The Black Death Hit The Shores Of Europe - 983 Words

The Black Death hit the shores of Europe in October 1347. After a long a tough journey, through the Black Sea, twelve ships or Genoese docked at the Sicilian Port. Those who greeted the ships had a horrifying site of dead sailors and the sailors who were alive were greatly ill. It is said that the sailors had awful fevers, were not able to keep food down, and they were covered in black boils that oozed blood and puss. This is where the name Black Death came from. Although the ships were ordered to leave the port, the Black Death claimed the lives of over 20 million people, about one third of the continent’s population during that time, over the next five year.1 In October 1347, twelve ships arrived at the port of Messina in Sicily. This town was one of the stopping points of the trade route from the East that brought silks and spices through the Old Silk Road, then through Crimea, across the Black Sea and into Europe. However, this time there were no silks and spices. The port authorities found scarcely anyone on board. Those who were found on board, had black boils and everything that came out of their body smelled awful. The very presence of the sailors was said to â€Å"deem public health† and were ordered to leave the port.2 The Black Death has been thought to be a mixture of bubonic, septicemic and pneumonic plague. A plague is a disease that are carried by rodents and is endemic to a number of regions of the world. The plague bacillus lives in the bloodstream of smallShow MoreRelatedThe Black Death, Dulce N. Parra1533 Words   |  7 Pages The Black Death Dulce N. Parra Period 3 â€Æ' Through the years of 1347 and 1350, a terrible plague took over Europe. In those three years, the plague killed approximately 25 million people or one-third of Europe’s population. Not one family did not lose a family member to the plague. About one hundred people died daily, and mostly of them were never buried in a proper manner. 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The plague was a looming presence, always in the back of people’s minds. The symptoms of the Black Death caused great strife for westerners. Giovanni Boccaccio, an Italian writer and poet, described the symptoms he saw during the first outbreak of the plague: â€Å"Not such were they as in the East, where an issue of blood from the nose was a manifest sign of inevitable death; but in men a womenRead MoreThe Effects of MTV on American Culture Essay3119 Words   |  13 Pagesthe network, the transformation from simply just music television to inappropriate reality shows, and the promotion of inappropriate content. Historically, MTV was created and first aired on television August 1, 1981. The first words spoken on the hit series were by one of MTV’s creators, John Lack: â€Å"Ladies and gentlemen, rock and roll. 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Sudden Death In Epilepsy Researchers Finger Possible Cause by Article

Essays on Sudden Death In Epilepsy: Researchers Finger Possible Cause by Couzin-Frankel Article The paper "Sudden Death In Epilepsy: Researchers Finger Possible Cause by Couzin-Frankel" is a good example of an article on medical science. Couzin-Frankel authored the article titled â€Å"Sudden Death In Epilepsy: Researchers Finger Possible Cause† and in this article, the author talks about research that helped in identifying the shutting down of the brain stem can cause death amongst patients experiencing epilepsy. For years physicians have no idea what were the causes of sudden death amongst patients experiencing epilepsy. Sudden death is most common amongst patients who experience seizures which are quite severe in nature. The author states that it has been estimated that more than 3000 individuals who are patients of epilepsy are experiencing sudden death. The author has even reported previous studies that have identified that a patient who experiences sudden death even experienced the collapse of their entire cardiorespiratory system and their brain functionality even was found to be stopped. The authors state that the researchers were not convinced with the idea that the collapse of the cardiorespiratory system caused sudden death and there must be something else that was causing the failure of the system. In order to find the connection, researchers performed an experiment in which mice went through mutations of the potassium ion channel gene as well as mutations in the sodium ion channel gene and these mice were induced with seizures. The outcome of this experiment was that mice experienced depolarization of the region called brain stem and it damaged one of the most important brain tissues that were in control of the smooth functioning of breath as well as heart and this caused sudden death.

The Role of Alan Turing in the History of Computing Free Essays

The role of Alan Turing in the history of computing Alan Mathison Turing was born on 23 June 1912, Paddington, London. He was a true pioneer in computer science and if it were not for this man, no one would probably be typing an essay based on him on a modern computer. He is renowned for his passion of mathematics and the invention of the Turing machine/test, breaking the German enigma code during World War One, and for making the first automated computing machine (the ACE). We will write a custom essay sample on The Role of Alan Turing in the History of Computing or any similar topic only for you Order Now At an early age he was sent to preparatory school by his parents, he attended these until enrolling at Sherbourne in 1926. His teachers there were surprised to find him working through the long way for the answers to questions, after Sherbourne Turing enrolled at King’s College where he became a mathematics scholar in 1931 where he began his studies in maths and logistics. He was elected at King’s and won the Smith’s award in 1936 for a paper he wrote on the â€Å"Gaussian error function†, this is when he began work to develop The Turing Machine. Copeland, 2004) But later in 1936 he moved to the United States to study at Princeton for two years where he studied the theory of computation and in 1937 presented a paper called â€Å"On computable numbers, with an application to the â€Å"Entscheidungs problem† and soon to challenge David Hilbert’s three questions put forward to the best of the mathematical minds, which were; Was maths complete? Was maths constant? , was maths decidable? (Hodges, 1992; Copeland 2004). Though his work on the Entscheidungs problem he began working on to define what a method was, and through that he came up with the Turing machine theory which can be said to be a mechanical process that was able to perform all the operations a person working with a logical system would be able to perform this theory compares human thought processes to that of a machine, which in the Turing machine theory are categorized as terms of inputs, outputs and machine states. The Turing machine is a simple computer. It’s limited to a logical set of instructions by reading and writing symbols on a tape and moving the tape one step to the left or right and then look at what’s written in the resulting square, each symbol had a specific way to be turned into a new symbol e. g. if the symbol is a â€Å"0† move it two spaces right and turn it into a â€Å"1†. So a algorithm for a calculation the list of instructions are quite long, but the complexity of instructions are very short. The Turing Machine at the time was the only one designed to perform multiple tasks and functions. Turing’s vision was what we currently use today as a modern computer (Copeland, 2012). Soon after this period World War two began and the Polish were bracing themselves from an invasion from the Germans, When Polish mathematician Marian Rejewski attempted to break the German enigma machine which is a mechanical ciphering machine which had the purpose of a message only being read and understood by the receiver. Marian made the polish bomby which works like a combination of many enigma machines e. g. if SAW stood for GJK then both would be put in the bomby and every possible combination would be sorted through and would stop when a possible match was found, this worked well until 1938 when Germany added two more rotors to the Enigma (Schmidl, 1998), sadly the Polish had to leave Poland and forced to team up with the English and French and this where Alan Turing’s true genius was put into application and saved hundreds and thousands of lives. Turing then put the Polish’s efforts into action, the British had a lot more resources which consisted of about ten thousand people working on the encoding of the Enigma, Turing created The Turing Bombe which was a lot more efficient than the bomby and it differed in the way that instead of trying to rely on a certain indicator decode a certain message sent, it went after the specific message using word probability. Once the message was solved a ’menu’ was put on the bombe and was then put in its proper setting, was given information and let it run until it matched with the rotors, Three to Seven months later a set of three rotors were place in the scrambler unit, this made the processing a lot faster as the scrambler unit made the current go from the fast, medium then the slow rotor. Eventually the codes made by the Germans became clearer and they lost their advantage in World War two, and the U boats who were sinking the supply ships from America and Canada to Great Britain, could not locate the supply ships for the first 23 days of June 1941 (Kozaczuk, 1984). After World war two Turing went to work for the National Physical Laboratory in 1945 where he made the first plan for the first Automated Computing Machine for the Association for Computing Engineering (the ACE). Unfortunately the ACE was never completed as he moved to the University of Manchester to develop an even more advanced computing machine (MADAM). With all of Turing’s work he had proved David Hilbert wrong with all three questions with the fact that a certain class of mathematical problems which could not be solved by automatic machines and had introduced the concept of a single theoretical universal computing machine, which of course is now known as the Turing Machine. In 1947 he tried to find out if there was any relationship with computers and nature and Turing was certain that by about the year 2050 that a thinking machine would mimic the thoughts of a human and it was in 1949 he published a paper called â€Å"intelligent machines† (Copeland, 2005) Alan Turing passed away on 7 June 1954, he was found in his bed with an half eaten apple beside his bed, which was apparently dipped in cyanide on purpose by himself so he could commit suicide as he was supposedly depressed after being found guilty of homosexuality by the British courts. But there is little evidence to support this theory of Turing committing suicide (Pease, 2012). Bibliography Schmidl, H. , (1998) On Enigma and a Method for its Decryption http://www. cs. miami. edu/~harald/enigma/index. html Kozaczuk, W. (1984), Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, (2nd ed. ), Frederick, Maryland: University Publications of America. Hodges, A. , (1992), Alan Turing: the enigma, London: Burnett Books. P. 26-34. Copeland, B. J. , (2004) The Essential Turing. Oxford: Oxford University Press Pease, R. , Alan Turing: Inquest’s suicide verdict ‘not supportable’ (June 26,2012). , BBC News, science and envi ronment. Copeland, B. J. , Alan Turing. net, the Turing archive for the history of computing (2012). How to cite The Role of Alan Turing in the History of Computing, Papers The Role of Alan Turing in the History of Computing Free Essays The role of Alan Turing in the history of computing Alan Mathison Turing was born on 23 June 1912, Paddington, London. He was a true pioneer in computer science and if it were not for this man, no one would probably be typing an essay based on him on a modern computer. He is renowned for his passion of mathematics and the invention of the Turing machine/test, breaking the German enigma code during World War One, and for making the first automated computing machine (the ACE). We will write a custom essay sample on The Role of Alan Turing in the History of Computing or any similar topic only for you Order Now At an early age he was sent to preparatory school by his parents, he attended these until enrolling at Sherbourne in 1926. His teachers there were surprised to find him working through the long way for the answers to questions, after Sherbourne Turing enrolled at King’s College where he became a mathematics scholar in 1931 where he began his studies in maths and logistics. He was elected at King’s and won the Smith’s award in 1936 for a paper he wrote on the â€Å"Gaussian error function†, this is when he began work to develop The Turing Machine. Copeland, 2004) But later in 1936 he moved to the United States to study at Princeton for two years where he studied the theory of computation and in 1937 presented a paper called â€Å"On computable numbers, with an application to the â€Å"Entscheidungs problem† and soon to challenge David Hilbert’s three questions put forward to the best of the mathematical minds, which were; Was maths complete? Was maths constant? , was maths decidable? (Hodges, 1992; Copeland 2004). Though his work on the Entscheidungs problem he began working on to define what a method was, and through that he came up with the Turing machine theory which can be said to be a mechanical process that was able to perform all the operations a person working with a logical system would be able to perform this theory compares human thought processes to that of a machine, which in the Turing machine theory are categorized as terms of inputs, outputs and machine states. The Turing machine is a simple computer. It’s limited to a logical set of instructions by reading and writing symbols on a tape and moving the tape one step to the left or right and then look at what’s written in the resulting square, each symbol had a specific way to be turned into a new symbol e. g. if the symbol is a â€Å"0† move it two spaces right and turn it into a â€Å"1†. So a algorithm for a calculation the list of instructions are quite long, but the complexity of instructions are very short. The Turing Machine at the time was the only one designed to perform multiple tasks and functions. Turing’s vision was what we currently use today as a modern computer (Copeland, 2012). Soon after this period World War two began and the Polish were bracing themselves from an invasion from the Germans, When Polish mathematician Marian Rejewski attempted to break the German enigma machine which is a mechanical ciphering machine which had the purpose of a message only being read and understood by the receiver. Marian made the polish bomby which works like a combination of many enigma machines e. g. if SAW stood for GJK then both would be put in the bomby and every possible combination would be sorted through and would stop when a possible match was found, this worked well until 1938 when Germany added two more rotors to the Enigma (Schmidl, 1998), sadly the Polish had to leave Poland and forced to team up with the English and French and this where Alan Turing’s true genius was put into application and saved hundreds and thousands of lives. Turing then put the Polish’s efforts into action, the British had a lot more resources which consisted of about ten thousand people working on the encoding of the Enigma, Turing created The Turing Bombe which was a lot more efficient than the bomby and it differed in the way that instead of trying to rely on a certain indicator decode a certain message sent, it went after the specific message using word probability. Once the message was solved a ’menu’ was put on the bombe and was then put in its proper setting, was given information and let it run until it matched with the rotors, Three to Seven months later a set of three rotors were place in the scrambler unit, this made the processing a lot faster as the scrambler unit made the current go from the fast, medium then the slow rotor. Eventually the codes made by the Germans became clearer and they lost their advantage in World War two, and the U boats who were sinking the supply ships from America and Canada to Great Britain, could not locate the supply ships for the first 23 days of June 1941 (Kozaczuk, 1984). After World war two Turing went to work for the National Physical Laboratory in 1945 where he made the first plan for the first Automated Computing Machine for the Association for Computing Engineering (the ACE). Unfortunately the ACE was never completed as he moved to the University of Manchester to develop an even more advanced computing machine (MADAM). With all of Turing’s work he had proved David Hilbert wrong with all three questions with the fact that a certain class of mathematical problems which could not be solved by automatic machines and had introduced the concept of a single theoretical universal computing machine, which of course is now known as the Turing Machine. In 1947 he tried to find out if there was any relationship with computers and nature and Turing was certain that by about the year 2050 that a thinking machine would mimic the thoughts of a human and it was in 1949 he published a paper called â€Å"intelligent machines† (Copeland, 2005) Alan Turing passed away on 7 June 1954, he was found in his bed with an half eaten apple beside his bed, which was apparently dipped in cyanide on purpose by himself so he could commit suicide as he was supposedly depressed after being found guilty of homosexuality by the British courts. But there is little evidence to support this theory of Turing committing suicide (Pease, 2012). Bibliography Schmidl, H. , (1998) On Enigma and a Method for its Decryption http://www. cs. miami. edu/~harald/enigma/index. html Kozaczuk, W. (1984), Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, (2nd ed. ), Frederick, Maryland: University Publications of America. Hodges, A. , (1992), Alan Turing: the enigma, London: Burnett Books. P. 26-34. Copeland, B. J. , (2004) The Essential Turing. Oxford: Oxford University Press Pease, R. , Alan Turing: Inquest’s suicide verdict ‘not supportable’ (June 26,2012). , BBC News, science and envi ronment. Copeland, B. J. , Alan Turing. net, the Turing archive for the history of computing (2012). How to cite The Role of Alan Turing in the History of Computing, Essay examples

Performed on the Waffy Biscuit Products

Question: Describe about the case study is performed on the Waffy biscuit products? Answer: Introduction As the average customer has been educated and become more conscious about the quality of the products bought by them, the concern of the quality standards to be followed by the companies of the products has also been increasing. The quality standards can be investigated and analysed through quality engineering techniques. Product Waffy Chocolate is the product selected for the quality engineering report. Waffy Chocolate is one of the flavours of the waffies produced and sold by Dukes, India. Dukes makes the Waffy products, in addition to many other products, like chocolates, confectionaries, newbies. The product is marketed and sold also, as gift packs that are best suitable for the birthday parties and other kinds of parties for the children as well as the adults and teenagers. The company offers the Waffy, Chocolate with various offers and the offer that is presently available, at the time of the consideration of the product for the quality engineering case study is the buy 1 get 1 offer. The offer allows the customer to get one Waffy free of cost, when one Waffy is bought. And at the same time, if the customer chooses to buy only one or only one Waffy is left in the rack of the shop, it would be sold for half of the cost. The company uses the selling strategy of buy 1 get 1 to attract more customers to buy the Waffies. Company Dukes, India has a tag line, Energy Unlimited and wishes to become a consistent source of sweet Delight. The company is taken to the greater heights, by channelizing its boundless energy to make the products that are universally accepted, satisfying and appealing and the product to under the universal banner of quality food. The company was started before two decades, on the name of Ravi Foods Pvt. Ltd, and created its niche in food segment called processed foods. The diversified foods have the customers within the mother country and also outside the mother country. The company successfully runs with 12 plants installed and working in India. Quality Concern The product, Waffy with chocolate flavour is nicely packed with fancy and elegant looking pack. The size is also bigger and it attracts the customer for more valued food content present in the pack. Since the product is offered with special offer, like buy 1 get 1, the customer becomes a little sceptic about the quality as well as the quantity of the product. However, as a standard company, following all the norms of the quality related to the product, it is important that whatever is specified on the pack must be justified. This quality engineering report on Waffy with chocolate flavour assess the quality factors, majorly on the weight of the overall product as well as the individual pieces of the product that in combination should be equal to the weight of the overall net weight of the product. Quality Assessment To conduct the quality assessment of the Waffy wafers, produced and marketed by Dukes, the weight of the overall wafer and each of the wafer in the packet are measured to check whether the sum of the all the wafers in the packet is equal to the net weight of the overall packet. Measurement Systems Analysis The measurement system analysis helps to assess the overall measurement system adequacy for specific application. When the process outputs are considered, there are two kinds of variation sources called, Measurement system variation, which is considerably large, when it is compared to the other one, however this system many not provide the complete and useful information needed Part to part variation Before the data is collected from the processes, the measurement system analysis is to be performed for confirming that the measurement made by the measurement system is consistent, accurate and can determine the discrimination among all the parts, chosen in the measurement. The measurement systems analysis is performed to find the answers for the following questions. Will the measurement system be discriminate between various parts, adequately? Can the measurement system be stable for over a period of time? Can the measurement system be accurate for the entire range of the parts? Assessment Procedure Two Waffy wafers are taken and the total weight of the packet is measured. The total weight is compared with the net weight printed on the packet of Wafers. Then the packet is opened and each of the wafer is measured accurately. Before the wafer is measured, the digital display is to be adjusted to zero, initially and the plate or base of the weighing machine has to be levelled horizontally. Phase 1 Now, the first Waffy packet is given to the operator 1 and the second packet is given to the operator 2. Initially, the operator 1 measures the overall weight and the individual wafer weight of the first packet and notes down all the readings shown in the weighing machine. Similarly, the candidate 2 weight the overall Waffy packet 2, both for the overall weight of the packet as well as the individual wafer of the packet and notes down all the readings shown in the weighing machine. Phase 2 In the phase 2, the Waffy packets are to be exchanged between the operator 1 and operator 2. After exchanging the wafer packets, again the same procedure has to be followed. The operator 1 weighs the weight of the Waffy packet 2 and the operator 2 weighs the Waffy packet 1 and again each of the findings of the readings must be noted on the paper, as before. The results of weights of each of the wafer from each of the packet are taken and considered as inputs to calculate RR percentage. The calculation should reveal the variation of the weight of the product, between the actual weight and the weight printed on the Waffy packet. If there is any variation, the extent of variation has to be calculated. The variation has to be analysed by drawing X and Y bars. The chart should show the variation between the weight after the manufacturing process and weight after the product is bought and consumed. Aim The aim of the quality engineering assessment for the Waffy chocolate flavour is to assess the quality standards followed by the company, in providing the accurate weight and so quantity, which is again one of the quality factors, which are set expectations to the customers. Objectives The objective of quality engineering assessment of the Waffy chocolate flavour product is to investigate the standards of quality of manufacturing process, in terms of producing and packing the wafers up to the weight determined by the company and investigates the variation if any. The final analysis is done on the basis of the results obtained from the Gage RR analysis and the control chart. Manufacturing Process The manufacturing process of the Waffy, chocolate flavoured waffies is simple and the process is very conventional. The manufacturing process is done in various stages. Dukes processes the manufacturing process of the Waffy biscuits in all its 12 plants installed in India. Stage 1 In the first stage all the ingredients are taken. The major ingredients needed for the Waffy biscuits are strtch, flour, sugr, soda, salt, flavours, preservatives, vanaspati, colors,e tc. During this stage, all the ingredients are procured and collected for the making of the waffy biscuits. Stage 2 These ingredients are taken in large amounts. As the first part or phase of the manufacturing process, the flour is taken and it is mixed with the starch, salt, soda and others with the water. After mixing the ingredients, a mixer and paste are formed. Stage 3 The paste is then taken into moulds. These moulds are pre-heated to some degrees of temperature already. The moulds are shaped in such a way that the wafers are produced in a particular shape after the process of baking. Stage 4 Then the cream is prepared. For the preparation of the cream, sugar, essence, colours, sugar and flavours are required. The cream is prepared in the planetary mixer. Stage 5 After the wafers and the cream are prepared, the following stage is to spread the cream that is prepared on the wafers. After the cream is pread on the wafer, the wafer is then sandwitched with another wafer. Stage 6 After the entire product is made, the sheets of the large wafer is cut to the required sizes. Stage 7 As th final stage, the wafers that are cut would be packed in the pre-determined size of the packets for the wafers. Gage RR Analysis Gage RR is one of the measurement system analysis techniques that makes use of the ANOVA or Analysis of Variance for Repeatability and Reproducibility. The technique can be applied not only for the gauges or gages, but also for various kinds of test methods, measuring instruments and other measuring systems. The Gage RR measures the variability amount that is induced right in the measurements, by the very measurement system. It compares the total variability found in determining the measurement system viability. According to the practicalities of the measured systems, there are many factors that affect the measurement system, as the following. Measuring instruments Test methods Operators Specifications Specimens or parts. The measurement or precision has importantly The two important aspects that are determined through Gage RR are, Repeatability that measures the variation resulted by a single operator or by a single instrument to measure the same product, measured under the same conditions. Reproducibility that is the measure of the same product that replicate the specimen, and this variation induced is measured when multiple operators or multiple laboratories or multiple instruments measure Need for the Gage RR study The study of Gage RR is used to compare the variation of the measurement system to the total process tolerance or variation. When a crossed Gage RR is used for the study, it can answer many questions, as follows. Whether the measurement system variability is small, when compared to the variability of the manufacturing process? Whether the measurement system variability is small, when compared with the limits of the process specification? How much the variability from the measurement system would be caused from the differences among the operators? Whether the measurement system would be able to discriminate among the parts? The measurement done for the Waffy biscuits has the following elements considered. Reproducibility for appraiser variation Repeatability for instrument variation Actual variation part as part to part variation The Gage RR analysis evaluates the appraisers and instrument contribution in the process of measurement. The analysis helps to resolve the data collected in terms of part to part variation and the corresponding measurement process of it. Product And Measurement Product Figure 1: The Waffy product from Dukes Measurements The packet consists of two slots covered with plastic wrapper. And the two slots are again packed with a small box, made of hard paper. So, the Waffies are covered in three layers, a plastic wrapper, paper wrapper and the final wrapper outside. Figure: Neutral Indication Figure: Total weight of the Waffy Figure: Weight of One Slot Figure: Weight of One Waffy The total weight of the Waffy = 92.498 g The net weight of the Waffies are given over the pack = 75 g the weight of the slot 1 = 40.784 g the weight of the slot 2 = 40.390 g and there are total 12 Waffies present in the total two slots. So, the operator 1 has taken the slot 1 with 6 Waffies and slot 2 with 6 Waffies in it for measurement and The operator 2 has taken the slot 1 and slot 2 with each 6 Waffies in them for the measurement initially. Operator 1 Slot 1 2 Measurement Operator 1 Sample Slot 1 Slot 2 Range 1 6.403 6.209 0.194 2 6.543 6.547 -0.004 3 6.094 6.409 -0.315 4 6.83 6.509 0.321 5 6.723 6.237 0.486 6 6.129 6.465 -0.336 Table 1: Slot 1 2 measurement by operator 1 Operator 2 Slot 1 2 Measurement Operator 2 Sample Slot 1 Slot 2 Range 1 6.098 6.192 0.094 2 6.945 6.654 0.291 3 6.439 6.488 0.049 4 6.435 6.439 0.004 5 6.456 6.498 0.042 6 6.851 6.122 0.729 Table 2: Slot 1 2 measurement by operator 2 The data collected for the weight of each of the Waffy present in both the slots and the equations for the Gage RR are calculated with the help of the spreadsheet. R = Average range measured by Operator 1 and Operator 2 = 0.003 g X a = Average Waffy measured by Operator 1 = 6.451 g X b = Average Waffy measured by Operator 2 = 6.468 g X diff = Xa Xb = -0.0164 g For net specified measurement is 75 g And there are 12 Waffies in the packet. So, the average weight of the Waffy = 75 / 12 = 6.25 and when the tolerance considered is 3%, then the Upper Specification Limit = 6.25 * 0.03 + 6.25 = 6.25 + 0.1875 = 6.4375 Lower Specification Limit = 6.25 - 6.25 * 0.03 = 6.0625 n = no. of samples taken = 12 t = no. of trials = 2 Repeatability = R * 4.56 = 0.129 * 4.56 = 0.0163 Repeat Percentage (%) = [Repeat / (USL LSL) ] * 100 = 4.357 Where, k = 3.65 = 0.060 Reproducibility percentage (%) = [ Reproducibility / (USL LSL) ] * 100 = 15.954 RR percentage (%) = = 16.538 The quality standard of the product of any company can be analysed through RR results and the standards are analysed as the following. If RR% 10%, the quality standard is good the product is world-class product If RR% 30%, the quality standard is acceptable and the product needs improvement, wherever possible If RR% 30%, the quality standard is poor and it is not acceptable The same calculations performed as shown in the spreadsheet. Operator 1 Operator 2 Sample Slot 1 Slot 2 Range Slot 1 Slot 2 Range 1 6.989 6.929 0.06 6.098 6.192 0.094 2 6.198 6.547 -0.349 6.945 6.654 0.291 3 6.094 6.409 -0.315 6.439 6.488 0.049 4 6.121 6.509 -0.388 6.435 6.439 0.004 5 6.723 6.434 0.289 6.456 6.498 0.042 6 6.002 6.465 -0.463 6.851 6.122 0.729 mean 6.3545 6.548833333 -0.194333333 6.537333333 6.398833333 0.2015 R= 0.003583333 Xa= 6.451666667 Xb= 6.468083333 Xdiff= -0.016416667 USL= 6.4375 LSL 6.0625 n= 12 t= 2 Repeat % = 4.357333333 Reproducibility = 0.060 Reprod. % = 15.954 RR % = 16.538 Table 3: Gage RR So, the final Gage RR percentage is 16.538, which is more than 10% and less than 30%. So, the quality standards of the product acceptable, but needs improvement wherever possible. Analysis With The Minitab Analysis of variance or ANOVA procedure is used by Minitab for calculating the variance components. And it uses the components for estimation of the variation of the percentage occurred from the measuring system. The variation of the percentage can be obtained from the Gage RR table. The table used for the ANOVA table is a two-way ANOVA table. The table includes the part, operator-by part interaction and also the operator. R Chart The R-chart is used for evaluation of the repeatability that is resulted in a process. Each of the point specified and pointed in the R-chart is the representation of the measurements made by the operators. In case any of the point falls far away from the control limit, the measurement is considered as that the operator finds it difficulty to measure the same piece or Waffy again, especially, as a contestant manner. Such operator measurement issues can be corrected after identification, while the measurement is being done. Xbar Chart Each of the point shown in the Xbar chart represents the variation of the part to part, according to the data given in the data set as results. It is easy to identify that most of the weights measured by the operators, fluctuate from the reference point called the control limits. The control limit in this case is also called as the blind zone of the respective equipment used. As a result of that, the measuring instrument could not differentiate various parts that are measured. In such cases, the measuring instrument, here in this case, the weighing machine to be effective, the pointed values are better to be out from the control limit or the blind zone to the possible extent. The identical patterns are also to be observed in this analysis, from the graph of the operator. It is because, it can represent the overall mean of the measured values from the data set given or entered. Figure 2: R chart and X bar Components Variation The chart shown for the component variation clues us regarding the variation in measurement when the same item is weighed at another instance. So, the measured value of the Waffy, when measured by the operator 1 does vary to the weight measured by the operator 2. The chart also clues us the overall components that would in turn result and contribute in the variation of the measurement data set. The more the difference between one to another part, the contribution is more to the overall variation, when compared to the other components, like repeatability, reproducibility or gage RR. Analysis Of Process Capability The process capability analysis is one of the statistical analysis methods that have the objective of comparing the outputs obtained from the in-control processes against the limits specified by using capability indices. The comparison can be obtained from the ratio of the spread that is found in between the specifications of the processes to the processs actual spread values. Conclusion The case study is performed on the Waffy biscuit products, manufactured and produced by Dukes company in India. The quality analysis of the Wafffy biscuit product is done on the basis of Gage RR. The product is Waffy and the company is Dukes. The quality concern that is considered for the case study is discussed followed by a quality assessment. A brief details about the measurement system analysis is done. Later the assessment procedure through which the assessment is conducted is discussed in various phases. Later the aim and objective of the case study is reported, which is to perform Gage RR for the selected products. The manufacturing product of the Wafffy biscuits by the company is detailed of how the Waffies are made in various stages. A detailed Gage RR analysis is discussed followed by the calculations performed based on the data collected through measurement of the weights of the Waffies. The analysis is further extended by using the software, Minitab, in which the R chart and X bar and component analysis is done and finally all the analysis reports are presented. 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