What is the standard deviation of individual bags

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Reference no: EM13854025


In November 2013, John Adams, a customer service representative of Americo Drilling Supplies (ADS), was summoned to the Houston warehouse of Drilling Contractors, Inc. (DCI), to inspect three boxcars of mud-treating agents that ADS had shipped to the Houston firm. DCI had filed a complaint that the 50 Pound bags of treating agents that it had just received from ADS were short-weight by approximately 5%.

The light-weight bags were initially detected by one of DCI's receiving clerks, who noticed that the rail road side scale tickets indicated that the net weights were significantly less on all three of the boxcars than those of identical shipments received on October 25, 2013. ADS's traffic department was called to determine if lighter-weight dunnage or pallets were used on the shipments. (This might explain the lighter weights.) ADS indicated, however, that no changes had been made in the loading or palletizing procedures. Hence, DCI randomly checked 50 of the bags and discovered that the average net weight was 47.51 pounds. They noted from past shipments that the bag net weights averaged exactly 50.0 pounds, with an acceptable standard deviation of 1.2 pounds. Consequently, they concluded that the sample indicated a significance short-weight. ADS, was then contacted, and Adams was sent to investigate the complaint and to issue a 5% credit to DCI.

DCI, however, was not completely satisfied with only the issuance of credit for the short shipment. The charts followed by their mud engineers on the drilling platforms were based on 50-pound bags of treating agents. Lighter-weight bags might result in poor chemical control during the drilling operation and might adversely affect drilling efficiency. (Mud-treating agents are used to control the pH and other chemical properties of the open during drilling operations.) This could cause severe economic consequences because of the extremely high cost of oil and natural gas well-drilling operations. Consequently, special use instructions had to accompany the delivery of these shipments to the drilling platforms. Moreover, the light-weight shipments had to be isolated in DCI warehouse, causing extra handling and poor space utilization. Hence, Adams was informed that CDI might seek a new supplier of mud-treating agents if in the future it received bags that deviated significantly below 50 pounds.

The quality control department at ADS suspected that the light-weight bags may have resulted from "growing pains" at the Orange plant. Because of the earlier energy crises, oil and natural gas exploration activity had greatly increased. This increased activity, in turn, created increased demand for products produced by related industries, including drilling muds. Consequently, ADS had to expand from one shift (6 A.M. to 2 P.M.) to a two-shift (2 P.M. to 10 P.M.) operation in Mid 2011s, and finally to a three-shift operation (24 hours per day) in September of 2013.

The additional night shift bagging crew was staffed entirely by new employees. The most experienced foremen were temporarily assigned to supervise the night shift. Most emphasis was placed on increasing the output of bags to meet the ever-increasing demand. It was suspected that only occasional reminders were made to double-check the bag weight feeder. (A double check is performed by systematically weighting a bag on a scale to determine if the proper weight is being loaded by the weight-feeder. If there is significant deviation from 50 pounds, corrective adjustments are made to the weight-release mechanism.)

To verify this expectation, the quantity control staff at ADS randomly sampled the bag output and prepared the following table. Six bags were sampled and weighted each hour.


Assume you are John Adams of ADS. Based on the following analysis, prepare a report to be submitted to both ADS and DCI Executives regarding the status of the filling process at ADS and recommend method to improve quality control at the filling station. Use the data provided in the Excel data file.

Insert all graphs and provide analysis in this word file after every question. Only The Word file is graded.

a- Calculate the Range Column in Excel (Largest-Smallest) and find mean and standard deviations for Average Weight, Smallest, Largest, and Range columns.

b- What is the standard deviation of individual bags if sample averages are based on 6 bags? Explain your finding. Hint: σx-bar = σ/sqrt(n). Having σx-bar based on part b calculation, solve for σ given n= 6

c- Construct a time series plot of all four variables (two graphs: one includes avg., smallest, and largest and the other has range) and discuss your findings based on the graphs.

d- Construct X-bar and R Charts, graph, and discuss your findings based on the control charts. Is it out of control? Why? Explain.

e- Is there any differences between performances of three shifts? Hint: (Carve out the morning, afternoon, and night shift data into three columns and graph their averages. Explain your findings.

f- Use One Way Analysis of Variance (ANOVA) to compare the three groups (shifts) to test if there is significant differences in the performance of three shift averages. Use Alpha =0.01. Can you conclude that night shift is to be blamed for most of the variation? Expalin

g- Assume Tolerance limits of 50±1.75 lbs. is specified in the sales contract and find the Process Capability index Cpk. Explain what it indicates and if process is capable to meet contractual agreement.

h- Redo part g for all three shifts separately and determine their Cpk. Note that you must find mean and standard deviation for each shift separately.

i- If the process average is adjusted to 50.0 lbs. and process standard deviation is reduced by 40%, what is the new Cpk? Are you comfortable for making such recommendation to management? Explain.

j- Find the control limits for an X-bar and R chart if a new improved process has average of 50.5 lbs. and R-bar of 1.2 lbs. Assume n=5 for new process control.

k- Provide complete conclusion regarding your findings and make recommendations regarding the filling process in your conclusion paragraph.

I am having difficulty doing this assignment. Please help me work it out. I am hoping all the answer is correct.

Attachment:- case analysis dataset.rar

Reference no: EM13854025

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