Statistical Quality Control Project - Case Study Example

STATISTICAL PROCESS CONTROL Name Professor’s Name Course name Date Statistical Quality Control Project Introduction Enhancing quality has always been at the heart of any organization especially the business oriented organizations. In an attempt to achieve this, many organizations have decided to adopt total quality management (Hart and Hart R, 2007). Total quality management aims at addressing the issues related to an organization's management and strategies (Omachonu and Joel (2004). The main areas of concern for total quality management include quality in stewardship, products and designs or processes in an organization. Relevant tools and techniques have to be employed to achieve quality control (Islam and Hossain, 2013). The relevant tools that can be applied in this case include statistical tools that can be adopted to inspect efficiency and consistency of various processes in an organization. For this reason, the concept of statistical quality management is introduced as one important tool for achieving quality control (Montgomery, 2009). Case study: Analysis of the bag-weight problem Wetland Drilling Inc. had presented complaints to Bayfield Mud Company after receiving shipped goods that did not meet the expected standards. Three Boxcars of Mudtreating agents did not meet the weight requirement recommended by the client. The weight was shipment recorded a shortage of 5% in weight for goods expected to weigh 50 pounds per bag. It was not the first time that the weight recorded was small than anticipated for shipped goods. Initially, a receiving clerk from West-Lands Company had identified the inconsistencies of the weights of the disputed boxcars to the weights of previously shipped boxcars. Bayfield distanced itself from making any alterations on the commodities weights during loading. Wetland engineers developed control limits and randomly selected boxcars for weighing that revealed the 2.49 pounds shortage per bag. The Wetland personnel even included a standard deviation of 1.2 pounds which enabled them come to a decision that there was weight deficit was significant. Bayfield decided to confirm this claims by the help of its control workforce. The Quality control team adopted a random sampling technique for the boxcars. Six samples were subjected to weighing at intervals of one hour. It is established that the problem is more frequent in the evening and late hours of the day. In addition, more underweight cases are recorded than normal weight. An example of the samples is illustrated below retrieved from the Bayfield case study. Results and Analysis Table 1 Hour 1 2 3 4 5 x R 4 55 70 50 30 51 51.2 40 5 49 38 64 36 47 46.8 28 6 59 62 40 54 64 55.8 28 7 36 33 49 48 56 44.4 24 8 50 67 53 43 40 50.6 23 9 44 52 46 47 44 46.6 27 10 70 45 40 47 41 48.6 8 11 57 54 62 45 36 50.8 29 12 56 54 47 52 62 54.2 26 13 40 70 58 58 44 54 20 14 52 58 40 33 46 45.8 30 15 57 70 52 59 59 59.4 18 16 62 58 42 33 55 50 17 17 40 42 49 59 48 47.6 29 18 64 49 42 57 50 52.4 20 19 58 39 52 48 50 49.4 22 20 60 50 41 41 50 48.4 10 21 52 47 48 58 40 49 19 22 55 40 56 49 45 49 16 23 47 48 50 50 48 48.6 3 24 50 50 49 51 51 50.2 2 25 51 50 52 51 62 53.2 12 Sample size (n) = 5 Mean of sample means (control limit) =  Average range of samples =  The standard deviation cannot be identified from the values. The lower and upper control limit has to be derived. The control chart will be preferred to derive this function. The upper and lower limit is useful in generating the X-Bar Chart. The following formulae will be adopted. Upper control limit (UCL) = (mean of the sample)+(mean factor)(average means of sample) Lower control limit (LCL) = (mean of the sample)-(mean factor)(average means of sample) A sample size of five will be selected (n=5) the data below can be useful in generating the control factor Chart. sample size n mean factor A2 upper range D4 lower range D3 2 1.88 3.263 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284 The upper control limit and the lower control limit are as shown below: UCL= +(0.557*18.04)= 54.28828 LCL=-(0.557*18.04)=34.15172 The analyzed data can be plotted in the graph below All sample means do not fall within the upper and lower control limits on the graph. There is a control point above the upper control limit. This implies that the statistical process is out of control. Table 2 (2.00am-8.00am) Hour 1 2 3 4 5 x R 4 55 70 50 30 51 51.2 40 5 49 38 64 36 47 46.8 28 6 59 62 40 54 64 55.8 28 7 36 33 49 48 56 44.4 24 8 50 67 53 43 40 50.6 23 The sample size (n)=5 Mean of the sample means (control limit) X=  Average range of samples R= UCL= 49.76+ (0.5777*28.4) = 66.16668 LCL= 49.76- (0.5777*28.4) = 33.3532 The calculated data can then be used to plot the X-bar control chart for the data analyzed from table 2. No points are the plotted graph crosses the upper and lower control limit. However the points not so close to the control limit. The The R-Chart Hour 1 2 3 4 5 x R 4 55 70 50 30 51 51.2 40 5 49 38 64 36 47 46.8 28 6 59 62 40 54 64 55.8 28 7 36 33 49 48 56 44.4 24 8 50 67 53 43 40 50.6 23 9 44 52 46 47 44 46.6 27 10 70 45 40 47 41 48.6 8 11 57 54 62 45 36 50.8 29 12 56 54 47 52 62 54.2 26 13 40 70 58 58 44 54 20 14 52 58 40 33 46 45.8 30 15 57 70 52 59 59 59.4 18 16 62 58 42 33 55 50 17 17 40 42 49 59 48 47.6 29 18 64 49 42 57 50 52.4 20 19 58 39 52 48 50 49.4 22 20 60 50 41 41 50 48.4 10 21 52 47 48 58 40 49 19 22 55 40 56 49 45 49 16 23 47 48 50 50 48 48.6 3 24 50 50 49 51 51 50.2 2 25 51 50 52 51 62 53.2 12 The range of samples will be considered in developing the R-chart. Sample (n) = 5 Average range of samples R =  The following formula will be used to determine the UCL and LCL of the R-Chart UCL = D4R LCL = D3R Where R= Average Range of Samples D3= Lower range control factor D4= Upper Range control factor sample size n mean factor A2 upper range D4 lower range D3 2 1.88 3.263 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284 From the chart the following values can be identified: Upper Range Control Factor (D4)= 2.115 Lower Range Control Factor (D3)= 0 Therefore , the UCLR and the LCLR can be calculated Upper Range Control Factor (UCLR) =2.115*20.5= 57.63575 Lower Range Control Factor (LCLR) =2.115*0= 0 The R chart measures that variability of a process. Too many points above the lower and upper control levels indicate a problem in the process. The points above the UCL are of major concern. Table 2 (2.00am-8.00am) Hour 1 2 3 4 5 x R 4 55 70 50 30 51 51.2 40 5 49 38 64 36 47 46.8 28 6 59 62 40 54 64 55.8 28 7 36 33 49 48 56 44.4 24 8 50 67 53 43 40 50.6 23 The variability is great when compared to the R-Chart. Many points have been plotted outside the control limit. Results From the data collected in Table 1 and 2, it can has been established from the X-Bar control charts that the statistical control process is out of control for the 25 hours. The R chart established that several points came close to the upper and lower control limit. The Table 2 R-Chart also established that there is a problem in the statistical control process. References Hart M.K & Hart R.F (2007). Introduction to Statistical Process Control Techniques. Retrieved on October 26th, 2015 from. Islam M & Hossain M (2013). Statistical Quality Control Approach in Typical Garments Manufacturing Industry in Bangladesh: A Case Study. Proceedings of 9th Asian Business Research Conference. Retrieved on October 26th, 2015 from. Omachonu V.K & Joel E (2004). Principles of Total Quality, Third Edition. London: CRC Press. Montgomery D.C. (2009). Introduction to Statistical Quality Control. New Jersey: John Wiley & Sons Inc. Read More