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Presentation on Copier Paper Report Affiliation: Introduction As a quality analyst at John and Sons Company, I understand that my job description entails looking at products, looking at systems, and looking at materials in order to ensure that there are no defects (Black et al., 2011). All of these activities are for ensuring that the products are subject to make in accordance to the standards set by the company. Since John and Sons Company manufactures fax machines, copiers, and printers that all use plain papers, there is thus need to ensure quality production on all of these three products. For this presentation, I am going to address on quality production of the copier machines that have the capacity of producing 99.5% of paper without getting jammed.
The basics to consider in quality assurance
In a copier manufacturing process, there is need of a quality analyst to ensure that the digital copier machine is running through specialized software. Quality control in the same machine is possible to achieve through constant monitoring on its performance. There is also need of performing daily calibrations of the digital copier machine (Chapman, 1991). Finally, a quality analysts may also engage in filing and archiving as a procedure of ensuring the set standards of a copier machine are subject to achieve.
Calculation on the average paper thickness
The average thickness is subject to compute by adding of the possible paper thickness levels of selected papers and then divides with the total numbers of data provided. The calculation is as shown below;
Average thickness = {0.00385 + 0.00358 + 0.00372 + 0.00418 + 0.00380 + 0.00399 + 0.00424 + 0.00375 + 0.00449 + 0.00422 + 0.00407 + 0.00434 + 0.00381 + 0.00421 + 0.00397 + 0.00425 + 0.00449 + 0.00462 + 0.00467 + 0.00404 + 0.00391 + 0.00431 + 0.00398 + 0.00415}/ 24
Total = 0.088966/24
Average = 0.00374
Therefore, the average paper thickness to use in the copier machine is 0.00374. Using this paper thickness would help at achieving a target of 99.5% of all paper used without jamming the machine.
Calculation of 99.5% Confidence Limit
The formula for confidence limit is given by;
Sample mean +/- critical value or z-score for 99.5% confidence * standard deviation /sqrt n
Through the above formula, there is need to compute the critical value and the standard deviation as well.
Part 1: Finding critical value for 99.5% confidence level
Graphical representation of 99.5% confidence interval
Step 1: subtract 100% to the confidence level in order to find α level, which is 100% - 99.5% = 0.5%.
Step 2: convert the result above into a decimal, which is 0.5%/100% = 0.005
Step 3: divide the result above by two (α/2), which is 0.005/2 = 0.0025
Step 4: follow by subtracting the value above from 1to find the area in the middle, which is 1 – 0.0025 = 0.9975
Step 5: follow by looking up the area from the step in z-table, which give 2.81. Therefore, 2.81 is the critical value of the 99.5% confidence level.
Part 2: calculating the standard deviation
Formula for standard deviation is (Mainland, 1956).
The μ is the mean, which is 0.00374 as calculated earlier.
0.00385 – 0.00374 = (0.00011) 2 = 0.0000000121
0.00358 – 0.00374 = (0.00016)2 = 0.0000000256
0.00372 – 0.00374 = (-0.00002)2 = 0.0000000004
0.00418 – 0.00374 = (0.00044)2 = 0.0000001936
0.00380 – 0.00374 = (0.00006)2 = 0.0000000036
0.00399 – 0.00374 = (0.00025)2 = 0.0000000625
0.00424 – 0.00374 = (0.0005)2 = 0.00000025
0.00375 – 0.00374 = (0.00001)2 = 0.0000000001
0.00449 – 0.00374 = (0.00075)2 = 0.0000005625
0.00422 – 0.00374 = (0.00048)2 = 0.0000002304
0.00407 – 0.00374 = (0.00033)2 = 0.0000001089
0.00434 – 0.00374 = (0.0006)2 = 0.00000036
0.00381 – 0.00374 = (0.00007)2 = 0.0000000049
0.00421 – 0.00374 = (0.00047)2 = 0.0000002209
0.00397 – 0.00374 = (0.00023)2 = 0.0000000529
0.00425 – 0.00374 = (0.00076)2 = 0.0000005776
0.00449 – 0.00374 = (0.00075)2 = 0.0000005625
0.00462 – 0.00374 = (0.00088)2 = 0.0000007744
0.00467 – 0.00374 = (0.00093)2 = 0.0000008649
0.00404 – 0.00374 = (0.0003)2 = 0.00000009
0.00391 – 0.00374 = (0.00017)2 = 0.0000000289
0.00431 – 0.00374 = (0.00057)2 = 0. 0000003249
0.00398 – 0.00374 = (0.00024)2 = 0.0000000576
0.00415 – 0.00374 = (0.00041)2 = 0.0000001681
Sum = 0.0000055373/24 = √ (2.3072 * 10-7) = 0.00048
Therefore, standard deviation is 0.00048
Now, confidence limit is given by;
Sample mean +/- critical value or z-score for 99.5% confidence * standard deviation /sqrt n (Mainland, 1956).
Where n=24, Critical value is 2.81, standard deviation is 0.00048 and sample mean is 0.00374
Confidence limit = 0.00374 +/- 2.81* 0.00048/√24 = 0.00374 +/- 2.81* 9.797958971*10-5
= 0.00374 +/- 2.753226471*10-4
Therefore; the upper confidence limit is 0.00040
The lower confidence limit is 0.003465
The Data Chart is as shown below;
Conclusion
The above calculations were all the process of determining the upper and lower confidence limit that would enable the copier into producing 99.5% of all the paper without getting jammed. The resulting outcome is that the company needs to recommend the use of 0.00374 thickness limit of the paper with upper confidence limit of 0.00040 and lower confidence limit is 0.003465.
References
Black, J. T., Kohser, R. A., & DeGarmo, E. P. (2011). DeGarmos materials and processes in manufacturing. Hoboken, NJ: John Wiley & Sons.
Chapman, J. (1991). Confidence limits and enclosure estimates: Some comments. Agricultural History Review, 39, 1, 48-51.
Mainland, D. (1956). Statistical tables for use with binomial samples: - contingency tests, confidence limits, and sample size estimates. New York: Dept. of Medical Statistics, New York Univ. College of Medicine