Operations and Supply Chain Management The Core

334 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
Mean or average
Standard deviation
Capability index
n
​∑​
​ ​x​ i ​
X ¯ i=1
​ = ​ _____ ​ [10.1]
n
__________
n
​∑​
​ ​(​x​
i=1
​σ = ​√
i ​ − X ¯ ​ ) 2 ​
__________ ​ ​​ [10.2]
n
​C​ pk ​ = min​ ​________
X ​ − LSL
​, USL − ________ X ​
[ 3σ 3σ
​] ​ [10.3]
LO10–5 Analyze process quality using statistics.
∙ Statistical process control involves monitoring the quality of a process as it is operating.
∙ Control charts are used to visually monitor the status of a process over time.
∙ Attributes are characteristics that can be evaluated as either conforming or not conforming to
the design specifications.
∙ P-charts and c-charts are used to monitor attribute characteristics.
∙ X ​ ¯ ​-charts and R-charts are used when the characteristic is a variable measure.
Statistical process control (SPC) Techniques for testing a random sample of output from a
process to determine whether the process is producing items within a prescribed range.
Attributes Quality characteristics that are classified as either conforming or not conforming to
specifications.
Variables Quality characteristics that are measured in actual weight, volume, inches, centimeters,
or other measure units.
Process control charts using attribute measurements
Total number of defective units from all samples
p ¯ ​ = ​ ______________________________________ ​ [10.4]
Number of samples × Sample size
________
p ¯ ​(1 − p ¯ ​)
​s​ p ​ = ​ √
________ ​ ​ [10.5]
n
​UCL = ​ ¯ p ​ + z ​s​ p ​ [10.6]
​LCL = ​ ¯ p ​ − z ​s​ p ​ or 0 if less than 0​ [10.7]
¯ c ​ = Average number of defects per unit​ [10.8]
​s​ c ​ = ​√ __
c ¯ ​ ​ ​
[10.9]
​UCL = ​ c ¯ ​ + z ​√ __
c ¯ ​ ​ ​
[10.10]
​LCL = ​ c ¯ ​ + z ​√ __
c ¯ ​ ​ or ​ 0 if less than 0​ [10.11]
Process control ​ ¯ X ​- and R-charts
UCL X ¯ ​ = ​ X ​ + z ​S X ¯ ​
and LCL X ¯ ​ = ​ X ¯ ​ ​ − z ​S X ¯ ​ [10.12]
m
​
​∑​ ​ X ¯ ​ j
j=1
X ​ = ​ _____ ​ [10.13]
m