Quality Management and Reliability - Essay Example

MN 5554 (Quality Management And Reliability) Reliability The domestic freezer can be regarded as a time-dependent unit, as it functions continuously over a period. It is a reparable unit, and is also meant to function under specific conditions. In the context of the reliability concept, the freezer's reliability is the probability that it will perform successfully (freeze the things placed in it) over a period of time without a breakdown. As an electronic, time-dependent unit, the stress on the freezer is generally of a steady nature. . The freezer generally is expected to function under relatively steady environmental conditions, at room temperature. It is also encapsulated. Its mission is to successfully perform the freezing of items placed in it. To measure time for a domestic freezer, a Reliability analysis in the context of the unit's Mean Time To Failure (MTTF), would be appropriate. As a unit normally connected in series, the freezer- for purposes of this analysis- can be considered as essentially comprised of : (1) A compressor (2) An Evaporator (3) A Solenoid valve The freezer's series connection means that a failure of either of the above units renders the freezer incapable of performance. Let RDS = Reliability of domestic freezer system RC = Reliability of compressor unit RV = Reliability of the Solenoid unit RA = Reliability of the Evaporator RDS(t), the freezer system's total Reliability over a period of time (t) is given by: e -ct . e -vt . e -at = e - (c +v +a)t where: c, v, and a are the constant failure rates for the compressor, solenoid valve and evaporator, respectively. The total failure rate for this freezer system, zDS,(t), is given by: zDS = -1/RDS(t) . d/dt {zDS(t)}[c +v +a] The freezer's Mean Time To Failure MTTF is Lim RDS (s) = 1/(c +v +a), as s tends to zero Where (s) = Laplace transform variable RDS(s) = Laplace transform variable of the freezer series system reliability. 2. The fire extinguisher in a warehouse must be stored under specified conditions. It is a device which functions on demand; hence it is time-dependent. Its mission can be described as the successful emission of gas when required, to put out fire in the warehouse. Temperature conditions in the warehouse must not fall below a certain critical level, as this may affect the condition of the gas in the extinguisher container; surrounding temperatures must also not rise above a certain value, as this may damage or change the constitution of the extinguisher-gas, or even cause it to evaporate altogether over time. The extinguisher's valve may be vulnerable to physical damage-an aspect of mechanical stress- depending on where and how the device is kept in the warehouse. The extinguisher is subject also to physical damage through reckless handling, or if it takes hard knocks by falling from a height, etc. The extinguisher in the warehouse may actually be required to function under conditions of varying operating stress, and perhaps environmental extremes. To measure time for the warehouse fire extinguisher, One may consider it as a 2-part unit: (1) The gas-release valve (2) The internal piston Let : The extinguisher valve's Reliability = RV, and RP = extinguisher piston's Reliability Then for this fire extinguisher, total reliability is There is a series connection between the valve and piston. Failure of either means a failure of the system. RSE , the extinguisher system's Reliability over a period t, is : e -vt . e -pt = e -(v + p)t where: v, p are the constant failure rates for valve and piston. The total failure rate for the extinguisher zSE(t) = -1/RSE . d/dt {RSE(t)} [v +p] and the Mean Time To Failure for the extinguisher is Lim RSE(s) = 1/ [v + p] as s tends to zero, where: (s) = Laplace transform variable RSE(s) = Laplace transform variable of extinguisher system's reliability 3 A car can be regarded as a time-dependent system, as it is essentially required to function demand, albeit regularly. It is a reparable system, and it is supposed to function under certain specified conditions- it is not manufactured to function under unlimited conditions. The environment for its performance must therefore take into account appropriate conditions for its various components. Varying degrees of mechanical stress, for instance, may arise from (a) the number of miles travelled per journey, (b) ruggedness of terrain during a journey, (c) wear and tear on the gear system when the car is used. The permissible degree of thermal stress should also be considered as part of the specified conditions under which the car should function, as: (d) heating of the engine, for instance, constitutes part of the heat-related stress on the car during use; (e) electrical stress may impact the car over time, as battery, spark plugs, lighting etc need to perform when the car is used- although generally, such components function under a low-stress routine. The specified conditions/environment for car performance should also take cognisance of surrounding temperature- a super-chilled battery certainly does not enhance the car's usability! . The car's mission is to perform on demand, by successfully moving from location . A to location B To measure time for a car, one needs a Reliability analysis as follows: The car must be considered on the basis of its Mean Time To Failure (MTTF), or failure rate; this is the average time between failures, for the car. We may- for ease of analysis- consider a car as a system connected in series, in 3 parts: (i) The Engine (ii) Electrical power devices (battery-centred, and connected in parallel) (iii) Proper alignment/attachment of the four wheels (a mechanical aspect) The above can be rationalised thus: (i) If the engine fails, the car cannot be driven (ii) Battery failure also implies the car has failed (it may not even start!) (iii) Failure of any of the four wheels renders the car immobile By the principle of Reliability, the reliability Rs that the car system performs without failure for a time t, is the probability that under normal operating conditions for the car battery, engine and wheels the car will successfully carry out its mission of moving from one place to another. This can be mathematically analysed thus; Rs = Reliability of car system Rb = Reliability of Battery Rw = Reliability of Wheels Re = Reliability of engine Where Rs (t), the car system's reliability to perform up to a time t, is: e -bt . e -xt . e -wt = e -(b +x +w) t where b, x and w represent the total failure rates for the battery, engine and car wheels respectively. The total failure rate for the car system k (t) = -1/Rs(t) . d/dt { Rs(t)} (b +x +w ) The car's mean time to failure MTTF is : Lim Rs(s) = 1/(b +x+ w), as s tends to zero, where: (s) = Laplace transform variable Rs(s) = Laplace transform variable of the car's series system reliability CATEGORISATION SCHEME FOR CAR Failure Type Category Failure Consequence 1. Fuel pump failure 1st class failure petrol can't get pumped into car engine 2. Silencer falls off 2nd class failure car is mechanically . impaired; motion is a struggle; pollution 3 Brake failure 1st class driving is risky; car movement uncon- trollable 4 Puncture 2nd class grinding, rough motion of car (ONE puncture assumed) 5 Puncture but can't change wheel 1st class car rendered unfit for the road 6. Bulb in courtesy lighter failure 3rd class minor, won't adversely affect car performance By the definition of maintainability, when maintenance action is initiated under stated conditions, the failed system will be restored within a specified down time. Hence for changing/repairing the electric plug fuse, the maintainability requirements are that (a) there must be a stated condition under which the repair action for the fuse is being carried out (b) the fuse should necessarily have had a fault (c) the repair action must not exceed a certain length of time to get the fuse back in working order; the length of repair time is the down time for the fuse/plug Likewise, for the renewal of the water tap washer, the maintainability requirements are that: (1) The tap's washer should actually have a fault (2) There must be a stated condition under which repair of the washer is carried out (3) The operation of repairing the washer (under the stated condition) must restore the washer to its usable mode within a certain period of time, which actually represents the down time for the washer. For the fuse/plug being changed, (1) First, it should be ascertained that there is a fault, hence a need to check the fuse for exactly what manner of fault it has. A difficulty with this is that sometimes the fault is not always readily diagnosable. (2) It is essential to see that the relevant tools for the job, having ascertained the fault, are available- sometimes conditions are not ideal, the right /exact tool may not be available, either because it is more specialised and therefore quite expensive hence relatively inaccessible. (3) The cover of the fuse/plug should be carefully unscrewed; if this is not observed there is the possibility- especially if it is an old plug- that its screw is too tight, and removing it may entail too much force, damaging either the screw-driver or plug screw, or both. (4) The Live, Earth and Neutral wires need to be carefully unscrewed for the bad fuse. (5) The bad fuse is removed- care must be taken; there is a difficulty when a nasty electric shock is received, due to contact with a naked or worn cable/coil (6) The new fuse is inserted. (7) The new cable is inserted following the pattern of the old one; there is a difficulty which may arise, where the colour convention is not carefully observed by the repairer(sometimes there are alternative colours for the Live or Earth terminals, and this may confuse some inexperienced person who is only familiar with one set of colours); as a result of which the Earth coil, for instance, gets placed in the Live terminal, or the Live cable in the Earth terminal; a nasty explosion could take place, damaging the fuse-in-repair (the repair is not successfully effected) ; one may even suffer as a victim of such explosion; all this extends down time for the fuse/plug. (8) The new fuse should be properly screwed all the way into the terminal after insertion, to avoid looseness or dangerous exposure. Loose connections bring about the problem of poor electrical contact, so that after replacement/repair, testing the fuse/plug reveals no performance, thereby necessitating a repeat of the process- again lengthening the down time (9) The cover for the fuse /plug should be carefully placed back and screwed on properly. For the tap washer, (1) The fault needs to be ascertained. There could be a problem with another part of the faucet, so care must be taken to ensure that the washer actually needs to be removed (2) The plughole of the sink should be blocked FIRST, before commencing on this repair. There is the possibility of difficulty with parts of the washer assembly falling off into the sink hole, and are thereby lost (3) The tap's headgear needs to be unscrewed; this presents difficulty in that it may be done by hand, or by unscrewing the retaining screw (which may be done by screw-driver) time may sometimes be lost in the process of deciding on method at this juncture- it may translate into down time (4)The headgear nut is to be removed- this is harder than it sounds. Practically, experience always plays a part in the repair/replace process, at every stage- particularly in operations such as this. The risk at this point exists that the basin may get cracked where the headgear nut is too tight- again perhaps the tap has been in use for quite some time, so over the period its tightened; grease would have to be applied, rather than exerting too much force on it, which definitely would cause damage (breakage) and the objective of repair becomes defeated, as well as down time hyper-extension. (5) The tap's base is held and a push is applied on the headgear nut in direction opposite to that (6) Water should be prised out of the tap (7) The new washer should be fitted (8) Tap threads should be greased (9) Reverse the process above to reassemble; experience again will be the solution to the difficulty at this juncture. It entails knowing the procedure backwards. This is not as easy as it sounds- a step in the procedure may be accidentally carried out in the reverse assembly procedure, necessitating a return to the stages before that; all this extends down time. References Lecture Outlines/Notes Kurtz, Meyer: Mechanical Engineers' Handbook, 1998 by John Wiley & Sons, Inc. . Read More