Marius Tazu and Titu Bajenescu in their book Failure Analysis describe a resistor as a two-terminal element that exhibits a voltage plunge which is straightforwardly comparative to the current by-passing it. When resistors are being manufactured, certain values are aimed at, these preferred values are based on a scale that starts at one point and which takes each step in a geometrical progression, that is, each value is some constant factor that times the previous value (James 1982). Modern manufacturing methods make it easier to achieve a very close tolerance and most of the existing tolerance series reflect the older manufacturing. Modern manufacturing techniques can now ensure that the majority of resistors in a batch are of almost exactly the marked value, so that large tolerance is a thing of the past. Carbon resistors are the most common types of composition resistors. Carbon resistors are cheap main purpose resistors used in electrical and electronic circuits. They are manufactured from a mixture finely ground carbon dust or graphite and a non conducting ceramic powder to bind it all together (Linden 2003). The ratio of carbon dust to ceramic determines the overall resistive of the combination, and the advanced percentage of carbon, the lower the entire resistance. Noise generated by resistors is caused by the movement of electrons contained by the resistor, which creates an unnecessary AC signal which becomes superimposed on top of the main DC signal. This kind of interference is categorized into two types: current noise and thermal noise.
Thermal noise is caused by the unsystematic motion of electrons within the resistive conductor. The voltage developed by thermal disturbance sets a boundary on the negligible voltage which can be augmented without being misplaced in the environment. The equation which determines the quantity of thermal interference is E2 = 4kTR (f2-f1), in this case k is Boltzmann’s invariable, T is the fixed temperature (in Kelvin), R is the opposition of the conductor, while (f2-f1) is the bandwidth. Current interference is the bunching as well as the discharge of electrons linked with current flow, and is present in resistors to varying degrees depending upon the technology employed, and it is measured and articulated as a utility of the entered voltage. Below are some resistors, their production process and the ranges of noise generation in each of them. The carbon masterpiece resistor was the foundation of the radio as well as television industries preceding the World War II. Their assembly includes carbon particles within a diallyl phthalate resin folder. The resin folder is subject to perfunctory motion relative to the carbon appropriate towards the forces produced by voltage tension, moisture access, perfunctory tension and thermal tension. These tensions cause the transmission sites on the position of contact to alter the resistance. The current bounces about from one trail to another by means of perceptible output causative to the current noise (Marius 2007). The noise levels range from -12Db to +6dB. The carbon was eclipsed by metal film resistors due to the rising cost of carbon composition resistors compared to the falling prices of the metal film devices. The thick film resistors provided more noise than is acceptable in professional sound recording applications.
The conduction path in the thick film is through the oxide components as they come into contact with one another within the fired goblet folder. These contact sites are locations intended for the bunching as well as the release of electrons and this is the cause for the noise in thick film resistors. The noise levels range between -18dB to -10dB. The metal film technology brought about considerable reductions in both the resistor volume as well as the interference. The metal film resistors are prepared through the desertion of a deposit of nickel chromium on top of a ceramic substrate (Ian1999). The breadth of this deposit is reliant on values plus it varies between 10 Angstroms to 500 Angstroms. The thicker the deposit, the fewer the interference inserted is. High values are noisier since the occlusions, face defects, plus non-uniform depositions are extra important to the production of interference when the nickel chromium deposit is minimal.
Metal film resistors have a noise range of -32 dB to -16dB. The wire wound resistors are made by loosely winding a special NiCr alloy wire element onto a cylindrical insulating core which is then either encased later in a modeled housing or is hermetically sealed. As a result the noise insertion caused by these devices comes from the tabs used to attach the fine wire to the coarse external leads. A typical noise rating is -38dB they offer low noise, great stability and a high wattage rating. The wire wound resistor has a tolerance of +_0.5%, 1%, 5% and 10% and a power rating of 0.5W to 5000 W.
Calculating the mean and the spread of data from machine 2
Mean value=10000/110 = 90.19
To get the Spread value first calculates the range which is the variation between the negligible value and the prevalent value in our data set: 1142-12=1130
Calculate the quartile between the data 12,12,19,19 1st quartile 41,41,83,83 2nd quartile 154,154,262,262 3rd quartile 410,410,593,593 4th quartile 790,790,969,969 5th quartile 1096,1096,1142 6th quartile (19+41)/2= 30 (154+83)/2= 118.5 (262+410)/2=336 (593+790)/2= 691.5 (969+1096)/2=1032.5
Inter-quartile range= 1032.5-30= 1002.5
Calculating the mean and the spread of data from machine 1
Mean value=10000/110 =90.91
To get the Spread value first calculates the range which is the difference between the smallest value and the largest value in our data set: 1142-1=1141
Calculate the quartile between the data 1,3,8,9- 1st quartile 19,41,72,83 – 2nd quartile 83,154,154,262 – 3rd quartile 262,410,410,593 4th quartile 593,790,790,969 5th quartile 969,1096,1096,1142 6th quartile (9+19)/2= 14 (83+83)/2= 83 (262+262)/2= 262 (593+593)/2= 593 (969+969)/2= 969
Inter-quartile range= 969-14= 955
From the above calculations the values of machine 2 are better distributed as compared to those of machine 1, hence, deviation found in machine 1 is smaller. Machine 1 requires calibration because there is no proper distribution between the value,s hence it becomes difficult to get the actual values since some are lost in the calculations. It is important to calibrate machine 1 since even the best calibrated instruments drift and lose the ability to give accurate measurements, this is the main reason that makes calibration necessary (Farago 1961). Calibration is an activity where the gadget in question is compared to a well-known reference value this means that the known reference used in the harmonization should be traceable so as to identify the standards used.
The measurements or values from machine 1 are deviating very much and there may be a drift that may lead to erroneous readings, therefore there is an urgent need for the machine to be well calibrated. With machine 1 it is easier to make a profit. This is because after calculating the tolerance for both the machines it was discovered that most of the resistors for machine 1 has a tolerance between 5% and 1% which means that most of them were sold at a better price and that their performance was better as compared to that of machine 2. From the data it is also evident that the resistors produced from machine 2 have a better fault tolerance as compared to those of machine 1 and also their distribution is much more comprehensive than that of machine 1. The prices for the resistors are given to one-thousands of a pound meaning that the prices will seem or appear to be friendly to the customers who will be purchasing the resistors and if a company is aiming at average people or third world country it will be a boom for them since it will be easier for them to afford. It is possible for a company to adjust its prices to the customers’ needs, especially if their customers are from third world countries, this will help a company in maintaining and gaining more customers (F Y Wu 2002). Comparing the two machines it’s evident that though machine 1 did not have a good spread range, the resistors from its production had a higher percentage of selling as compared to machine 2: Rejection rate= number rejected/number produced * 100%
For machine 1 the rejection rate was:
(1/10000) * 100 =0.01%
The rejection rate for machine 2 was:
(12/10000) * 100= 0.12%)
As of the exceeding calculations, we can be able to infer that the rejection rate for both machines was below 1 percentage but the rejection rate for machine 2 was higher as compared to that of machine 1, hence the yield for machine 1 was higher than that of machine 2.