Worst Case Tolerance and Statistical Tolerance Analysis and SPC

Embedded pictures are not showing here :( i'll post those graphs upon request if anyone want to see it.(its normal distribution with one side t-test using minitab)

Worst Case Tolerance

And

Statistical Tolerance

Analysis

PREPARED BY

Young Kim

REVISION PAGE:

REVISION        DATE                           DESCRIPTION

      N/C                        05-20-2013                  Initial Release

1.0  Introduction:

The following report demonstrates Worst Case Tolerance Analysis, WCTA, and Statistical Tolerance Analysis, STA .

2.0  PROBLEM

The part is failing due to clearance between circuit card from male part of assembly and a metal contacting device of female part of assembly.

3.0  OBJECTIVE

Using WCTA, STA, and statistical analysis to find suitable tolerance limit to eliminate or reduce probability of making parts outside of extreme tolerance zone.

4.0  REFERENCE DOCUMENTS:

A. Engineering drawing of part
B. Lecture slide

5.0  REFERENCE SOFTWARE:

A.      Microsoft Excel

B.      Microsoft Word

C.      Minitab 16

6.0  ASSEMBLY OVERVIEW:

The circuit card in male part of assembly which transmits the electrical current  is inserted between metal contacting device attached to female part of assembly to  provide power to main source.

7.0  ASSUMPTIONS:

For the calculation of STA, following assumptions were made

a. Parts are independent to each other

b. The tolerances are normally distributed

For the statistical analysis, following assumptions were made

a. The assembly tolerances are normally distributed
b. Standard deviation is Ti/3

8.0  DRAWING:

The following engineering drawing was used to identify necessary dimensions and its tolerances.

9.0  Data and Calculations

Dimension and Tolerance Data
Dimension Number	Dimension(d)	Ti
1A	0.87	0.1
1B	1.75	0.08
2A	1.94	0.12
2B	1.13	0.12
2C	0.4	0.1
Nominal Assembly Dimension Calculation
Bottom Contact Surface	Dimension Used	dn
Male	1B	1.75
Female	2A	1.94
Nominal Assembly  dimension (dnb)=  1.94-1.75 =    0.19
Top Contact Surface	Dimension Used	dn
Male	1A,1B	2.62
Female	2A,2C	2.34
Nominal Assembly  dimension(dnt )=  2.62 - 2.34 = 0.28
WORST CASE TOLERANCE ANALYSIS(WCTA)
Bottom Contact Surface
Dimension Used	Ti	Σ Ti	dnt	Max interference(dnt+Σ Ti)	Max Clearance(dnt-Σ Ti)
1B,2A	0.08, 0.12	0.2	0.19	0.39	-0.01
Top Contact Surface
Dimension Used	Ti	Σ Ti	dnb	Max interference(dnb+Σ Ti)	Max Clearance(dnt-Σ Ti)
1A,1B,2A,2C	0.08, 0.1, 0.12, 0.1	0.4	0.28	0.68	-0.12
Note: negative(-) sign indicates that there are clearance between male and female part when they are assembled
STATISTICAL TOLERANCE ANALYSIS(STA)
Bottom Contact Surface
Dimension Used	Ti	[ΣTi2](1/2)	dnt	Max Interference(dnt+[ΣTi2](1/2))	Min Interference(dnb-[ΣTi2](1/2))
1B, 2A	0.08, 0.12	0.144222051	0.19	0.334222051	0.045777949
Top Contact Surface
Dimension Used	Ti	[ΣTi2](1/2)	dnb	Max Interference(dnt+[ΣTi2](1/2))	Min Interference (dnb-[ΣTi2](1/2))
1A,1B,2A,2C	0.08, 0.1, 0.12, 0.1	0.201990099	0.28	0.481990099	0.078009901

10.0          STATISTICAL ANALYSIS

WCTA	Mean(Nominal)	Std(Ti/3)
Bottom Contact	0.19	0.06666667
	Mean(Nominal)	Std(Ti/3)
Top contact	0.28	0.13333333
STA	Mean(Nominal)	Std(Ti/3)
Bottom Contact	0.19	0.04807402
	Mean(Nominal)	Std(Ti/3)
Top Contact	0.28	0.06733003

11.0          EXPLANATION

We have a combined probability of 0.0027 of making parts with clearance on either top or bottom part of circuit card when using tolerances from WCTA. However, if we apply tolerance from STA, we have 0 probability of making parts with clearance, in other words, male and female parts produced will always have contact.

12.0          RECOMANDATION

The calculated nominal dimension interference for top and bottom part of circuit card is 0.19 and 0.28, respectively. Meaning that if we can reduce our worst case assembly tolerance to less than 0.19 for bottom circuit board assembly and less than 0.28 for top circuit board assembly, we will have 0 rejection rates. However, this is under the assumption that the production process is stable and capable of producing these parts within these specifications. Statistically, we have very low probability of making these parts out of our extreme tolerance zone.  The reason company is having such a high rejection rate, despite the low probability of producing parts out of specification, is because the production process might be either not stable or out of control or both. I would recommend, before we modify any design of this product, to monitor the production process to see if there are any assignable cause variation present. After confirming that the production process is stable and capable, and then I would recommend company to redesign the part with tighter tolerance to reduce the variation within the assembly. Although there could be many other modifications that can fix this problem, tightening the tolerance would cost least to fix the problem. One obvious solution to this problem is to tightening the tolerances.