# SAMPLE |
1 |
2 |
3 |
4 |
5 |
AVERAGE |
RANGE |
1 |
4.5 |
4.2 |
4.2 |
4.3 |
4.3 |
4.3 |
0.3 |
2 |
4.6 |
4.5 |
4.4 |
4.7 |
4.3 |
4.5 |
0.4 |
3 |
4.5 |
4.6 |
4.4 |
4.4 |
4.6 |
4.5 |
0.2 |
4 |
4.7 |
4.6 |
4.8 |
4.5 |
4.9 |
4.7 |
0.4 |
AVERAGE |
4.5 |
0.325 |
C. MEAN / X-BAR = 4.5
STANDARD DEVIATION = 0.086
Z = 3
SAMPLE SIZE(N) = 5
UCL = X-BAR + (Z * STDEV / SQRT(N)) = 4.5 + (3 * 0.086 / SQRT(5)) = 4.6154
LCL = X-BAR - (Z * STDEV / SQRT(N)) = 4.5 - (3 * 0.086 / SQRT(5)) = 4.3846
NO, THE PROCESS IS NOT IN CONTROL AS THE MEAN OBSERVATIONS ARE EXCEEDING THE UCL
D. RANGE = LARGEST OBSERVATION - SMALLEST OBSERVATION
XBAR = 4.5
RBAR = 0.325
A2 VALUE CORRESPONDING TO N = 5 = 0.577
D3 & D4 VALUES CORRESPONDING TO N = 5 = 0, 2.115
CONTROL LIMITS FOR XBAR
UCL X = XBAR + (A2 * RBAR) = 4.5 + (0.577 * 0.325) = 4.6875
LCL X = XBAR - (A2 * RBAR) = 4.5 - (0.577 * 0.325) = 4.3125
NO, BECAUSE THERE ARE POINTS EXCEEDING BOTH THE UCL AND LCL
CONTROL LIMITS FOR RBAR
UCL R = RBAR * D4 = 0.325 * 2.115 = 0.6874
LCL R = RBAR * D3 = 0.325 * 0 = 0
YES, SINCE ALL THE POINTS ARE WITHIN THE CONTROL LIMITS
**THE QUESTION DOES NOT MENTION THE SAMPLE SIZE FOR ANY PART. I HAVE ASSUMED A SIZE OF N = 5 GIVEN FOR 4 SAMPLES, IF THERE ARE ANY PROBLEMS YOU FACE, JUST LEAVE A COMMENT ANC I WILL GET BACK TO YOU AS SOON AS POSSIBLE.
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