Concerned that management of job-oriented accidents has remained a daunting challenge for all stakeholders in Nigeria oil-industry, a longitudinal study was made to appraise the patterning of episodic incidence of industrial accidents in a typical oil and gas company operating in the Nigeria flank of the oil-rich Niger Delta Basin. A 10-year historical accident data were characterized and found to have absorbing chain properties. Four open-and-shot transition states namely : fatality, accident, near-miss and unsafe act, that are subject to ergodicity, were identified and used to craft a value digraph which define the stable transition probability matrix. The results, which suggest that on the average, 59% of staff are wasted through fatality or severe accidents, also points to escalating rates of fatalities and disabilities stemming from accidents thus calling for the need to review the existing hazard operations studies (HAZOPS) and hazard identification schemes (HAZIDS) so as to assist in whittling down, as low as reasonably practicable, the perceived unpleasant trend. The author is of the opinion that industrial accident victims, unlike in road traffic accident (RTA), habituate several times before entering the absorbing state.