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III. PROCESS MANAGEMENT II.C.1 BUSINESS MEASURES/PERFORMANCE MEASURES
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Operations Level Metrics
Six sigma provides new metrics for managing complexoperations. Business effectiveness measures track howwell products are meeting customer needs (externalfocus). Breyfogle indicates that they should have alonger-term perspective and reflect the total variationthat the customer sees.
Operational efficiency measures relate to the cost andtime required to produce the products. They providekey linkages between detailed process measures andsummary business results, and help identify importantrelationships and root causes.
V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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Customer Service
The customer driven company is beginning to emerge inAmerica. The public demands and expects betterquality products and service. One sample programfollows:
C Listen to the customer and determine needsC Define a service strategyC Set standards of performanceC Select and train the right employeesC Recognize and reward accomplishment
There is the need to listen to the customer, provide avision, provide training, improve the process, find ordevelop response metrics, and measure the results. About 70% of customers who leave a company do sobecause of service quality.
V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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Customer Retention
Most organizations spend the bulk of their resources onattaining new customers and smaller amounts onretaining customers. High customer satisfactionnumbers do not necessarily mean the company hasgood customer retention and good customer loyalty. Ithas been found that current customers are worth asmuch as five times more than new customers. The costof retaining a current customer is only one-fourth thecost of acquiring a new customer.
Another study showed that companies will boost profitsby about 100% by just retaining 5% more of theircustomers.
V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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Customer Retention (Continued)
Furlong lists some techniques for getting to knowcustomers better:
C Don’t use your own instincts as dataC See the world from the customer’s sideC People high in the organization are out of touchC Get customers to talkC 90% of unhappy customers won’t complainC Do research to retain customersC Determine how satisfied customers areC Conduct research on customer expectationsC Develop a customer profileC Share the results of customer research studiesC Don’t go overboard on the details and measurementC Coordinate and use research effortsC Understand that sometimes research does not help
V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION
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Customer Loyalty
The value of a loyal customer is not measured on thebasis of one gigantic purchase, but rather on his/herlifetime worth. Loyal customers account for a highproportion of sales and profit growth. Customerretention generates repeat sales, and it is cheaper toretain customers. Customer loyalty is something thatmust be demonstrated through an act of execution,trust, or delightful service. Customers become partners.
VI. MEASURE - DATA V.A.2 PROCESS CHARACTERISTICS/ANALYSIS TOOLS
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Circle Diagrams
On occasion, a circle diagram can help conceptualizethe relationship between work elements in order tooptimize work activities. Shown below is a hypotheticalanalysis of the work load for a shipping employee usinga Venn (or circle) diagram.
VII. MEASURE - STATISTICS V.E.2 PROBABILITY/OTHER DISTRIBUTIONS
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Bivariate Normal Distribution
The joint distribution of two variables is called abivariate distribution. Bivariate distributions may bediscrete or continuous.
The graphical representation of a bivariate distributionis a three dimensional plot, with the x and y-axisrepresenting the independent variables and the z-axisrepresenting the frequency for discrete data or theprobability for continuous data.
A special case of the bivariate distribution is thebivariate normal distribution shown below:
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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Identifying Characteristics
The identification of characteristics to be measured in aprocess capability study should meet the followingrequirements:
C The characteristic should be indicative of a keyfactor in the quality of the product or process
C It should be possible to adjust the value of thecharacteristic
C The operating conditions that affect the measuredcharacteristic should be defined and controlled
Selecting one, or possibly two, key dimensions providesa manageable method of evaluating the processcapability. The characteristic selected may also bedetermined by the history of the part and the parameterthat has been the most difficult to control.
Customer purchase order requirements or industrystandards may also determine the characteristics thatare required to be measured.
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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R2
R d
Identifying Specifications/Tolerances
The process specifications or tolerances are determinedeither by customer requirements, industry standards, orthe organization’s engineering department.
Developing Sampling Plans
The appropriate sampling plan for conducting processcapability studies depends upon the purpose andwhether there are customer or standards requirementsfor the study.
If the process is currently running and is in control,control chart data may be used to calculate the processcapability indices. If the process fits a normaldistribution and is in statistical control, then thestandard deviation can be estimated from:
For new processes a pilot run may be used to estimatethe process capability. A design of experiments can beused to determine the optimum values of the processvariables which yield the lowest process variation.
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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Verifying Stability and Normality
If only common causes of variation are present in aprocess, then the output of the process forms adistribution that is stable over time and is predictable. If special causes of variation are present, the processoutput is not stable over time.
The Figure below depicts an unstable process with bothprocess average and variation out-of-control. Theprocess may also be unstable if either the processaverage or variation is out-of-control.
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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Verifying Stability and Normality (Cont’d)
The validity of the normality assumption may be testedusing the chi square hypothesis test. To perform thistest, the data is partitioned into data ranges. Thenumber of data points in each range is then comparedwith the number predicted from a normal distribution.
Continuous data may be tested using a variety ofgoodness-of-fit tests.
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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68.27%
95.45%
99.73%:-3F :-2F :-1F : :+1F :+2F :+3F
The Normal Distribution
When all special causes of variation are eliminated,many variable data processes, when sampled andplotted, produce a bell-shaped distribution. If the baseof the histogram is divided into six (6) equal lengths(three on each side of the average), the amount of datain each interval exhibits the following percentages:
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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LOWER UPPER
X - LSL USL - XZ Z
S S
X - Z =
The Z Value
The area outside of specification for a normal curve canbe determined by a Z value.
The Z transformation formula is:
This transformation will convert the original values tothe number of standard deviations away from the mean. The result allows one to use a single standard normaltable to describe areas under the curve (probability ofoccurrence).
VII. MEASURE - STATISTICS V.F.3 PROCESS CAPABILITY/CAPABILITY STUDIES
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X- μZ =
σ100 - 150 50
Z = = - = -2.520 20
Z Value Example
Tenth grade students weights follow a normaldistribution with a mean μ = 150 lb and a standarddeviation of 20 lb. What is the probability of a studentweighing less than 100 lb?
μ = 150
x = 100
σ = 20
Since the normal table has values about the mean, a Zvalue of - 2.5 can be treated as 2.5.
P(Z = - to -2.5) = 0.0062. That is, 0.62% of the studentswill weigh less than 100 lb.
VII. MEASURE - STATISTICS V.F.1 PROCESS CAPABILITY / CAPABILITY INDICES
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Capability Index Failure Rates
There is a direct link between the calculated Cp (and Pp
values) with the standard normal (Z value) table. A Cp of1.0 is the loss suffered at a Z value of 3.0 (doubled, sincethe table is one sided). Refer to the Table below.
VII. MEASURE - STATISTICS V.F.1 PROCESS CAPABILITY / CAPABILITY INDICES
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Index Failure Rates (Continued)
In the prior Table, ppm equals parts per million ofnonconformance (or failure) when the process:
C Is centered on XC Has a two-tailed specificationC Is normally distributedC Has no significant shifts in average or dispersion
When the Cp, Cpk, Pp, and Ppk values are 1.0 or less, Zvalues and the standard normal table can be used todetermine failure rates. With the drive for increasinglydependable products, there is a need for failure rates inthe Cp range of 1.5 to 2.0.