Statistical Process Control - Assignment Example

Statistical Process Control Task Learning Outcome 1 There are two basic types of the sampling process, the normal, the tightened and the reduced. The normal inspection is conducted by accessing all the observation and evaluating them to ensure they fall within the acceptable limits (Campbell, Stonehouse, & Houston, 2002). The other inspection method is the reduced inspection method. In the reduced inspection of the data is examined on a small portion of the data set and then examine to determine if they meet the quality control procedure (Farnham, 2010). Task 2 – Learning Outcome 1.2 Chance (or common) causes account for the uncontrollable, natural variation present in any repetitive process. A process that is operating with only chance causes of variation is said to be in statistical control or in control. The chance causes are an inherent part of the process (Hussey, 2012). Assignable (or special) causes are those whose effect can be detected and controlled. Assignable causes are not the part of chance causes. A process that is operating in the presence of assignable causes is said to be an out-of-control process. Task 3 – Learning Outcomes 1.3, 1.4, 2.1, 2.2 and 2.3 A factory mass produces resistors of various standard values, in order to test the production processes samples are taken. The following 15 tables show one batch of samples. Data Set 1 Data Set 2 Data Set 3 Sample Resistance (Ohms) Sample Resistance (Ohms) Sample Resistance (Ohms) 1 119 1 178.5 1 238 2 120 2 180 2 240 3 119 3 178.5 3 238 4 121 4 181.5 4 242 5 118 5 177 5 236 6 120 6 180 6 240 7 119 7 178.5 7 238 8 122 8 183 8 244 9 123 9 184.5 9 246 10 120 10 180 10 240 11 121 11 181.5 11 242 12 119 12 178.5 12 238 13 118 13 177 13 236 14 123 14 184.5 14 246 15 120 15 180 15 240 16 121 16 181.5 16 242 17 119 17 178.5 17 238 18 118 18 177 18 236 Data Set 4 Data Set 5 Data Set 6 Sample Resistance (Ohms) Sample Resistance (Ohms) Sample Resistance (Ohms) 1 297.5 1 357 1 416.5 2 300 2 360 2 420 3 297.5 3 357 3 416.5 4 302.5 4 363 4 423.5 5 295 5 354 5 413 6 300 6 360 6 420 7 297.5 7 357 7 416.5 8 305 8 366 8 427 9 307.5 9 369 9 430.5 10 300 10 360 10 420 11 302.5 11 363 11 423.5 12 297.5 12 357 12 416.5 13 295 13 354 13 413 14 307.5 14 369 14 430.5 15 300 15 360 15 420 16 302.5 16 363 16 423.5 17 297.5 17 357 17 416.5 18 295 18 354 18 413 Data Set 7 Data Set 8 Data Set 9 Sample Resistance (Ohms) Sample Resistance (Ohms) Sample Resistance (Ohms) 1 476 1 535.5 1 595 2 480 2 540 2 600 3 476 3 535.5 3 595 4 484 4 544.5 4 605 5 472 5 531 5 590 6 480 6 540 6 600 7 476 7 535.5 7 595 8 488 8 549 8 610 9 492 9 553.5 9 615 10 480 10 540 10 600 11 484 11 544.5 11 605 12 476 12 535.5 12 595 13 472 13 531 13 590 14 492 14 553.5 14 615 15 480 15 540 15 600 16 484 16 544.5 16 605 17 476 17 535.5 17 595 18 472 18 531 18 590 Data Set 10 Data Set 11 Data Set 12 Sample Resistance (Ohms) Sample Resistance (Ohms) Sample Resistance (Ohms) 1 654.5 1 714 1 773.5 2 660 2 720 2 780 3 654.5 3 714 3 773.5 4 665.5 4 726 4 786.5 5 649 5 708 5 767 6 660 6 720 6 780 7 654.5 7 714 7 773.5 8 671 8 732 8 793 9 676.5 9 738 9 799.5 10 660 10 720 10 780 11 665.5 11 726 11 786.5 12 654.5 12 714 12 773.5 13 649 13 708 13 767 14 676.5 14 738 14 799.5 15 660 15 720 15 780 16 665.5 16 726 16 786.5 17 654.5 17 714 17 773.5 18 649 18 708 18 767 Data Set 13 Data Set 14 Data Set 15 Sample Resistance (Ohms) Sample Resistance (Ohms) Sample Resistance (Ohms) 1 833 1 892.5 1 952 2 840 2 900 2 960 3 833 3 892.5 3 952 4 847 4 907.5 4 968 5 826 5 885 5 944 6 840 6 900 6 960 7 833 7 892.5 7 952 8 854 8 915 8 976 9 861 9 922.5 9 984 10 840 10 900 10 960 11 847 11 907.5 11 968 12 833 12 892.5 12 952 13 826 13 885 13 944 14 861 14 922.5 14 984 15 840 15 900 15 960 16 847 16 907.5 16 968 17 833 17 892.5 17 952 18 826 18 885 18 944 1. For your given data set of ungrouped data calculate the mean, range and standard deviation.   dataset 1 data set 2 data set 3 data set 4 data set 5 data set 6 data set 7 data set 8 Mean 9.5 120 180 240 300 360 420 480 Standard Deviation 5.338539 1.57181 2.357716 3.143621 3.929526 4.715431 5.501337 6.287242 Range 17 5 7.5 10 12.5 15 17.5 20   data set 9 data set 10 data set 11 data set 12 data set 13 data set14 data set 15 data set 16 Mean 540 600 660 720 780 840 900 960 Standard Deviation 7.073147 7.859052 8.644958 9.430863 10.21677 11.00267 11.78858 12.57448 Range 22.5 25 27.5 30 32.5 35 37.5 40 The above table indicate the mean, standard deviation and the range of resistance ohms. 2. From the information you correlated: a. Identify the relationship between the normal curve and the mean values From the analysis of normal probability test, it can be observed that the resistance of data set 1, resistance of data set 2, resistance of data set 3, resistance of data set 4, resistance of data set 5, resistance of data set 6, resistance of data set 7, resistance of data set 8, resistance of data set 9, resistance of data set 10, resistance of data set 11, resistance of data set 12, resistance of data set 13, resistance of data set 14, and resistance of data set 15 are showing to be normally distributed and hence obey the assumption of normality. The histogram and the normal distribution curve, it can be observed that the resistance of data set 1, resistance of data set 2, resistance of data set 3, resistance of data set 4, resistance of data set 5, resistance of data set 6, resistance of data set 7, resistance of data set 8, resistance of data set 9, resistance of data set 10, resistance of data set 11, resistance of data set 12, resistance of data set 13, resistance of data set 14, and resistance of data set 15 are normally distributed about the mean of the resistor. The values of the resistors are normally distributed about the mean of the data sets. b. Select and group the data based on variable and attribute inspection methodology. 3. Using appropriate control charts, calculate the limits you would use From above control chart for the variable of the resistor of all the data set 1, data set 2, data set 3, data set 4, data set 5, data set 6, data set 7, data set 8, data set 9, data set 10, data set 11, data set 12, data set 13, data set 14, and data set 15. The lower limit is equal to 11.25 while the upper limit is equal to 46.26 the sample range is equal to 28.75. The sample mean of the resistor has a mean of 540 resistor ohms, the upper limit is equal to 546 and the lower limit is equal to 534. 4. Construct an appropriate control chart for variable inspection methodology, showing rejects per unit and percentage defects per batch The control chart of the resistor is the run chart of the variable inspection. From this analysis, it can be observed that the number of rums about the median is 2, the expected number of runs is 10, the longest run about median is 9, the approximate p- value for the subgroup is 0.000, and the approximate p- value of the mixture is 1. From the run chart of the resistor, it can be observed that the lowest value of the resistor is equal to 100 while the maximum is 900. 5. Develop and implement an inspection control program for your data. Identify: Systematic definition of quality control and statistical control The statistical quality control is the application of the statistical methodology in quality control. Statistics is concerned with drawing inferences from random samples. Hence SQC included all the techniques in the quality control which are concerned with sampling and with evaluating sample in order to take adequate decisions on material, products, manufacturing, organization etc. the statistical control of quality is application of statistical principles and techniques in all stages of design, production, maintenance and services, directed towards the economic satisfaction. The inspection method used the sampling of all the The control charts The control charts used in this study are, x bar chart of resistors both of the sample mean and the median. The study also used the run chart of the resistor in the study. The frequency of inspection and or the batch size (Kutner, and JNachtsheim 2005). The frequency of inspection used is the data set of all the resistors in ohms for all the data set. The method of quality control is implemented through the run chart of resistor. Bibliography: Campbell, G, Stonehouse, G & Houston, B 2002, “Business Strategy,”Heinemann, Oxford, Farnham, D 2010, “Managing in a business context,” CIPD Publishing, London, UK Hussey, DE 2012 “Strategic management: from theory to implementation,” utterworth- , Oxford, UK. Kutner, M. and J Nachtsheim (2005). Applied Linear Statistical Models (5th ed.). New York: McGraw-Hill/Irwin. Read More