Townhouse Paint Company, one of his largest accounts. The purchasing agent for T
ID: 428334 • Letter: T
Question
Townhouse Paint Company, one of his largest accounts. The purchasing agent for Townhouse Paint was complaining that the tubes of paint tint it had received over the last couple of weeks were not within the specification range of 4.90 to 5.10 ounces.
The off-weighed tubes had not been detected by Townhouse's receiving clerks and had not been weighed or otherwise checked by their quality control staff. The problem arose when Townhouse began to use the tube of tinting agent and found that the paint colors were not matching the specifications. The mixing charts used by the salespeople in Townhouse's retail stores were based on 5-ounce tubes of tinting agent. Overfilled or underfilled tubes would result in improper paint mixes, and therefore in colors that did not meet customer's expectations.
In consequence, Townhouse had to issue special instructions to its entire retail staff that would allow them to compensate for the off-weight tubes. The Townhouse purchasing agent made it clear that a new supplier would be sought if the problem recurred. Paint Tint's quality control department was immediately summoned to assist in determining the cause of the problem.
Paint Tint's quality manager, Mike Mathews, decided to collect some data to analyze the problem. The plant is a three-shift operation and Wilson collected samples from each shift for 15 days. Samples always consisted of 10 randomly selected tubes of paint tint. The data is provided in the spreadsheet named New Paint Tint Data.xls.
Analyze the data provided with respect to process control. Can you identify any issues that may explain the weight problem?
Analyze the data provided with respect to process capability. How would you rate the ability of Paint Tint's production process to meet Townhouse Paint's requirements? What are the implications of your evaluation?
If Paint Tint ships 10,000 tubes of tint how many can Townhouse expect to be out of specification (assuming nothing changes)?
Sample 1 2 3 4 5 6 7 8 9 10 1 4.90 5.03 5.00 5.03 5.02 4.92 5.04 4.92 4.95 5.02 2 5.07 4.90 5.02 4.98 5.01 4.95 4.99 5.02 5.01 4.97 3 5.01 4.95 5.03 4.92 4.97 5.04 5.02 4.98 5.01 5.03 4 5.05 5.04 5.00 5.06 4.94 5.02 5.03 5.00 4.95 4.99 5 4.98 4.95 4.94 5.15 4.95 4.99 4.97 5.00 4.95 4.99 6 5.02 5.04 4.96 5.03 5.04 5.02 5.00 5.01 5.02 4.99 7 4.96 4.96 4.92 5.01 4.98 5.00 4.98 5.00 4.94 5.08 8 4.99 4.97 5.04 5.02 5.02 4.99 5.00 5.00 5.05 4.95 9 5.06 4.95 5.01 5.00 4.95 5.08 5.03 4.93 5.03 5.03 10 4.96 5.00 5.05 5.03 5.01 5.02 5.02 4.96 5.02 4.94 11 4.96 4.92 4.96 5.00 5.02 5.15 4.98 4.91 5.02 5.03 12 4.95 4.96 5.00 5.08 5.03 5.02 4.94 4.99 5.00 5.03 13 4.96 5.00 5.06 4.98 5.00 5.02 5.00 5.01 4.95 5.00 14 5.10 4.96 5.00 4.95 4.98 5.00 4.99 4.98 5.03 5.00 15 5.05 5.02 4.95 4.97 4.98 5.04 4.96 4.97 4.98 5.03 16 5.03 4.99 4.98 4.99 4.98 5.01 4.99 5.01 4.98 4.95 17 5.02 5.03 4.98 5.06 5.04 5.04 4.99 4.98 4.97 4.99 18 5.09 5.03 5.02 4.99 5.04 4.97 4.99 4.94 5.00 4.96 19 4.99 5.03 5.01 5.02 5.01 4.99 5.08 5.05 4.95 5.04 20 5.08 4.97 4.93 4.84 5.07 4.95 4.93 4.99 4.82 5.05 21 5.00 4.98 5.05 5.00 5.01 5.00 4.99 4.98 5.00 4.97 22 5.00 5.01 4.95 5.01 4.99 4.98 4.96 5.00 4.94 4.98 23 5.10 4.93 4.92 4.93 5.05 4.96 4.86 5.08 4.96 5.12 24 4.96 5.01 5.06 5.07 4.95 4.94 5.03 4.97 5.02 5.02 25 5.02 5.05 5.00 5.01 5.03 5.00 5.01 4.97 5.07 5.02 26 5.16 4.96 4.99 5.00 4.98 4.99 5.01 5.07 4.95 5.03 27 5.00 4.98 5.06 4.97 5.00 4.97 5.01 5.03 4.92 4.99 28 5.03 4.90 4.95 5.01 5.01 4.94 4.98 4.98 5.00 5.01 29 5.00 4.97 5.05 5.07 4.94 4.96 5.05 4.91 4.96 4.91 30 4.97 4.94 5.01 5.00 5.02 4.95 5.01 5.01 5.08 5.01 31 5.01 4.94 5.00 5.00 4.96 4.98 5.01 4.97 5.00 4.98 32 4.97 4.91 5.15 4.96 4.91 5.07 5.15 4.95 4.91 5.11 33 4.98 4.99 5.02 4.99 4.97 4.97 5.08 5.03 5.04 5.01 34 4.95 4.95 5.06 5.02 4.94 4.99 4.97 4.97 4.96 5.02 35 4.90 4.92 4.97 4.92 5.04 5.03 4.91 4.95 4.98 5.05 36 4.94 4.99 5.04 5.02 5.06 5.08 4.96 4.99 4.95 4.99 37 5.02 4.95 5.00 4.98 5.04 5.02 4.99 5.05 5.02 5.06 38 5.01 4.98 5.10 5.10 5.00 5.10 5.06 4.98 5.04 5.03 39 5.02 5.02 5.02 4.92 5.03 5.02 5.04 4.96 5.05 5.01 40 4.96 4.97 4.93 5.01 5.00 5.04 4.98 5.08 4.94 5.02 41 5.11 5.05 4.93 5.13 4.98 4.88 4.99 4.90 5.03 5.04 42 5.04 4.96 4.97 5.03 5.04 5.04 5.04 4.99 5.04 4.99 43 5.06 4.97 5.00 5.00 5.03 5.08 4.97 4.98 5.00 4.97 44 5.02 5.02 4.86 4.98 4.93 4.97 5.05 4.97 5.03 4.92 45 5.01 5.03 4.97 5.01 4.98 4.95 4.96 5.03 4.99 5.06Explanation / Answer
1. Standard deviation = 0.048
Average = 4.98
Process capability for UCL =5.1 and LCL =4.9 is given by UCL-LCL /6 sigma
Cp = 5.1-4.9 / 0.048x6
= 0.2 /0.288 = 0.694
which indicates the inability of the process to produce items within specifications.
The process is out of control,as 9 values are on higher side of USL and 5 values are lower than LSL.
With this proportion, Out of 10000, we expect follwing number to be out of control
HIgher values = 9x10000/450 = 200
Lower values = 5x10000/450 = 111
Hence 311 values are expected to fall out of limits which is the primary cause of colour difference.
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