1 INTRO-1 (1) THE SIX SIGMA BLACK BELT PRIMER by Quality Council of Indiana - All rights reserved Fourth Edition - September, 2014 Quality Council of Indiana 602 West Paris Avenue West Terre Haute, IN TEL: FAX:
2 INTRO-7 (2) CSSBB Primer Contents I. CERTIFICATION OVERVIEW... I-1 CSSBB EXAM... I-3 CSSBB BODY OF KNOWLEDGE... I-6 II. ENTERPRISE-WIDE DEPLOYMENT... II-1 ORGANIZATION-WIDE CONSIDERATIONS... II-2 SIX SIGMA/LEAN FUNDAMENTALS... II-2 IMPROVEMENT METHODOLOGIES... II-34 SYSTEMS AND PROCESSES... II-42 STRATEGIC PLANNING... II-47 LEADERSHIP... II-57 ROLES AND RESPONSIBILITIES... II-57 ORGANIZATIONAL ROADBLOCKS... II-63 III. PROCESS MANAGEMENT... III-1 OVERVIEW... III-2 STAKEHOLDER IMPACT... III-8 CRITICAL REQUIREMENTS... III-11 BENCHMARKING... III-11 BUSINESS MEASURES... III- PERFORMANCE MEASURES... III- FINANCIAL MEASURES... III-20
3 III- (138) III. PROCESS MANAGEMENT II.C.1 BUSINESS MEASURES/PERFORMANCE MEASURES Business Level Metrics Business level metrics are typically financial (external) and operational (internal) summaries for shareholders and management. Business (executive) level metrics comprise summaries of detailed operations and financial results reported monthly, quarterly, or annually.
4 III- (139) III. PROCESS MANAGEMENT II.C.1 BUSINESS MEASURES/PERFORMANCE MEASURES Operations Level Metrics Six sigma provides new metrics for managing complex operations. Business effectiveness measures track how well products are meeting customer needs (external focus). Breyfogle indicates that they should have a longer-term perspective and reflect the total variation that the customer sees. Operational efficiency measures relate to the cost and time required to produce the products. They provide key linkages between detailed process measures and summary business results, and help identify important relationships and root causes.
5 V-7 (320) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION External Customer Segmentation (Cont d) The consumer customer market differs from the business market as follows: C The consumer market has a large number of customers C The majority of consumer purchases are small in actual dollar amounts C The transaction is usually a simple purchase C Most consumers are not very knowledgeable about the product C The supplier does not share proprietary information with the consumer
6 V-7 (321) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION External Customer Segmentation (Cont d) In contrast, the business customer acts in the following manner: C There are a very small number of business customers C The amount purchased per transaction is quite large C The purchase is handled through specialized personnel C The customer may know more about the requirements than the producer C The supplier may allow the customer access to all sorts of information It is also important to look at the market for the next two to five years and estimate how it will change and grow.
7 V-8 (322) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION Customer Service The customer driven company is beginning to emerge in America. The public demands and expects better quality products and service. One sample program follows: C Listen to the customer and determine needs C Define a service strategy C Set standards of performance C Select and train the right employees C Recognize and reward accomplishment There is the need to listen to the customer, provide a vision, provide training, improve the process, find or develop response metrics, and measure the results. About 70% of customers who leave a company do so because of service quality.
8 V-8 (323) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION Customer Retention Most organizations spend the bulk of their resources on attaining new customers and smaller amounts on retaining customers. High customer satisfaction numbers do not necessarily mean the company has good customer retention and good customer loyalty. It has been found that current customers are worth as much as five times more than new customers. The cost of retaining a current customer is only one-fourth the cost of acquiring a new customer. Another study showed that companies will boost profits by about 100% by just retaining 5% more of their customers.
9 V-9 (324) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION Customer Retention (Continued) Furlong lists some techniques for getting to know customers better: C Don t use your own instincts as data C See the world from the customer s side C People high in the organization are out of touch C Get customers to talk C 90% of unhappy customers won t complain C Do research to retain customers C Determine how satisfied customers are C Conduct research on customer expectations C Develop a customer profile C Share the results of customer research studies C Don t go overboard on the details and measurement C Coordinate and use research efforts C Understand that sometimes research does not help
10 V-9 (325) V. DEFINE IV.A.1 VOICE OF THE CUSTOMER/IDENTIFICATION Customer Loyalty The value of a loyal customer is not measured on the basis of one gigantic purchase, but rather on his/her lifetime worth. Loyal customers account for a high proportion of sales and profit growth. Customer retention generates repeat sales, and it is cheaper to retain customers. Customer loyalty is something that must be demonstrated through an act of execution, trust, or delightful service. Customers become partners.
11 VI-33 (473) VI. MEASURE - DATA PROCESS CHARACTERISTICS/ANALYSIS TOOLS V.A.2 Circle Diagrams (Continued) 4. ACT 1. PLAN 3. CHECK 2. DO The PDCA Cycle Precise, but Biased Unbiased, but not Precise Unbiased and Precise Bias and Precision Distinction
12 VI-34 (474) VI. MEASURE - DATA PROCESS CHARACTERISTICS/ANALYSIS TOOLS V.A.2 Circle Diagrams On occasion, a circle diagram can help conceptualize the relationship between work elements in order to optimize work activities. Shown below is a hypothetical analysis of the work load for a shipping employee using a Venn (or circle) diagram. Packing 0.30 Shipping Data Entry 0.20 Pulling Stock Making CDs 0.10
13 VII-43 (623) VII. MEASURE - STATISTICS PROBABILITY/OTHER DISTRIBUTIONS V.E.2 Hypergeometric Distribution (Continued) From a group of 20 products, 10 are selected at random for testing. What is the probability that the 10 selected contain the 5 best units? N = 20, n = 10, d = 5, (N-d) = and r = 5 5 CC 5 5 n n! P r = 20 note that C r = C10 r! n - r! 5!! 5!10! 5!10!! 10!10! P r = = = 0.03 = 1.63% 20! 5!10! 20! 10!10! The mean and the variance of the hypergeometric distribution are: nm nm m N - n = = 1 - N N N N - 1
14 VII-44 (624) VII. MEASURE - STATISTICS PROBABILITY/OTHER DISTRIBUTIONS V.E.2 Choosing A Discrete Distribution Start Modeling a rate with no upper bound for the number of successes? Yes Poisson No Binomial Yes Probability of success same on all trials? Yes Fixed number of trials? No No Hypergeometric Negative Binomial No Probability of success the same on all trials and number of successes = 1? Yes Geometric
15 VII-45 (625) VII. MEASURE - STATISTICS PROBABILITY/OTHER DISTRIBUTIONS V.E.2 Bivariate Normal Distribution The joint distribution of two variables is called a bivariate distribution. Bivariate distributions may be discrete or continuous. The graphical representation of a bivariate distribution is a three dimensional plot, with the x and y-axis representing the independent variables and the z-axis representing the frequency for discrete data or the probability for continuous data. A special case of the bivariate distribution is the bivariate normal distribution shown below:
16 VII-54 (637) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Identifying Characteristics The identification of characteristics to be measured in a process capability study should meet the following requirements: C The characteristic should be indicative of a key factor in the quality of the product or process C It should be possible to adjust the value of the characteristic C The operating conditions that affect the measured characteristic should be defined and controlled Selecting one, or possibly two, key dimensions provides a manageable method of evaluating the process capability. The characteristic selected may also be determined by the history of the part and the parameter that has been the most difficult to control. Customer purchase order requirements or industry standards may also determine the characteristics that are required to be measured.
17 VII-55 (638) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Identifying Specifications/Tolerances The process specifications or tolerances are determined either by customer requirements, industry standards, or the organization s engineering department. Developing Sampling Plans The appropriate sampling plan for conducting process capability studies depends upon the purpose and whether there are customer or standards requirements for the study. If the process is currently running and is in control, control chart data may be used to calculate the process capability indices. If the process fits a normal distribution and is in statistical control, then the standard deviation can be estimated from: R R d 2 For new processes a pilot run may be used to estimate the process capability. A design of experiments can be used to determine the optimum values of the process variables which yield the lowest process variation.
18 VII-56 (639) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Verifying Stability and Normality If only common causes of variation are present in a process, then the output of the process forms a distribution that is stable over time and is predictable. If special causes of variation are present, the process output is not stable over time. The Figure below depicts an unstable process with both process average and variation out-of-control. The process may also be unstable if either the process average or variation is out-of-control.
19 VII-57 (640) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Verifying Stability and Normality (Cont d) The validity of the normality assumption may be tested using the chi square hypothesis test. To perform this test, the data is partitioned into data ranges. The number of data points in each range is then compared with the number predicted from a normal distribution. Continuous data may be tested using a variety of goodness-of-fit tests.
20 VII-58 (641) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 The Normal Distribution When all special causes of variation are eliminated, many variable data processes, when sampled and plotted, produce a bell-shaped distribution. If the base of the histogram is divided into six (6) equal lengths (three on each side of the average), the amount of data in each interval exhibits the following percentages: 68.27% 95.45% :-3F :-2F :-1F : :+1F :+2F :+3F 99.73%
21 VII-58 (642) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 The Z Value The area outside of specification for a normal curve can be determined by a Z value. X - LSL Z LOWER Z S The Z transformation formula is: UPPER USL - X S Z = X - This transformation will convert the original values to the number of standard deviations away from the mean. The result allows one to use a single standard normal table to describe areas under the curve (probability of occurrence).
22 VII-59 (643) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Z Value (Continued) There are several ways to display the normal (standardized) distribution: 1. As a number under the curve, up to the Z value P(Z = - to 1) = As a number beyond the Z value P(Z =1 to + ) = 0.87
23 VII-59 (644) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Z Value (Continued) 3. As a number under the curve, and at a distance from the mean. P(Z = 0 to 1) = The standard normal table in this Primer uses the second method of calculating the probability of occurrence.
24 VII-60 (645) VII. MEASURE - STATISTICS PROCESS CAPABILITY/CAPABILITY STUDIES V.F.3 Z Value Example Tenth grade students weights follow a normal distribution with a mean μ = 0 lb and a standard deviation of 20 lb. What is the probability of a student weighing less than 100 lb? μ = 0 x = 100 σ = 20 X- μ Z = σ Z = = - = Since the normal table has values about the mean, a Z value of can be treated as 2.5. P(Z = - to -2.5) = That is, 0.62% of the students will weigh less than 100 lb.
25 VII-62 (646) VII. MEASURE - STATISTICS PROCESS CAPABILITY / CAPABILITY INDICES V.F.1 Capability Index Failure Rates There is a direct link between the calculated C p (and P p values) with the standard normal (Z value) table. A C p of 1.0 is the loss suffered at a Z value of 3.0 (doubled, since the table is one sided). Refer to the Table below. Cp Z value ppm , , ,
26 VII-62 (647) VII. MEASURE - STATISTICS PROCESS CAPABILITY / CAPABILITY INDICES V.F.1 Index Failure Rates (Continued) In the prior Table, ppm equals parts per million of nonconformance (or failure) when the process: C Is centered on X C Has a two-tailed specification C Is normally distributed C Has no significant shifts in average or dispersion When the C p, C pk, P p, and P pk values are 1.0 or less, Z values and the standard normal table can be used to determine failure rates. With the drive for increasingly dependable products, there is a need for failure rates in the C p range of 1.5 to 2.0.
27 X-12 (937) X. CONTROL VIII.A.4 SPC/CONTROL CHART SELECTION X - R Control Chart Product Name: Tablets Variable: Removal Torques Averages Ranges Date Start 1/12/10 Time Sample Measurement Total Average x Range R special /12 1/13 7:05 7:10 7:35 8:10 8: 9:10 9:12 9:33 11:40 11:43 12:05 13:05 13:45 13:55 14:20 14:55 7:00 7:55 9:00 9:12 9: Chart No. 1 Process Closure Department Specification Limits: LSL = 10 LBS USL = 22 LBS Units of Measure: Operator Bill LBS special special special run UCL =.5 X X =.4 LCL =13.3 X UCL = 7.6 R R = 3.6 LCL = 0 R This start up process smoothed out from data set 10 on. The chart would need new control limits from that point.
28 X-35 (962) X. CONTROL VIII.A.6 SPC/CONTROL CHART ANALYSIS Control Chart Interpretation Five Common Rules (Rule 2) 4 out of 5 points in zone B (Rule 4) 8 or more consecutive points on one side of center line UCL Zone A Zone B Zone C Zone C (Rule 1) A point beyond the control limit (Rule 3) 2 out of 3 points in zone A Zone B Zone A UCL (Rule 5) A trend is 6 or more consecutive points increasing or decreasing Comment: Some authorities say 7 or more consecutive points for both Rules 4 and 5. Other Unusual Patterns UCL Zone A Zone B (Rule 6) Stratification or more points in zone C (Rule 7) Mixture or systematic variation Zone C Zone C Zone B Zone A UCL
29 XII-8 (1055) XII. APPENDIX Table V - t Distribution t α d.f. t.100 t.050 * t.025 ** t.010 t.005 d.f inf inf. * one tail 5% α risk ** two tail 5% α risk
30 XII-12 (1059) XII. APPENDIX Table IX - Control Chart Factors CHART FOR AVERAGES CHART FOR STANDARD DEVIATIONS CHART FOR RANGES Sample Observations Control limit Factors Center Line Factors Control Limit Factors Center Line Factors Control Limit Factors n A 2 A 3 c 4 B 3 B 4 d 2 D 3 D X R Charts CL x A R UCL LCL x R R D R 4 D R 3 2 X S Charts CL x A S UCL LCL x R R B S 4 B S 3 3 Approximate capability R d 2 Approximate capability S c 4
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