MSA pdf Assignment 01
pdf
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Conestoga College *
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8000
Subject
Statistics
Date
Feb 20, 2024
Type
Pages
14
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Assignment 1A ( /60)
Accuracy Studies
Course: Measurement System and Process Evaluations –
QUAL8016
Student Names: Jaykishan Brahmbhatt ( 8929804)
Janam Patel (8911416)
Stavan Shah (8944626)
Varshil Patel (8843716)
Date: 2023-09-28
Assignment 1A Instructions
Stability Study:
•
Obtain the stability data from the instructor (see the excel sheet) and add it to slide 4.
•
Describe the stability procedure used to obtain the stability data in slide 4.
•
Perform the stability study and analyze the results in slide 5
Bias Study:
•
Obtain the bias data from your measurements (group work, see the excel sheet) and add it to slide 6.
•
Describe the procedure used to obtain the bias data in slide 6.
•
Perform the Bias study and analyze the results in slides 7 and 8.
Linearity Study:
•
Obtain the linearity data from measurements (group work, see the excel sheet) and add it to slide 9.
•
Describe the procedure used to obtain the linearity in slide 9.
•
Perform the linearity study and analyze the results in slide 10.
Measurement System and Instrument Resolution:
•
Answer the questions in Slide 11
Complete the executive summary in slide 3.
Complete the conclusions and recommendations in slide 12.
Complete the references in slide 13. Note: class presentations need to be referenced as well.
Executive Summary (3)
1.
Stability Study
2.
Bias Analysis
3.
Linearity Analysis
4.
Measurement System and Instrument Resolution
5.
Conclusions and Recommendations
6.
Reference and Writing
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Stability Study
Stability Procedure (4 pts)
List the procedure used to obtain the stability data:
1.
Select a representative production part with measurements in the middle of the production range as the reference sample for stability analysis. The exact true value is not needed for this analysis.
2.
Measure this part 3 to 5 times daily for at least 20 days, ensuring measurements are taken at different times. These measurements should be carried out by the regular operator responsible for production measurements.
3.
In Minitab, create X-bar and R control charts by navigating to "Stat" > "Control Charts" > "Variable Charts for Subgroup" > "Xbar-
R…" and plot the collected data for analysis.
Number of parts used: 1
Who took the measurements: Instructor
Sample size: 5
Sample frequency: Daily
Stability Data (0.5 pts)
Insert stability data here (Instructor to provide data)
Day
1
2
3
4
5
1
2.5
2.49
2.5
2.51
2.48
2
2.51
2.5
2.51
2.49
2.5
3
2.49
2.48
2.48
2.49
2.47
4
2.49
2.5
2.49
2.5
2.5
5
2.49
2.5
2.48
2.49
2.48
6
2.49
2.48
2.47
2.48
2.49
7
2.45
2.48
2.48
2.49
2.5
8
2.5
2.51
2.5
2.49
2.49
9
2.5
2.48
2.49
2.51
2.48
10
2.5
2.49
2.51
2.49
2.5
11
2.48
2.47
2.48
2.49
2.47
12
2.49
2.5
2.49
2.48
2.49
13
2.51
2.5
2.48
2.49
2.51
14
2.49
2.48
2.47
2.48
2.49
15
2.47
2.48
2.48
2.49
2.5
16
2.5
2.51
2.5
2.49
2.49
17
2.51
2.5
2.48
2.49
2.51
18
2.49
2.48
2.47
2.48
2.49
19
2.48
2.48
2.48
2.49
2.5
20
2.49
2.49
2.5
2.49
2.4
Stability Study (Cont
…)
Perform the Stability Study in Minitab using the data in the previous slide and analyze the results below. Xbar-R Charts (1 pt)
Insert the Xbar and R charts here
Stability results analysis (5 pts)
•
Is this measurement system stable? Explain your answer. (5)
1.
After studying both graphs in sample range graph one point is showing out of control condition so we can say that measurement system is unstable. We cannot continue with measurement system analysis.
Bias Analysis
Bias Procedure (2 pts)
Describe the procedure used to obtain the bias data:
•
Take a single component and determine its true or reference value, for instance obtained from a laboratory Coordinate Measuring Machine (CMM).
•
First, measure this component at least ten times in a row using a single measuring instrument operated by a single appraiser.
•
Calculate the bias for each measurement as follows: Bias = Measurement Xi - True Value
•
Next, employ a one-sample t-test to conduct a hypothesis test for the bias. You can find this option in statistical analysis software ( Here we used Minitab) under "Basic Statistics" and then selecting "1-Sample t-test."
Bias Data (0.5 pts)
•
Insert bias data here
Number
Readings (m
Bias
1
26.74
0.03
2
26.71
0
3
26.75
0.04
4
26.78
0.07
5
26.75
0.04
6
26.72
0.01
7
26.71
0
8
26.71
0
9
26.78
0.07
10
26.79
0.08
11
26.75
0.04
12
26.78
0.07
13
26.74
0.03
14
26.72
0.01
15
26.73
0.02
16
26.69
-0.02
17
26.63
-0.08
18
26.73
0.02
19
26.67
-0.04
20
26.68
-0.03
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Bias Analysis (Cont
…)
Perform the Bias Study in Minitab using the data in the previous slide and analyze the results below
1 sample t-test results (1 pts)
•
Attach histogram of the data here
Bias Results Analysis (2 pts)
•
Are there any anomalies in the data? Explain. (2)
1.
Yes by studying graph we can say that there could be anomalies or outliers as first and last bin values are different from rest of the data set.
Bias Analysis (Cont
…)
Perform the Bias Study in Minitab using the data in the previous slide and analyze the results below
1 sample t-test results (1 pt)
•
Attach p-value results and bias histogram here
Bias Results Analysis (4 pts)
•
Using the numerical results, is the measurement system accurate? Explain. (2)
1.
Yes
2.
As p-value is greater than 0.05 we can say that measurement system is accurate.
•
Using the graphical results, is the measurement system accurate? Explain. (2)
1.
Yes
2.
As Zero (Ho: bias mean = 0) is inside the 95% confidence interval we can say that measurement system is accurate.
Linearity Analysis
Linearity Procedure (2 pts)
Describe the procedure used to obtain the linearity data:
1. Obtain a minimum of 5 parts that encompass the operating range of the measurement gauge.
2. Send these parts to the lab for precise measurements to determine their true values.
3. A single operator, who typically utilizes the gauge, should measure each of the 5 parts at least 10 consecutive times using the same gauge.
4. Utilize Minitab to conduct a Linearity Study, which will calculate the bias for each measurement and the average bias at each reference value. Additionally, it will generate a linear regression plot depicting the average bias against reference values, including the best-fit line and confidence interval bands. You can access this analysis in Minitab under "Stat" > "Quality Tools" > "Gauge Study" > "Gage Linearity and Bias Study."
Linearity Data (1 pt) •
Insert Linearity Data here
Reference 29.77
31.38
57.71
37.86
26.76
1
29.73
31.37
57.6
38.14
26.74
2
29.76
31.37
57.65
37.9
26.71
3
29.72
31.36
57.62
37.85
26.75
4
29.85
31.33
57.65
37.94
26.78
5
29.82
31.34
57.8
37.97
26.75
6
29.83
31.38
57.79
37.8
26.72
7
29.7
31.41
57.68
37.95
26.71
8
29.84
31.4
57.85
37.76
26.71
9
29.79
31.32
57.66
37.82
26.78
10
29.81
31.44
57.75
37.83
26.79
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Linearity Analysis (Cont
…)
Perform the Linearity Study in Minitab using the data in the previous slide and analyze the results below
Linearity results (1 pt)
•
Attach the linearity results here (regression plot with numerical results)
Linearity results Analysis (6 pts)
•
Is Linearity acceptable, based on the numerical results? Explain your answer. (2)
1.
Yes
2.
slope p-value is greater than 0.05 and the intercept p-value greater than 0.05.
•
Is Linearity acceptable, based on the regression plot? Explain your answer. (2)
1.
Yes
2.
Bias=0 line lies entirely inside the 95% confidence bands.
•
Is bias acceptable at all dimensions? Explain your answer. (2)
1.
Bias is acceptable at all dimensions, not changing significantly across the operating range as slope P-value is greater than 0.05.
Measurement System and Instrument Resolution (15 pts)
•
What are the 5 elements of this measurement system? (5)
1.
S
- Standard W
- Work piece I
- Instrument P
- Person and Procedures E
- Environment
•
What is the actual resolution of the instrument used in this study? Explain your answer. (2)
1.
Instrument used in this study is Vernier Calliper. It has resolution of 0.01 mm. The smallest unit it can measured is 0.01 mm
•
What is the required instrument resolution, based on the specifications? Show calculations. (4)
•
The required instrument resolution is the difference between ULS and LSL divided by 10. Instrument resolution = (ULS-LSL)/10=0.1/10=0.01mm.
•
What is the required instrument resolution for a 6 sigma process, based on the process variation? Assume the process mean is in the center of the specification width. Show your calculations (4)
1.
Required resolution = (process variation)/10 = (6*sigma)/10=(6*0.04073)/10=0.02443. So, the required resolution is 0.02mm.
Conclusions and Recommendations (6 pts)
•
Is this measurement system accurate? Use the results from the bias and linearity analysis to answer this question. (2)
1.
Yes measurement system is accurate as Bias is statistically zero and Linearity is acceptable.
•
Provide 2 potential root causes of bias in this measurement system. Use the list of possible causes for bias and linearity to answer this question. (2)
1.
Worn instrument, equipment or fixture
2.
Repeatability
•
Make 2 recommendations to improve the accuracy of this measurement system based on the root causes identified. (2)
1.
Create a routine maintenance and calibration program for all measurement tools and fixtures.
2.
Continuous monitor measurement data which can result in early detection of variations. Also, operator training to minimize measurement variability.
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References and Writing
•
References (1)
•
Rahman, A. (2023, September 11). Measurement System and Process Evaluations
. Econestoga. Retrieved September 28, 2023, from https://conestoga.desire2learn.com/d2l/home/879121
•
•
MONTGOMERY, D. C. (2020). Introduction to statistical quality control (6th ed., pp. 29-34). Wiley. https://reader.texidium.com/dist/#/book/16837
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