Question

A company packages a bulk product in bags with a 50-pound label weight. During a typical day's operation of the fill process, 22 subgroups of five bag fills are observed. Using the observed data, 1 and Rare calculated to be 52.9364 pounds and 1.6818 pounds, respectively. When the 22 I's and 22 Rs are plotted with respect to the appropriate control limits, the first 6 subgroups are found to be out of control. We found that the elimination of a start-up problem brought the filling process into statistical control with 7-53.5875 and R = 1.2937. (a) Recalling that the fill weight i and R charts are based on subgroups of size 5, and assuming that the fill weights are approximately normally distributed, calculate the natural tolerance limits for the process. (Round your answers to 4 decimal places.) Answer is complete but not entirely correct. Natural tolarence limits are |[ 53.3340 51.8410 (b) Suppose that management wishes to reduce the mean fill weight in order to save money by "giving away" less product. However, since customers expect each bag to contain at least 50 pounds of product, management wishes to leave some process leeway. Therefore, after the mean fill weight is reduced, the lower natural tolerance limit is to be no less than 51.5 lb. Based on the natural tolerance limits, how much can the mean fill weight be reduced? If the product costs $5 per pound, and if 1 million bags are sold per year, what is the yearly cost reduction achieved by lowering the mean fill weight? (Round mean answer to 4 decimal places.) X Answer is not complete. pounds The mean fill weight can be reduced by Annual cost reduction

Answer 1

Solution : According to the given data, the following as, Given that. a ) Compute Upper and lower Control limits by using ă= 52.5875 and R = 1,2937 oblain the revised upper Control limit (uch) for x. ucl =łt A₂ 52.5875+0.57781.2937 = 52. 5875+0.7465 From the factors for Constructing variable control charts a 53.334 Thus, the upper Control limit (UCL) for ł is 53,334 (CL) for oblain lower Control limit the revised še LCL = X- A₂ 52.5875 0.577x 1.2937 52. 5875 -0.7465 11 51.841 From the factors for Constructing variables Control Charts

Thus, the lower Control limit (LCL) for Ğ is 5.84) obtain the revised upper control limit (LCL) for Ri when 025 UCL = DA 2.114X 1.2937 = 2.735 Thus, the upper control limit (UCL) for R is 2.735 obtain the revised lower control limit (LL) for R when nosa. LCL =D3 - Ox 1.2937 =0 Thus the lower control limit (Lel) for ais a ab Control the remaining 16 points lie inside the limits (UCL) and (LCL), then the process has out-of-control points. That is, the process is statical control in

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