PROFIT-FUNCTION OF TWO SIMILAR WARM STANDBY NAVY SHIP SYSTEM SUBJECT TO FAILURE DUE TO AGEING SHIPS IN NEED OF MAINTENANCE, DELAYED ACQUISITIONS BY THE MINISTRY OF DEFENCE, AND HUMAN ERROR. DR. ASHOK KUMAR SAINI Assoc. Prof.(Maths), BLJS College, Tosham (Bhiwani) Haryana, India Abstract- In this paper we have taken failure due to ageing ships in need of maintenance, delayed acquisitions by the Ministry of Defence, and human error. When the main unit fails then warm standby system becomes operative. Failure due to human error cannot occur simultaneously in both the units and after failure the unit undergoes Type-I or Type-II or Type-III repair facility immediately. Applying the regenerative point technique with renewal process theory the various reliability parameters MTSF, Availability, Busy period, Benefit-Function analysis have been evaluated. Keywords- Warm Standby, failure due to ageing ships in need of maintenance, delayed acquisitions by the Ministry of Defence, and human error, first come first serve, MTSF, Availability, Busy period, Benefit -Function. I. INTRODUCTION Laxmi were unable to detect INS Trishul and prevent the side on collision. No casualties were List of Indian Naval accidents reported. An article in India Today reports that since 1990, the April 2006: INS Prahar (K98), Veer class Indian Navy has lost one warship in peacetime every corvette, sank after colliding with the MV Rajiv five years. Since 2004, it has lost one naval Gandhi vessel about 20 nautical miles away from combatant every two years. While peacetime losses the Goa coast. No casualties were reported. The of warships are not uncommon (since the World War commanding officer of the ship, Lieutenant II, the US Navy has lost 16 warships in accidents; Commander Yogesh Tripathi was found guilty Russia's nuclear submarine Kursk sank in August of negligence by an Indian Navy court- 2000 after a faulty torpedo exploded during a training martial and dismissed from service. exercise), the magazine mentioned that few global September 2006: INS Dunagiri (F36), Nilgiri navies have such a dubious record. According to class frigate, collided with a Shipping the Times of India, while some of accidents reported Corporation of India merchant vessel, the MV since August 2013 were serious, many of them were Kiti, off the coast of Mumbai. There were no trivial incidents exaggerated in public. casualties, but the Dunagiri suffered damage and required extensive repairs. These accidents have been attributed to ageing ships January 2008: INS Sindhughosh (S55), a Kilo- in need of maintenance, delayed acquisitions by class submarine, collided with a foreign the Ministry of Defence, and human error. However merchant vessel MV Leeds Castle while trying naval commentators also argue that as India's large to surface in waters north of Mumbai. The navy of 160 ships clocks around 12,000 ship-days at submarine was taking part in fleet-level war sea every year, in varied waters and weather, some games, when the accident occurred. The Navy incidents are inevitable. Captains of erring ships are termed it a minor incident with no casualties dismissed from their command following an reported. enquiry. The accident on board INS Sindhuratna August 2009: A collision of the missile (S59) led to the resignation of the then Chief of Naval corvette INS Kuthar (P46) with destroyer INS Staff (CNS) Admiral D K Joshi on 26 February 2014, Ranvir (D54) in the Bay of Bengal was traced to who owned moral responsibility. a rudder failure, compounded by a flawed maneuver. 2000 - 2010 December 2005: INS Trishul (F43), a Talwar- 2010 - present class frigate, collided with a commercial In 2010, three crew men on destroyer INS vessel, Ambuja Laxmi, outside the Mumbai Mumbai (D62) were instantly killed when harbor, while returning from a training mission. an AK-630 Close-in weapon system went off as These class of ships use stealth technologies and safety drills were not followed. a special hull design to ensure a reduced radar January 2011: INS Vindhyagiri (F42), a Nilgiri- cross section. Radar systems installed by the port class frigate, capsized after a collision with a authorities and those on board the Ambuja Cyprus-flagged merchant vessel MV Proceedings of 20th IRF International Conference, 1st March 2015, Chennai, India, ISBN: 978-93-84209-01-8 43 Profit-Function of Two Similar Warm Standby Navy Ship System Subject To Failure Due to Ageing Ships In Need of Maintenance, Delayed Acquisitions By The Ministry of Defence, And Human Error Nordlake near the Sunk Rock light house, February 2014: On 26 February, INS following which a major fire broke out in the Sindhuratna (S59), a Kilo-class submarine, had a ship's engine and boiler room. Everyone on fire detected on board when trials were being board was evacuated as soon as the fire broke conducted which resulted in smoke leading to out and hence there were no casualties. INS suffocation and death of two officers. Seven Vindhyagiri was later decommissioned. sailors were reported injured and were airlifted August 2013: Blasts ripped through the torpedo to the naval base hospital in Mumbai. According compartment of the INS Sindhurakshak to the naval board of inquiry, the fire was caused (S63) while it was berthed at the naval dockyard due to problems in the cables of the vessel. This off the Mumbai coast. Fifteen Sailors and three particular incident led to the resignation of Chief officers were killed.[15] Other sources state that a of Naval Staff (CNS) Admiral D K Joshi on 26 small explosion occurred around midnight which February 2014, who owned moral responsibility then triggered the two larger explosions. The for the incidents in the past few months. disaster was thought to be the Indian navy's March 2014: INS Kolkata, had a malfunction on worst since the sinking of the frigate INS board which led to a toxic gas leak killing Khukri by a Pakistani submarine during the 1971 Commander Kuntal Wadhwa instantly. It seems war. that the ship suffered malfunction in its carbon December 2013: INS Konkan (M72), dioxide unit while undergoing machinery trials, a Pondicherry-class minesweeper under the leading to gas leakage. Since the ship was not Eastern Naval Command, caught fire at the naval commissioned at the time of the incident, the dockyard at Visakhapatnamwhile undergoing enquiry into the mishap will be done repairs. The fire engulfed much of the ship's by Mazagon Dock Limited, where the ship was interior before it was put off. No casualties were constructed. reported. May 2014: INS Ganga (F22) suffered a minor December 2013: In the second incident in the explosion in the boiler room while undergoing a same month, INS Talwar (F40), the lead ship of refit at the Mumbai dockyard. Four people the Talwar class frigate of the Indian Navy, suffered minor injuries. There was no fire and no collided with a fishing trawler injuring four of equipment was damaged. the 27 people on board the trawler and sinking it. November 2014: A Torpedo Recovery Vessel of The fishing trawler was operating without the Astravahini class (A-73) sank 30 NM off lights. The captain of the ship was subsequently the Vizag coast during a routine mission to stripped of command. recover torpedoes fired by fleet ships during a December 2013: In the third incident in the same routine exercise. The accident resulted in the month, INS Tarkash (F50), again a Talwar class tragic death of one sailor while four others were frigate, suffered damage to its hull when it hit reported as missing however 23 other personnel the jetty while docking at the Mumbai naval were rescued by SAR teams deployed right after base. The navy ordered a board of inquiry. the incident. January 2014: INS Betwa (F39), an indigenously built Brahmaputra class guided missile frigate, Stochastic behavior of systems operating under ran aground and collided with an unidentified changing environments has widely been studied. object while approaching the Mumbai naval Dhillon , B.S. and Natesan, J. (1983) studied an base. The sonar system of the frigate was outdoor power systems in fluctuating environment . cracked, leading to faulty readings and an Kan Cheng (1985) has studied reliability analysis of a ingress of saltwater into sensitive equipment. system in a randomly changing environment. Jinhua January 2014: In the second incident in the same Cao (1989) has studied a man machine system month, INS Vipul (K46), a veer class corvette of operating under changing environment subject to a the elite 22nd Killer Missile Vessel Squadron, Markov process with two states. The change in was detected with a hole in its pillar operating conditions viz. fluctuations of voltage, compartment which forced the ship back into the corrosive atmosphere, very low gravity etc. may harbor while it was on an operational make a system completely inoperative. Severe deployment. environmental conditions can make the actual February 2014: On 3 February, INS Airavat mission duration longer than the ideal mission (L24), a Shardul class amphibious warfare duration. In this paper we have taken failure due to vessel, ran aground while returning to its home ageing ships in need of maintenance, delayed base at Visakhapatnam, causing slight damage to acquisitions by the Ministry of Defence, and human its propellers. Following the incident, its error. When the main operative unit fails then warm commanding officer, Captain JPS Virk, was standby system becomes operative. Failure due to relieved of command pending the findings of a human error cannot occur simultaneously in both the Board of Inquiry. units and after failure the unit undergoes repair facility of Type- II by ordinary repairman or Type III Proceedings of 20th IRF International Conference, 1st March 2015, Chennai, India, ISBN: 978-93-84209-01-8 44 Profit-Function of Two Similar Warm Standby Navy Ship System Subject To Failure Due to Ageing Ships In Need of Maintenance, Delayed Acquisitions By The Ministry of Defence, And Human Error by multispecialty repairman immediately when 1(ASDAFasdaf, urI , Onasdaf) The operating unit failure failure due to ageing ships in need of maintenance, due to ageing ships in need of maintenance, delayed delayed acquisitions by the Ministry of Defence.