1) Triangle Packaging Machinery wants to test the quality of its cereal bag filling machines. The firm’s quality analyst took 35 samples of size 7 each from a cereal-bag-filling machine. The results were overall mean = 57.75 pounds; average range = 1.78 pounds.
a) Determine the upper and lower control limits of the x-chart, where sigma = 3
b) Determine the upper and lower control limits of the R-chart, where sigma = 3
2) The results of an inspection of component samples taken over
the past 10 days at Advance Auto Parts are as given below. The
sample size is 100.
Day |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Defective |
7 |
6 |
6 |
9 |
5 |
6 |
0 |
8 |
9 |
1 |
a) Construct a 3-sigma p-chart using this information.
b) Using the control chart in part (a), and finding that the number of defectives on the next three days are 12, 5, and 13, is the process in control?
3) Telephone inquiries of hundred Discover Card’s customers are monitored daily at random. Incidents of incorrect information or other nonconformities (such as impoliteness to customers) are recorded. The data for last week follow:
Day |
1 |
2 |
3 |
4 |
5 |
Number of Non-conformities |
5 |
10 |
23 |
20 |
15 |
Construct a 3-standard deviation c-chart of nonconformities.
4) Oklahoma LED’s production process yields lightbulbs with an average life of 1,800 hours and s = 100 hours. The tolerance upper and lower specification limits are 2,400 hours and 1,600 hours, respectively. Is this process capable of producing lightbulbs to specification?
Answer 1:
D4, D3 and A2 are taken from the table of factors computing 3 sigma control limits, sample size=7
overall mean= Xbarbar= 57.75, overall range= Rbar= 1.78
a.
A2 (n=7) |
0.419 | ||
control limits for X bar, | |||
CL or Xbarbar | 57.750 | ||
UCL=Xbarbar+ (A2)*Rbar | 58.496 | ||
LCL=Xbarbar- (A2)*Rbar | 57.004 |
b.
D4 (n=7)= | 1.924 | ||
D3 (n=7)= | 0.076 | ||
control limits for Range, | |||
CL or R-bar | 1.780 | ||
UCL=R-bar*D4 | 3.425 | ||
LCL=R-bar*D3 | 0.135 |
1) Triangle Packaging Machinery wants to test the quality of its cereal bag filling machines. The...
4. A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [13, 16, 21, 16]; Machine #2 measurements [ 22, 24, 23, 21]; Machine #3 measurements [ 15, 24, 13, 12]. Using the factors for three sigma control limits, what are x-bar chart...
Refer to Table 56.1 - Factors for Computing Control Chart Limits (sigma) for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvels Lifelong Lawn Lid. The results were: Overal mean = 54.75 lb.: Average range R 164 b. a) For the given sample size, the control limits for 3-sigma x chart are Upper Control Limit (UCL) - D. (round your response to three decimal places). Lower Control Limit (LCL)-1. (round your response...
2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data develop limits for the control chart, plot the control chart, and determine whether the process is in control (Please keep two decimal points.) Number of Sheet flaws 1 2 0 1 2 3 4 5...
2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control. (Please keep two decimal points.) Number of flaws Sheet 1 2 0 1 2 3 4 5...
Refer to Table 56.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.: Average range R = 1.78 lb. a) For the given sample size, the controllimits for 3-sigma x chart are: Upper Control Limit (UCL)- b. (round your response to three decimal places). Lower Control Limit (LCL:) - (round your...
2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control. (Please keep two decimal points.) Number of flaws Sheet 1 1 2 3 4 5 6 2...
2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control. (Please keep two decimal points.) Number of flaws Sheet 1 2 3 4 1 2 0 1...
2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control. (Please keep two decimal points.) Number of flaws Sheet 1 2 3 4 1 2 0 1...
Data was collected from a textile finishing process. Samples were collected daily and the number of nonconformities were recorded. (recall more than one nonconformity can be present on each unit) Day Number of units produced Number of Nonconformities 1 13 60 2 12 43 3 19 55 4 14 44 5 18 55 6 13 40 7 24 61 8 15 49 9 16 66 10 11 41 Using Minitab: 1. Construct an appropriate control chart for the above data....
Question 4 [20 marks] By utilising Annexure A, answer the following questions: (a) 15 samples of n 8 have been taken from a cleaning operation. The average sample range for the 20 samples was 0.016 minute, and the average mean was 3 minutes. Determine the three-sigma control limits for this process. (4 marks) (b) 15 samples of n 10 observations have been taken from a milling process. The average sample range is 0.01 centimetres. Determine upper and lower control limits...