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A Study on Six Sigma Techniques And Its application in reduction of seat rejection At BOSCH LTD.
Submitted bySuyog Gholap(107269) R.Rahul(107254) Chandra shekhar.L(107266) Sudip Pal(107237) K.Seshi Kiran Reddy(107249)
Introduction to Six Sigma:Sigma () is a letter in the Greek alphabet that has become the statistical symbol and metric of process variation. The sigma scale of measure is perfectly correlated to such characteristics as defects-per-unit, parts-per-million defectives, and the probability of a failure. Six is the number of sigma measured in a process, when the variation around the target is such that only 3.4 outputs out of one million are defects under the assumption that the process average may drift over the long term by as much as 1.5 standard deviations. Six sigma may be defined in several ways. Tomkins defines Six Sigma to be a program aimed at the near-elimination of defects from every product, process and transaction. Harry (1998) defines Six Sigma to be a strategic initiative to boost profitability, increase market share and improve customer satisfaction through statistical tools that can lead to breakthrough quantum gains in quality. Six sigma was launched by Motorola in 1987. It was the result of a series of changes in the quality area starting in the late 1970s, with ambitious ten-fold improvement drives. The top-level management along with CEO Robert Galvin developed a concept called Six Sigma. After some internal pilot implementations, Galvin, in 1987, formulated the goal of achieving Six-Sigma capability by 1992 in a memo to all Motorola employees. The results in terms of reduction in process variation were on-track and cost savings totaled US$13 billion and improvement in labor productivity achieved 204% increase over the period 19871997.In the wake of successes at Motorola, some leading electronic companies such as IBM, DEC, and Texas Instruments launched Six Sigma initiatives in early 1990s. However, it was not until 1995 when GE and Allied Signal launched Six Sigma as strategic initiatives that a rapid dissemination took place in non-electronic industries all over the world. In early 1997, the Samsung and LG Groups in Korea began to introduce Six Sigma within their companies. The results were amazingly good in those companies. For instance, Samsung SDI, which is a company under the Samsung Group, reported that the cost savings by Six Sigma projects totaled US$150 million. At the present time, the number of large companies applying Six Sigma in Korea is growing exponentially, with a strong vertical deployment into many small- and medium-size enterprises as well. Six sigma tells us how good our products, services and processes really are through statistical measurement of quality level. It is a new management strategy under leadership of top-level management to create quality innovation and total customer satisfaction. It is also a quality culture. It provides a means of doing things right the first time and to work smarter by using data information. It also provides an atmosphere for solving many CTQ (critical-to-quality) problems through team efforts. CTQ could be a critical process/product result characteristic to quality, or a critical reason to quality characteristic.
Defect rate, PPM and DPMO:The defect rate, denoted by p, is the ratio of the number of defective items which are out of specification to the total number of items processed (or inspected). Defect rate or fraction of defective items has been used in industry for a long time. The number of defective items out of one million inspected items is called the ppm (parts-per-million) defect rate. Sometimes a ppm defect rate cannot be properly used, in particular, in the cases of service work. In this case, a DPMO (defects per million opportunities) is often used. DPMO is the number of defective opportunities which do not meet the required specification out of one million possible opportunities.
Standard Deviation:In probability theory and statistics, standard deviation is a measure of the variability or dispersion of a population, a data set, or a probability distribution. A low standard deviation indicates that the data points tend to be very close to the same value (the mean), while high standard deviation indicates that the data are spread out over a large range of values. For example, the average height for adult men in the United States is about 70 inches, with a standard deviation of around 3 inches. This means that most men (about 68%, assuming a normal distribution) have a height within 3 inches of the mean (67 inches 73 inches), while almost all men (about 95%) have a height within 6 inches of the mean (64 inches 76 inches). If the standard deviation were zero, then all men would be exactly 70 inches high. If the standard deviation were 20 inches, then men would have much more variable heights, with a typical range of about 50 to 90 inches.
Fig: A data set with a mean of 50 (shown in blue) and a standard deviation () of 20.
Fig: A plot of a normal distribution (or bell curve). Each colored band has a width of one standard deviation. In addition to expressing the variability of a population, standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. (Typically the reported margin of error is about twice the standard deviation,
the radius of a 95% confidence interval.) In science, researchers commonly report the standard deviation of experimental data, and only effects that fall far outside the range of standard deviation are considered statistically significant. Standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the risk. Consider a population consisting of the following values
There are eight data points in total, with a mean (or average) value of 5:
To calculate the standard deviation, we compute the difference of each data point from the mean, and square the result:
Next we average these values and take the square root, which gives the standard deviation:
Therefore, the population above has a standard deviation of 2. Note that we are assuming that we are dealing with a complete population. If our 8 values are obtained by random sampling from some parent population, we might prefer to compute the sample standard deviation using a denominator of 7 instead of 8. The standard deviation of a discrete random variable is the root-mean-square (RMS) deviation of its values from the mean. If the random variable X takes on N values (which are real numbers) with equal
probability, then its standard deviation can be calculated as follows:
Find the mean, , of the values. For each value xi calculate its deviation ( Calculate the squares of these deviations. Find the mean of the squared deviations. This quantity is the variance 2. Take the square root of the variance. ) from the mean.
This calculation is described by the following formula:
is the arithmetic mean of the values xi, defined as:
If not all values have equal probability, but the probability of value xi equals pi, the standard deviation can be computed by:
And N' is the number of non-zero weight elements.
For exampleSuppose we wished to find the standard deviation of the data set consisting of the values 3, 7, 7, and 19. Step 1: find the arithmetic mean (average) of 3, 7, 7, and 19,
Step 2: find the deviation of each number from the mean,
Step 3: square each of the deviations, which amplifies large deviations and makes negative values positive,
Step 4: find the mean of those squared deviations,
Step 5: take the non-negative square root of the quotient (converting squared units back to regular units),
So, the standard deviation of the set is 6. This example also shows that, in general, the standard deviation is different from the mean absolute deviation (which is 5 in this example).Note that if the above data set represented only a sample from a greater population, a modified standard deviation would be calculated to estimate the population standard deviation, which would give 6.93 for this example.
Rules for normally distributed data
Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for 68.27 % of the set; while two standard deviations from the mean (medium and dark blue) account for 95.45%; three standard deviations (light, medium, and dark blue) account for 99.73%; and four standard deviations account for 99.994%. The two points of the curve which are one standard deviation from the mean are also the inflection points. The central limit theorem says that the distribution of a sum of many independent, identically distributed random variables tends towards the normal distribution. If a data distribution is approximately normal then about 68% of the values are within 1 standard deviation of the mean (mathematically, , where is the arithmetic mean), about 95% of the values are within two standard deviations ( 2), and about 99.7% lie within 3 standard deviations ( 3). This is known as the 68-95-99.7 rule, or the empirical rule. For various values of z, the percentage of values expected to lie in the symmetric confidence interval (z,z) are as follows: z 1 1.645 1.960 2 2.576 3 percentage 68.2689492% 90% 95% 95.4499736% 99% 99.7300204%
3.2906 4 5 6 7
99.9% 99.993666% 99.9999426697% 99.9999998027% 99.9999999997440%
In Fig: Dark blue is less than one standard