3.1. Timeframe selection

In order to ensure relevance to current operations, the timeframe selected should be representative of both the technologies and operating conditions (e.g. helicopter types used). Selection might be attempted by consulting summaries of helicopter activity issued by institutions of international reach e.g. International Association of Oil and Gas Producers (OGP, 2012), national aviation authorities of countries that focus on the type of mission under study and helicopter accident studies (e.g. EHEST, 2010).

3.2. Definition of terms

This assures the comparability of data issued by different sources and should include definitions at a high level, where needed.

3.3. Identification of relevant countries

Given that international treaties require national authorities to be responsible for accident investigations, analysis of helicopter accidents requires the identification of the countries where the mission of interest is known or expected to occur. The sources mentioned in Section 3.1 can be used for country identification.

3.4. Operational data collection

Accident rates enable interpretation of accidents with regards to the size of operations. Therefore, the sources of such data should be identified (Section 3.1) and the variables to be used for the calculation of accident rates selected. For example, although flying hours typically estimate time at risk, other metrics reflect alternative safety perspectives, e.g. cycles of take-off and landing (Oil and Gas UK, 2011). Data completeness checks are required to assess the quality of such data (Nascimento et al., Reference Nascimento, Majumdar and Ochieng2012b) and to make recommendations for improved data collection and dissemination where needed.

3.5. Accident data collection

The reports issued by national accident investigation authorities might be complemented by those published by unofficial sources (e.g. those in Section 3.1). From such sources and the literature, variables of potential relevance to accidents (e.g. phases of flight) should be identified and a bespoke cause classification scheme developed. This might start from existing mature classification schemes (e.g. that of the European Coordination Centre for Accident and Incident Reporting Systems – ECCAIRS), which can be adapted as necessary to capture the finest possible level of detail with respect to the factors associated with the occurrences. However, given the potentially different accident models and investigation stop rules employed by the original accident investigators, varying levels of detail might be reported, which may prevent causal analysis at the desired level of detail. Following data extraction, completeness checks are applied.

3.6. Statistical analysis

In order to understand complex relationships and make inferences about unpredictable data (e.g. accidents), rigorous statistical analysis is required. A three-fold analysis plan is desirable as this enables the examination of accident characteristics from different and complimentary viewpoints. A bivariate analysis follows the analysis of rates to confirm the results obtained, investigate the variables for which accident rates are unavailable or inapplicable and cover any gaps caused by suboptimal quality data. Subsequently, a multivariate analysis identifies the multi-way interactions among variables and generates predictions based on past accident data. The tests to be applied depend on the characteristics and distributions of the data. Section 4 presents the tests used in this paper during the implementation of the framework.

4.1. Timeframe selection

Worldwide offshore helicopter operations between 1997 and 2011 fulfilled the conditions outlined in Section 3.1 (Oil and Gas UK, 2011).

4.2. Definition of terms

The accident statistics of offshore helicopter operations are frequently understated since the USA National Transportation Safety Board (NTSB) does not classify certain catastrophic types of occurrences as “accidents” (Williams, Reference Williams2012). To overcome this, the International Civil Aviation Organisation's (ICAO) definition of accident is refined in this paper as follows:

This definition addresses flights over other hostile environments (e.g. rough seas) that might destroy aircraft after relatively successful forced landings. The need to account for this aspect of helicopter operations has led to on-going revisions of regulations (e.g. EASA, 2012).

4.3. Identification of relevant countries

A total of 50 countries were identified from summaries of petroleum activity (BP, 2010) and helicopter safety analyses.

4.4. Operational data collection

Public domain data were complete to support the calculation of rates only for flight hours between 1997 and 2009 (OGP, 2012). The calculation of daylight and night-time flying hours was based on estimates whereby 3% of the worldwide and 8·46% of North Sea's total annual flying hours occur at night (Nascimento et al., Reference Nascimento, Majumdar and Ochieng2012b). The remainder of the night-time flying hours were split between the remaining flying regions (see Section 4.6.1) in proportion to the total flying hours in each region.

4.5. Accident data collection – sources and sampling strategy

Accident information was sought from the reports issued by the official accident investigation authorities of the 50 relevant countries. Of these, 46 target databases were available online. Checking the accident information gathered against the analyses outlined in Section 2 was needed, as typically, developing countries did not share accident information online.

Given the definition of an accident adopted, additional revision of the reported incidents in the countries of interest was needed. All the incidents available from the 46 databases were checked, as well as those reported to the USA's Accident/Incident Data System (AIDS) (FAA, 2012), Canadian Civil Aviation Daily Occurrence Reporting System (CADORS) (Transport Canada, 2012), British Mandatory Occurrence Reporting (MOR) scheme and Australian Transportation Safety Bureau (ATSB). The search words of Baker et al. (Reference Baker, Shanahan, Haaland, Brady and Li2011) were used, complemented by “ditching”, “water landing”, “oil”, “gas” and “ship”. This led to the incorporation of 16 catastrophic ditching “incidents” into this paper's “accident” dataset, all in the USA. The destruction of such helicopters was confirmed by checking the FAA aircraft registry.

Further searches were conducted using websites specialised in the sharing of aircraft-related information (e.g. Flight Safety Foundation, 2012). To minimise uncertainties, only accidents that matched the definition used in this paper and reported by at least two independent sources were included. Finally, the non-specialised press was checked for non-technical information e.g. if the accident occurred at night.

4.6. Identification of variables relevant to accidents and data completeness

A total of 139 variables of potential relevance to accidents were identified. Of these, 63 variables covered the demographic characteristics of each pilot (e.g. age) and 13 described the operating environment (e.g. meteorological conditions, cockpit instrumentation and autopilot fit). With the threshold for data completeness established at 90% (worldwide and across each regional dataset), the variables included in the analyses are outlined below.

4.6.1. Regions of occurrence

Instead of focussing on an artificial per-country grouping strategy, this paper uses the following OGP classification of offshore helicopter areas based upon the similarity of operational characteristics (OGP, 2012):

• • Gulf of Mexico (GOM);

• • North Sea (NS);

• • Other regions.

Since “other regions” encompassed areas of dissimilar characteristics (e.g. typical weather conditions in Canada and Africa), re-clustering was required. This was based on aspects relevant to safety that were derived from Nascimento et al. (Reference Nascimento, Majumdar, Ochieng and Jarvis2012c), as shown in Table 1.

Table 1. Clustering of “other regions”.

¹ Accidents happened in Saudi Arabia, United Arab Emirates, Iran and Qatar.

² Accidents happened in China, Taiwan, Indonesia, Thailand, Malaysia and Myanmar.

³ Commonwealth of Independent States. Accidents happened in Azerbaijan, Russia and Ukraine.

⁴ Accidents happened in Angola, Nigeria, Congo and Cameroon.

⁵ See Table 2.

Table 2. Helicopter category classification scheme.

4.6.3. Phases of flight

The phases of flight used in this paper account for the physical loads imposed on offshore helicopters and the cognitive effort of pilots (Teixeira, Reference Teixeira2006). However, the lack of detail in a considerable part of the dataset led to the clustering of phases as in Table 3. Despite the reduced ability to discriminate phases of flight, such clustered phases closely matched those of the UK Civil Aviation Authority (CAA, 2005), indicating their external validity.

Table 3. Flight phases classification scheme.

4.7. Development of accident cause classification scheme

Given the need to account for varying levels of detail reported by the different sources, the cause classification scheme reflected the finest level of detail found across the whole dataset, and hence took the high-level form presented in the Appendix. Causes were attributed to the “precipitating factor” or “the first event” that initiated the accident (Oil and Gas UK, 2011; Harris, Reference Harris2006, respectively). It is important to note that limited accident datasets do not allow for complex multivariate causal analysis (Majumdar et al., Reference Majumdar, Mak, Lettington and Nalder2009).

The findings of the original accident investigations were categorised using the scheme. For accidents without official investigation reports, the findings reported by the OGP were accepted on the basis of privileged information, e.g. from insurance claims. The remaining accidents were discussed among the authors and a conservative approach taken by frequently assigning “unknown or unavailable” as the accident cause. Most such accidents were the catastrophic ditchings originally classified as incidents, and hence not subject to complete investigations. The accidents stemming from operational causes were further classified as pilot-related whenever the reports indicated that they could have been avoided by appropriate piloting. However, this is not labelling such accidents as caused by pilot errors, as this labelling has previously been found premature and inconsistent across official accident reports (e.g. Hollnagel, Reference Hollnagel2009). This classification highlights opportunities for developing pilot-supportive tools (e.g. better automation modes).

4.8. Statistical analysis

For all the statistical tests, significance was established at p<0·050.

4.8.1. Analysis of accident rates

Given the sample sizes involved, the Shapiro-Wilk and Levene tests were used to check the normality of the distributions and the homogeneity of variance, respectively. Because in all cases at least one such assumption of parametric data was violated, non-parametric techniques were required. See Field (Reference Field2009) and Agresti (Reference Agresti2002) for details of the statistical tests mentioned above and outlined below.

4.8.1.1. The Kolmogorov-Smirnov Z (KS-Z) procedure

This procedure tested the null hypothesis whereby the distributions of accident rates across two conditions (i.e. daytime and night-time) were the same. Such a test ranks the data points in ascending order in each group separately and calculates the maximum absolute difference (D) between the observed cumulative distribution functions for both samples. The test is useful with small sample sizes, i.e., N<25 per group and its statistic is calculated as shown below, where n ₁ and n ₂ are the sample sizes in each condition.

(1)$$Z = {\rm max} _{\,j| D_j |} \sqrt {\displaystyle{{n_1 n_2} \over {n_1 + \; n_2}}} $$

4.8.1.2. The Moses Test of Extreme Reaction (MTER)

This investigated the null hypothesis that the extreme values observed for accident rates were equally likely to occur in both conditions studied (i.e., daytime and night-time). In this test, observations from both conditions are combined and ranked, and the probability, under the null hypothesis, that the range (r) of the control condition (i.e., daytime) is not greater than the observed range (m+k) is calculated by the following equation:

(2)$$P(r \le m + k) = \; \displaystyle{{\mathop \sum \nolimits_{i = 0}^k \left( {\matrix{ {i + m - 2} \cr i \cr}} \right)\left( {\matrix{ {n + 1 - i} \cr {n - i} \cr}} \right)} \over {\left( {\matrix{ {m + n} \cr m \cr}} \right)}}$$

where m and n are the number of observations in the control and experimental groups respectively (Sprent and Smeeton, Reference Sprent and Smeeton2001).

4.8.1.3. Kruskal-Wallis (KW)

This procedure tested the null hypothesis that the distributions of accident rates across k experimental conditions (i.e. the regions of occurrence) were the same. In this test, observations for all groups are jointly sorted and ranked and, for each group, the sum of ranks R _i and the number of observations n _i is obtained. With N as the total sample size, the test statistic is computed as:

(3)$$H = \; \displaystyle{{12} \over {N(N - 1)}}\; \mathop \sum \limits_{i = 1}^k \displaystyle{{R_i^2} \over {n_i}} - 3\; (N + 1)$$

where H follows a chi-square distribution with (k−1) degrees of freedom. In case significant results are found, post-hoc tests are used to identify where the differences lie, as described below.

4.8.1.4. The Mann-Whitney test with Bonferroni correction (MW/B)

This test was applied to each pair-wise combination of conditions drawn from the previous step to test the null hypothesis whereby the two samples were from populations with the same distribution functions. In this test, the observations in both groups are combined and ranked. The number of times that a score from one group precedes a score from the other group, and vice versa, is then calculated. The Mann-Whitney U statistic is the smaller of these two numbers, given by the following equation:

(4)$$U = \; n_1 n_2 + \; \displaystyle{{n_1 (n_1 + 1)} \over 2} - \; R_1 $$

where n ₁ and n ₂ are the sample sizes of both groups being compared, R ₁ is the sum of ranks for group 1 (assumed with the smallest U), and the significance levels of U are given by specific algorithms. The Bonferroni correction avoids falsely rejecting the null hypothesis by using a more stringent rejection criterion given by the initial significance level divided by the number of pairs under analysis. Because it consistently presented the lowest and most spaced-in-time accident rates, the North Sea was chosen as the control group for these tests.

4.8.2. Bivariate accident analyses

The Pearson's chi-square test was applied to investigate the null hypothesis whereby the categorical variables were independent when analysed in pairs. Based on the binomial distributions of marginal frequencies, this test compares the actual counts across the events of the variables with the counts that would be expected if the variables were independent. The greater the discrepancy, the larger the dependency (also called “association”). The discrepancy is calculated by the chi-square statistic, as follows:

(5)$${\rm X}^2 = \mathop \sum \limits_{i = 1}^r \mathop \sum \limits_{\,j = 1}^k \displaystyle{{(n_{{\rm ij}} - \mu _{{\rm ij}} )^2} \over {\mu _{{\rm ij}}}} $$

where n _ij and μ _ij are the observed and expected frequencies, and i and j represent rows and columns in the contingency tables, respectively. This test requires that not less than 80% of the cells in such tables have expected frequencies greater than five and that no single expected frequency is lower than unity. When this was violated, Fisher's exact test was used. This calculates exact probabilities based on the hyper-geometric distribution of inner cell counts. In both cases, clustering of categories was needed to avoid null cell frequencies. For example, the Single Engine (SE) category was formed from the fusion of SP and ST, and LT/MT was formed from the fusion between LT and MT. Furthermore, the “ground manoeuvres” category was created from the fusion between the parked and taxiing flight phases, and the “arrival segment” was formed from the fusion between approach and landing.

4.8.3. Multivariate accident analysis

Given the characteristics of the data, the exploration of possible interactions between more than two accident variables was embedded in the logistic regression analysis. This was used to predict the events of dependent variables (i.e., causes and outcomes of accidents) by modelling the linear relationship between the natural logarithm of the odds of such variables and the explanatory variables i.e., regions of operation, aircraft categories, phases of flight, lighting conditions and all possible interactions between such variables in the former case; and such variables, accident causes and all possible interactions between these variables in the latter case. The odds are defined as the ratio between the probability of an event of the dependent variable occurring (i.e., π) over the probability of such event not occurring (i.e., 1-π). The logistic regression is expressed as follows:

(6)$$\ln (\pi /1 - \pi ) = b_0 + \mathop \sum \limits_{i = 1}^{\rm n} b_i X_i $$

where b _o is the constant and X _i are the explanatory variables with their coefficients b _i. Such a regression, frequently used in transport research, uses maximum likelihood estimation to maximise the probability of obtaining the observed results given the fitted regression coefficients.

In order to ensure that the standard errors of the b coefficients were not excessively large, unobserved combinations of predictors needed to be avoided. This required further clustering of categories (e.g., LT, MT and HT clustered into the Multi-Engine (ME) category). The forward stepwise model fitting strategy based on the log-likelihood statistic was used to account for the exploratory nature of this study. Overdispersion and multicollinearity were not present in the data.