Two Basic Types of Inspection Used in Sampling for Process Control - Report Example

Name Course Date Unit 036: Statistical Process Control 1. Two basic types of inspection used in sampling for process control The two types of sampling used in inspection are: a) Sampling inspection by attributes b) Sampling inspection by variables a) Sampling inspection by attributes This is a method used to evaluate the quality or the characteristics of an item and classifying them as nonconforming or conforming depending on whether it is conforming to the standard specification. They can be characterized in terms of quantity or quality. The numbers of items which have nonconforming attributes are counted and if the number has not been exceeded, the lot is accepted. The advantage of this method is it simple to use and is more robust (Das, 2008). b) Sampling inspection by variables This method is used to evaluate the quality of items by measuring the value of the variable characterizing the inspected commodity. This method begins by selecting a number of items and measuring the characteristics or the dimensions so as to know if the characteristics of the sample are within the particular limits but not the actual value of the characteristics. The acceptance of a lot is based on the calculations of the variability or the average of the measurements in accordance with the set standards. This method requires smaller sample size compared to attribute method. It also provides more information about the effects of the process or mean on the quality (Das, 2008; Ravindran, 2008). 2. Significance of natural and assignable causes of variation Causes of variation are important during a quality inspection of a product. Thus, an understanding variation is essential for the management and success of operation process. Variation can be classified as natural variation and assignable variation. Natural variation is common or chance causes of variability, which occurs and cannot be traced to a particular cause. It is created by number of influences of minor factors within a predictable range and little can be done other than revise the change the fundamental process. This variation is the sum of a number of effects of multifaceted interaction of random cause, which may be slight. A set of random or common causes that creates variation in the product quality may originate from the variation from the input to the process. An old machine, for example, has a higher degree of natural variability compared to a new machine. Sources of this variation include temperature changes, vibration of the equipment, changes in the emotion and physical conditions of the operator or electrical changes. The process is stable if the common variations are present (Harry, 2010; Ravindran, 2008). Assignable variation represents large unsatisfactory interruptions to the normal performance process. They are those effects which can be detected and controlled. A process operating with the existence of assignable causes is said to be out of control. They may include defective raw materials, improperly adjusted machine or operator error. These effects can be traced in order to change the equipment, operation technique or the materials used. A control chart may be used for monitoring the process in order to detect the presence of assignable causes. Thus, if the plot point is outside the limits of the control charts, the assignable cause is likely to have occurred. The process of variability can be reduced by identifying these occurrences and working to remove the causes from their process (Harry, 2010). 3. Frequency distribution and mean, range and standard deviation The table for Frequency distribution Class Frequency x mid x mid f xmid - x (xmid - x)2 (xmid - x)2f 825 - 929 9 827 7443 -13.61 185.232 1667.089 830 - 834 14 832 11648 -8.61 74.132 1037.849 935 - 939 1 837 837 -3.61 13.032 13.032 840 - 844 12 842 10104 1.39 1.932 23.185 845 - 849 9 847 7623 6.39 40.832 367.489 850 - 854 1 852 852 11.39 129.732 129.732 855 - 859 2 857 1714 16.39 268.632 537.2642 960 - 964 6 862 5172 21.39 457.532 2745.193 Total 54 45393 31.12 1171.057 6520.833 Mean is given by == 840.61 ohms Sample standard deviation, = ohms The range is given by 861.9 - 826 = 35.9 ohms 4. Characteristics of the normal curve to the distribution of the means of small samples Small samples in distribution graph shows normal distribution. For example, column 1, 2, and 3 are almost symmetrical about the central point. The same observation is shown in columns 2, 3 and 4. The last three columns are skewed. For normal the distribution, the median position coincides with the mean and the mode. The calculated mean value, which is 840.61 ohms, and the median, 844.5, does not coincide in the data set. 5. Appropriate control chart limits The upper control limit = Average value + 3 x Standard deviation = 840.61 + (3x11.092) = 873.886 ohms The lower control limit = Average value – 3 x Standard deviation = 840.61 - (3x11.092) = 807.334 ohms 6. Control charts for variables, rejects per unit and percentage defectives per batch 7. Control program for an application Control Program Defective motors X = Subgroup Id (1 to 18) Numdef = Number of defective items in sub-group Size = Total number of items in sub-group Serial read numdef Data: Serial read size Data: Let x = Sequence 1 to 18 Lines solid solid dot dot Xlimits 0 18 Xtic offset 0 1 Ylimits 0 10 Ytic offset 18 P control chart numdef size x 8. Ungrouped data (the mean, range and standard deviation) Table showing the data set Resistors (ohms) Sample number 1 2 3 Mean Range 1 833 833.1 832 832.7 2 2 840 840 841 840.333 1 3 833 833.3 835 833.767 2 4 847 847.4 847.5 847.3 0.5 5 826 826.5 826.6 826.367 0.6 6 840 840.6 840.8 840.467 0.8 7 833 833.7 833.9 833.533 0.9 8 854 854.8 854.7 854.5 0.8 9 861 861.9 861.6 861.5 0.9 10 840 840.8 840.5 840.433 0.8 11 847 847.7 847.6 847.433 0.6 12 833 833.6 833.7 833.433 0.7 13 826 826.5 826.8 826.433 0.8 14 861 861.4 861.9 861.433 0.9 15 840 840.3 840.4 840.233 0.4 16 847 847.4 847.8 847.4 0.8 17 833 833.5 833.4 833.3 0.5 18 826 826.6 826.3 826.3 0.6 Total 15126.87 15.6 Standard deviation, σ =, where dn =2.059 (Hartley’s constant) (Das, 2008). Sample size, n = 3 Therefore, σ = 0.867/3 = 0.289 ohms Standard errors = = 3 x 0.289/= 0.5 9. Relationship between the normal curve and the mean values The process mean is approximately at the median position, indicating that there generally normal distribution. 10. Select and group the data based on variable and attribute inspection methodology. Based on variables aspects of the data, it is assumed that the quality of the characteristics of the data set follow normal distribution with the standard deviation σ and the mean, x. The attributes aspects suppose that random samples of fixed value of the number size n taken from a group with a given number of defective products. Therefore, the number of defects follows binomial distribution. 11. Control charts, calculate the limits Control limits = = 840.3810.5 ohms Upper control limit = 840.881 ohms Lower control limit = 839.881 ohms Range chart Control line = 2.57 = 2.57 x 0.867 = 2.228 ohms 12. Control chart for variable inspection methodology, showing rejects per unit and percentage defects per batch Control chart References Walker, H. F. (2012). The certified quality inspector handbook. Milwaukee, Wis: ASQ Quality Press. Das, (2008). Statistical Methods (Combined), Tata McGraw-Hill Education Harry, M. J. (2010). Practitioner's guide for statistics and lean six sigma for process improvements. Hoboken, N.J: John Wiley & Sons. Ravindran A. R,, (2008). Operations Research Applications, Operations Research Series CRC Press Read More