuing roll of the aircraft because of the uncommanded retraction of the left wing leading edge slats [...] and the loss of stall warning and slat disagreement systems resulting from maintenance-induced damage leading to the separation of the No. 1 engine and pylon assembly at a critical point during takeoff. The separation resulted from damage by improper maintenance procedures which led to failure of the pylon structure.
Let's analyse this statement with the method of (2). First, we list the crucial events, and denote each by a simple phrase. Second, we determine all relations between the events given by true assertions of the form: 'why ..... because .... .

A Simple Example

Let's take a simple hypothetical example to illustrate the method.

Stage 1.

The crucial events are

Stage 2.

'Why did the aircraft hit the ground? Because it stalled'

Well, actually no, maybe not. If the aircraft was at 100 feet, this would be true. But the aircraft was at 3000 feet. I write this 'why?....because' relation as [2]~>[1].

'Why did the aircraft hit the ground? Because it stalled and did not recover in time

We need to return to Stage 1 and modify.

Stage 1'.

The crucial events are

Stage 2'.

[2] /\ [3] ~> [1]    (here, '/\' is formal notation for 'and')

Event [1] fulfils the FAA definition of accident. We have three events, one being the accident, and the other two causally related to it (which we determined by asking 'why?....because'. We observe that there were two causally determining events for [1], and both of these events had to pertain for [1] inevitably to occur. Events [2] and [3] are thus jointly necessary but not individually sufficient.

We critiqued the initial result, and went back to modify the derivation. This revisiting is usual in formal methods, and could be named the 'inevitable intertwining' or 'spiral' (Note 1). The final causal relation that we obtained in Stage 2' holds as well for the airplane at 100 feet as for the airplane at 3000 feet. Simply at 100 feet, noone expects a stall recovery to be effected in time. Since we're 'expecting' it, does it need to be said? In an accident report, yes. A clear statement could lead to useful research into stall recovery in less than 100 feet. If it's not said, no-one will remark it.

Analysing the Probable Cause of the Chicago DC-10 Accident

First, a list of events mentioned in the statement of probable cause:

Second, the apparent relationship between events as asserted in the 'probable cause' appears to be a complex causal chain of the form
[8] ~> [7] ~> [5] /\ [6] /\ [4] ~> [3] ~> [2] ~> [1]
So, the accident report considers a 'probable cause' to be a causal chain. It singles out this causal chain as the most important interconnection of events. However, the stall warning system is an indication to the pilots of what was happening, as is also the slat disagreement system, and their loss ([5] and [6]) only affects at most pilots' behavior, and not directly the control systems of the aircraft. They certainly play no direct role in [3], [2] or [1]. Specifically, although why [3]? because [4] /\ [5] /\ [6]' is true, so is why [3]? because [4]'. Therefore one could conclude that [5] and [6] are superfluous in statement of this causal chain, since if it is a correct causal assertion, the following is also a causal chain leading to the accident:
[8] ~> [7] ~> [4] ~> [3] ~> [2] ~> [1]

However, during the discussion, the report says:

The simulator tests showed that, even with the loss of the number two and number four spoilers, sufficient lateral control was available from the ailerons and other spoilers to offset the asymmetric lift caused by left slat retraction at airspeeds above that at which the wing would stall. However the stall speed for the left wing increased to 159 KIAS.
(KIAS denotes 'Knots Indicated Air Speed', i.e., the figure displayed on the Air Speed Indicators in the cockpit.) The report is saying explicitly that [4] did not inevitably lead to [3]. The airplane remained controllable. That entails that [4] did not inevitably result in [3]. This statement is simply inconsistent with the assertion of 'probable cause' (Note 2).

The solution is that something is missing from the causal chain expressed in the 'probable cause' statement. This omission is, however, contained clearly in the body of the report.

The evidence was conclusive that the aircraft was being flown in accordance with the carrier's prescribed engine failure procedures. [...] Since the wing and engine cannot be seen from the cockpit and the slat position indicating system was inoperative, there would have been no indication to the flight crew of the slat retraction and its subsequent performance penalty. Therefore, the first officer [the pilot flying] continued to comply with carrier procedures and maintained the commanded pitch attitude [...] which decelerated the aircraft towards V2, and at V2 + 6, 159 KIAS, the roll to the left began. [...] There would be little or no [impending-stall-indicating] buffet. [...] Since the roll to the left began at V2 + 6 and since the pilots were aware that V2 was well above the aircraft's stall speed, the probably did not suspect that the roll to the left indicated a stall. In fact, the roll probably confused them, especially since the stick-shaker [a stall warning] had not activated.
This says clearly that because the flight crew were unaware of the slat retraction, they didn't know that the stall speed had increased, and they flew the airplane 'in accordance with procedures which dictated a speed slower than the new increased stall speed. It was thus inevitable that the airplane's left wing would stall. There was no indication to the pilots of this impending stall because the stall warning system was also inoperative. Had there been, one imagines that they would have reacted immediately (the indications are that they were excellent pilots, who the report says were flying exactly 'by the book') and the airplane could have been controlled (the report has stated, above, that the airplane was controllable, derived from simulator tests).

Hence the report says that pilots' ignorance of the asymmetrical flap condition and impending stall allowed the stall of the left wing to take place. Thus is an essential causal factor missing from the 'probable cause' statement:

[5] /\ [6] ~> [9] ~> [3]
where and the causal chain should read
[8] ~> [7] ~> [5] /\ [6] /\ [4] ~> [9] ~> [3] ~> [2] ~> [1]

So the logic of the report is faulty. The 'probable cause' statement includes an incomplete causal chain. A simple semi-formal analysis of the report itself, namely just asking what does it say were the critical events and what does it say are their causal relationships, exposes this incompleteness, and demonstrates the inconsistency in the report itself.

Well, OK, an engineer might reply, this doesn't satisfy the logical nit-pickers, but we can all figure this out from the report for ourselves, so why worry?

There was considerable public interest at the time concerning the engineering of the DC-10 because of the accident. McDonnell Douglas issued a report (3) in an attempt 'To Set The Record Straight':

There is no point, as rule as old as Aristotle tells us, in debating a question that can be settled simply by examining the facts. [....]
[The circumstances of the accident] gave rise to important - to urgent - questions. [Questions follow.]
Naturally, properly, discussion of the DC-10 continued as long as such questions remained unanswered. And not all of them were answered quickly. [..]
The answers, when they emerged, were clear and conclusive. They proved that the DC-10 meets the tougest standards of aerospace technology.
They proved, too, that the Chicago accident did not result from any deficiencies of aircraft design, and that steps taken shortly after the accident had eliminated any possibility of recurrence.
In a section entitled The Basic Questions, they asked and answered:

McDonnell Douglas clearly felt the need to clarify public perceptions of the accident by enumerating and commenting the facts. It is a laudable goal, one which I support and which is supported by all the engineers working within democratic societies whom I have ever met.

First, we can imagine that a clear, consistent, complete explanation to the public of what had gone wrong, a goal of the NTSB, McDonnell Douglas, and the airlines, could have followed directly and unambiguously from the NTSB report without the intervention of McDonnell Douglas, had the NTSB report conclusion been complete and had the report itself not been inconsistent.

Second, McDonnell Douglas's 'Basic Questions' generally follow the 'probable cause' statement of the NTSB report. As factor [9] was not included from the 'probable cause' statement, so it does not appear in the 'Basic Questions'. An answer is given, however, namely that the stall warning system's redundancy "exceeds industry standards for transport aircraft.". We can conclude

The NTSB in fact drew both these conclusions, even though they do not explicitly pertain to the 'probable cause' statement. The report's 'Safety Recommendations' (Class II, Priority Action A-79-99) recommended that
[...] if certification is based upon demonstrated controllability of the aircraft under condition of asymmetry, insure that asymmetric warning systems, stall warning systems, or other critical systems needed to provide the pilot with information essential to safe flight are completely redundant.
(This is the clause of A-79-99 pertaining to the DC-10. The McDonnell Douglas report states that the DC-10 was the only wide-body cabin airliner to have demonstrated the ability to fly with asymmetrical slats, which it did during certification.)

Simple formalisation has shown infelicities in the NTSB report of its conclusions concerning the Chicago crash. McDonnell Douglas felt the need for public clarification, and a clear statement of the facts. However, full information on one necessary causal factor was not provided in their clarification. This is consistent with the omission of this factor from the statement of probable cause in the NTSB report. We can imagine that public and professional discussion of the accident, an essential factor for safety progress in a democratic society, could have been aided by simple formalisation, which demonstrates this omission.

This is not the only example to demonstrate advantages of this simple formalism. In (2), I demonstrated using the same technique that two necessary causal factors, the position of an earth bank and the state of the runway surface, were omitted from the 'Causes' statement of the report on the A320 accident in Warsaw in September 1993. Both of these are under direct control of the Polish Authorities, yet recommendations to the authorities were only that the system of collecting and distributing meteorological information should be adapted to conform to ICAO Convention Annex 3 standards, and that the bank should be described in the AIP Poland (the official description of airports). One can thus observe from the formalisation that the recommendation prima facie does not conform precisely to all the necessary causal factors, and imagine that it would have helped the goals of accident analysis to have addressed this apparent disparity in the report itself.

I conclude that formalisation helps. It enables us to check not only the events, but also the reasoning concerning those events and the derivation of the conclusions and recommendations in an accident report.


References link back to the first mention.
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(1): National Transportation Safety Board, Aircraft Accident Report, American Airlines, Inc. DC-10-10, N110AA, Chicago-O'Hare International Airport, Chicago, Illinois, May 25, 1979., Report NTSB-AAR-79-17, NTSB, Washington, DC, 1979. Also in (4). Back

(2): Peter Ladkin, The X-31 and A320 Warsaw Crashes: Whodunnit?. Back

(3): McDonnell Douglas Corporation The DC-10: A Special Report, McDonnell Douglas Corp., 1979. Also in (4). Back

(4): John H. Fielder and Douglas Birch, eds., The DC-10 Case, State University of New York Press, 1992.

(5): W. Swartout and R. Balzer The Inevitable Intertwining of Specification and Implementation, Communications of the ACM 25(7):438-440, July 1982. Back

(6): B. W. Boehm A Spiral Model of Software Development and Enhancement, ACM SIGSOFT Software Engineering Notes 11(4):14-24, August 1986. Back

(7): P. B. Ladkin Time for Causes, to appear in in September 1996. Back


(Note 1): After Swartout and Balzer (5) and Boehm (6), respectively. Back

(Note 2): This provides yet another reason why the 'causes' relation cannot be identified with the temporal logic 'leads to' relation. See (7). Back