Mechanical Systems Reliability - Assignment Example

Running Head: Title of work Name Name of Instructor Subject Institution Date Mechanical reliability system Abstract Mechanical reliability is a field that deals with the functionality of a given component, given certain conditions on a specific period of time. A reliable component is the one which is robust and is able to withstand harsh environmental conditions and, the various consumer usages. The system engineers have to ensure that, there is little mistake during the design process and, the component should be robust. This is achieved by use of probabilistic method such as weibull distribution Birolini (2010, 25-28). Weilbul distribution serves as an important tool in the analysis of numerical data to ascertain the duration of life span of components, machines. The mean life span of a component may be achieved, by employing statistical method. In this paper, the life span of washing machines is evaluated and, recommendation tabled before the management on the findings. The aspect of cycle economy is currently escalating the economy and the management has to keep with the current market environment. This arises as of a matter of fact, where products have to be either recycled, incinerated of being disposed. Introduction Analysis of end life of components and machines is an important aspect to the management. Washing machines have taking a leading trend in most homes. The ever changing busy world calls for machines that aid in doing work. This is calls for proper design so as to ensure their usability is durable and serves the customers satisfactorily. The knowledge of reliability of components also, helps in the recycling of components. This is because, it enhances the elimination of waste Holland (2004, pp17-42). Moreover, the knowledge may impact the recycling of the material due to the fact that, its end life would have been determined. The companies have to adhere to the environment polices that restrict the pollution of waste due to the disposal of waste products. This has called for the need to not only concentrate to the manufacturing and selling of the products, but also the determination of their life cycles. The company under consideration is known as `Widget Inc’. Various washing machines were taken under test to ascertain their life cycle. The data of the failure time were recorded in which runs concurrently with the expected life. Various methodological aspects are in cooperated in the analysis of the life times of various machines. Methodology The analysis of reliability of a given system takes advantage of the parametric values of a given component. The employment of probabilistic approach gives way on the knowledge of the mean time of a given component or the mean failure. In this paper weibull distribution takes advantage of the life data approach, whereby it indicates the successive period of functionality of a given machine or component. This may be done in either cycles or hours. The 20 machines put under consideration had the following months of failure. Table 1 Arranging in ascending order the rank of failure we have the following data. Table 2 Number Ti ln(Ti) Number Ti ln(Ti) 1 3.8 1.335 11 25 3.219 2 4.8 1.569 12 30 3.401 3 5.1 1.629 13 40 3.689 4 5.2 1.649 14 50 3.912 5 6.2 1.825 15 60 4.094 6 6.7 1.902 16 70 4.248 7 10 2.302 17 80 4.382 8 12 2.485 18 90 4.500 9 15 2.708 19 140 4.942 10 20 2.996 20 200 5.300 The next procedure in cooperates the determination of the median rank. Median rank =                      Table 3 Number(N) Time to fail Median rank Number(N) Time to fail Median rank 1 3.8 1.25 11 25 44.58 2 4.8 7.08 12 30 48.75 3 5.1 11.25 13 40 52.92 4 5.2 15.41 14 50 57.08 5 6.2 19.58 15 60 61.25 6 6.7 23.75 16 70 65.41 7 10 27.92 17 80 69.58 8 12 32.08 18 90 73.75 9 15 36.25 19 140 77.92 10 20 40.41 20 200 82.08 The values of these sample yields to a weibull probabilistic table as shown below. From the graph, we determine the beta function which is the gradient of the straight line obtained from the plotted points. Taking points (10, 27.92) and (90, 102)  The slope which is the beta function elaborates the degree of failure of the components. When the beta function is less than 1, this indicates that there is an infant mortality. A beta function that is equal to 1 indicates the rate of failure is independent, whereas the beta function that greater than 1 indicates that the rate of wear is out of the failure. The graph has the horizontal scale indicating the failure of age. Values on the vertical scale indicate the percentage when the fail would age. The value of the life time occurs at the 63.2% which gives a value of five years. It is obtained after a straight horizontal line is joined with the vertical line. The solution of any time we expect to guaranteed on a given Item may be calculated of graphically solved from the weibull distribution table The solution may be found by;  Arjun (2010, pp21-49) Plotting at the graph the reliability of the machine to last for about sixty months is seen to be about 90%.Rank regression may be used where a straight line is determined that fits all the points. The summation of the least square is minimized. The values of the straight line yield an equation in the form. From the graph this yields an equation in this form. The correlation co efficient also finds its application in establishing the validity of the reliability of a given system or component. It is given by  At times this ascertains that the best probability that matches the data the log functions are employed. This may aid in the determination of material characteristic and the aging factor. Discussions The analysis from the weibull distributions indicates the washing machines are liable to reuse in their respective life cycles. The result from empirical data indicates the washing machines may be reliable for about 11-14 years. This is valid if there is proper use of the machine and the instructions are adhered to. Moreover, the machine tends to follow a normal probability curve which is a failure mechanism. The beta function gives the hint on whether there is need for planned inspections and, regular overhauls. A beta function which is less than or equal to one clearly stipulates that overhauling would be of great importance in the life cycle of a given component. The forecasting technique embraces the need for planned maintenance program of a given component. It may also lead to the decision of replacing certain items, so as to improve its reliability or, to completely do away with it. The time interval for an overhaul to take place may be determined through this method and, would assist the managers to keep the records. Failure mechanism obeys the law of natural wear of components due to long term usage Relia (2006). The outcome of weibull distribution gives the mean lives at higher levels. The knowledge equips the managers on how to choose a reliability level of a given component so as it may fit its requirement. It is essential to save the premature disposal of equipments, as this is one way of saving resources that a given firm may incur cost. This yields to reduced costs of production, leading to higher profit margins. The use of other method in determining the life cycles of various components proved to be difficult that calls for the use of this weibull technique. The older method required the whole assembly of the components to be disassembled. Moreover, the deteriorations of the component is not indicated. It is seen that a small sample of components would be used to assume the life cycle of whole components which in real sense is not the true case. The distribution of beta function The reliability of a given component may be improved through various ways such as fault tolerance and Fault avoidance. Fault tolerance embraces the aspect of using more complex designs while making a given component. However, this method may end up being costly as the resources used are expensive. Fault avoidance is the system that is mostly preferred as it is less expensive. In this technique, there is the use of high quality which are heavily reliable are used. The choice of the component to be increased its reliability serves as a challenge more so, to the reliability engineer Ireson (1999, pp97-103). It proves difficult whether only one component should be improved its reliability or both. The choice should be arrived so that efficiency is achieved at low costs, and the desired approach is viable. The choice may be determined by adding variables like cost which may not necessarily rely on cash, but may also be dependent on time. A relationship between the cost of the component and its reliability may be determined as a first priority. Furthermore the cost function of the components needs to be quantified. For instance  Where =cost of component =reliability of the component. The function accommodates the present reliability of a component; the maximum expected reliability and changes in the value of costs Nelson (2004, pp12-38). The different value of cost is brought about by factors such as design parameters, the technology used and the supplier of the material matters. This constitutes different cost that may be incurred. The cost takes the axiom to be exponential, as it is difficult to add reliability to a component. Cost functions are non linear of which they take an asymptotic shape when their maximum level is attained. Ci (ri)-a functional cost of a component reliability f-ability to improve a given component Rmin,i-the reliability at the present time during the optimization process. R max, i-optimum reliability expected during optimization process. The analysis of the cost functions leads to the reliability of given component may remain constant but not to a lower value. Feasibility also may serve as an important tool in the analysis or reliability Little (2005, pp27-74). It is the hardness of a given component reliability as compared to other components. The weighting factors such a technology, ergonomics and its operational principle of a given component may be used to determine the reliability of a given component. Analysis of the operation data aids in the determination of the re use of a given component. In the analysis of these data, some aspects ought to be considered so as to ensure the correct test is achieved. These may include; the level of the water during its operation for the case of a washing machine. Weather conditions also serve an effect that may influence the data such as temperature and humidity Keceioglu (2003, pp22-33). The operation of the machine has also to be considered. Some achiness may be working for longer hours as compared to others. More over the duration a given machine takes to accomplish a given work cycle has to be factored in. In carrying out the test of a washing machine the variable have to be noted as they determine various characteristics performance. The regression analysis will in cooperate the rational speed of the motor of a washing machine say (w), the temperature (T) voltage and power. This assists in determination of individual behavior of the variables to the life cycle of the machine. The use of regression method makes it easier for management to easily estimate the future life cycle. Various variables can be analyzed making it a suitable approach. The different aspects may be broken down say the motor, casing as such. Each component’s reliability may be tested to ascertain which component in actual sense determines the durability of a given component. Determination of reliability needs for use of statistical method that gives provision for analysis of data. The expected life for a given component to be exhausted is brought about by the knowledge of life cycle. It is indeed true that the analysis of the weibull distribution would indicate higher life cycles more so, if the wear system remains constant. Further techniques prove to be worthwhile hence improve the performance of reliability of a component. The technique of apportionment allows time for proper design to be effected. The figure at hand is cost estimated making the design concept. The operational function is accompanied by the specifications of the reliability data O’ Connor (2002. pp.121-132). Another technique may be the employment of similarity approach where the performance traits of similar components may be compared and a conclusive prediction is arrived. The environmental conditions have to be considered so as to avoid much alteration of the results. More over the use of prediction may be employed. The aspect of testing may not necessarily be employed to improve the reliability of a given component. It is important to ascertain the number of units that may be tested to envisage the failure rate of a given component. In addition, a weibayes line may be applied where the lower limits of a given weibull distribution may yield to a new design that is reliable. Occurrences of zero failure may be compromised due to some circumstances. Exponential reliability takes advantage of the Mean Time To Fail. The value of the beta function approximates to 1.This is equivalent to the infant mortality and the rate of the wear. Webayes distribution may be used even when there is no reported failure. This technique is important for continuous evaluation of components performance Blischeke (2000, pp722-730). This arise especially when a given component say a washing machine taking 200 months that may not incur failure. Their lives are extended using this technique. In conclusion, the knowledge of mechanical system reliability is of much importance as it assists, design engineers to approximate the life cycle of various components. This may assist the company in minimizing its cost thereby incurring high profits. It is with no doubt that several techniques are eloping up on how to manage the cycle environment so as to fit competitively in the global market arena. References Arjun, G (2010). Probability and statistical models. London: Springer Heidelberg Dordrecht. pp 21-49. Birolini, A (2010). Reliability Engineering. 6th ed. Italy: Springer Heidelberg Dordrecht. pp 25-28. Blischeke, W and Murthy, D (2000). Reliability, Modelling, prediction and optimization. Canada: John Wiley and sons. pp720-730. Hollland, A and Rausand, M (2004). System Reliability Theory. Canada: John Wiley and sons. pp17-42. Ireson W, Coombs, F and Moss, R (1995). Handbook of reliability Engineering. 2nd ed. U. S. A: Mc Graw Hill. pp97-103 Kecceioglu.D. (2003). Robust Engineering. Design by reliability with emphasis on mechanical components and structural reliability. Vol 1 (1), pp22-34 Little, R (2005). Mechanical reliability Improvement. New York: Taylor and Francis e- library. pp27-74 Nelson, W. (2004). Applied Life data analysis. Canada: John Wiley and sons. pp12-38. O’Connor, D (2002). Practical reliability Engineering. England: John Wiley and sons. Pp 121-145. Relia, A. (2006). Weibull distribution. Available: http//www.neilstoolbox.com. Last accessed 20th Feb 2011 Read More

The employment of probabilistic approach gives way on the knowledge of the mean time of a given component or the mean failure. In this paper weibull distribution takes advantage of the life data approach, whereby it indicates the successive period of functionality of a given machine or component. This may be done in either cycles or hours. The 20 machines put under consideration had the following months of failure. Table 1 Arranging in ascending order the rank of failure we have the following data.

Table 2 Number Ti ln(Ti) Number Ti ln(Ti) 1 3.8 1.335 11 25 3.219 2 4.8 1.569 12 30 3.401 3 5.1 1.629 13 40 3.689 4 5.2 1.649 14 50 3.912 5 6.2 1.825 15 60 4.094 6 6.7 1.902 16 70 4.248 7 10 2.302 17 80 4.382 8 12 2.485 18 90 4.500 9 15 2.708 19 140 4.942 10 20 2.996 20 200 5.300 The next procedure in cooperates the determination of the median rank. Median rank =                      Table 3 Number(N) Time to fail Median rank Number(N) Time to fail Median rank 1 3.8 1.25 11 25 44.58 2 4.8 7.

08 12 30 48.75 3 5.1 11.25 13 40 52.92 4 5.2 15.41 14 50 57.08 5 6.2 19.58 15 60 61.25 6 6.7 23.75 16 70 65.41 7 10 27.92 17 80 69.58 8 12 32.08 18 90 73.75 9 15 36.25 19 140 77.92 10 20 40.41 20 200 82.08 The values of these sample yields to a weibull probabilistic table as shown below. From the graph, we determine the beta function which is the gradient of the straight line obtained from the plotted points. Taking points (10, 27.92) and (90, 102)  The slope which is the beta function elaborates the degree of failure of the components.

When the beta function is less than 1, this indicates that there is an infant mortality. A beta function that is equal to 1 indicates the rate of failure is independent, whereas the beta function that greater than 1 indicates that the rate of wear is out of the failure. The graph has the horizontal scale indicating the failure of age. Values on the vertical scale indicate the percentage when the fail would age. The value of the life time occurs at the 63.2% which gives a value of five years. It is obtained after a straight horizontal line is joined with the vertical line.

The solution of any time we expect to guaranteed on a given Item may be calculated of graphically solved from the weibull distribution table The solution may be found by;  Arjun (2010, pp21-49) Plotting at the graph the reliability of the machine to last for about sixty months is seen to be about 90%.Rank regression may be used where a straight line is determined that fits all the points. The summation of the least square is minimized. The values of the straight line yield an equation in the form.

From the graph this yields an equation in this form. The correlation co efficient also finds its application in establishing the validity of the reliability of a given system or component. It is given by  At times this ascertains that the best probability that matches the data the log functions are employed. This may aid in the determination of material characteristic and the aging factor. Discussions The analysis from the weibull distributions indicates the washing machines are liable to reuse in their respective life cycles.

The result from empirical data indicates the washing machines may be reliable for about 11-14 years. This is valid if there is proper use of the machine and the instructions are adhered to. Moreover, the machine tends to follow a normal probability curve which is a failure mechanism. The beta function gives the hint on whether there is need for planned inspections and, regular overhauls. A beta function which is less than or equal to one clearly stipulates that overhauling would be of great importance in the life cycle of a given component.

The forecasting technique embraces the need for planned maintenance program of a given component. It may also lead to the decision of replacing certain items, so as to improve its reliability or, to completely do away with it.

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