DSC 211 Fall 2015 BUSINESS STATISTICS II CASE 1: Green Valley Assembly (GVA) Company - Process Improvement Via Teaming 1. Green Valley. This company assembles consumer electronic products for major manufacturers. The quality of the assembly work is very important -- the major manufacturers will go elsewhere if Green Valley cannot produce high quality work. 2. Process Improvement Efforts Using Teams. The Operations Department of GVA has been encouraging the development of work teams and, within teams, building pride and cooperation towards team goals of high productivity at high levels of quality. Top managers believe that these approaches will lead not only to better worker satisfaction but also to higher levels of productivity and quality. For one area where GVA has been experimenting with these work team approaches, they have now just completed a six-month trial. There are several thousand employees involved. The purpose of this trial is to determine if team approaches lead to improved productivity, quality and satisfaction. The previous (before trial) key measures of productivity are as follows: Productivity Distribution for all workers: Completed Units/Hr: Proportion of workforce: Average Productivity for all workers: 10 -11 14% >11-12 34% >12-13 36% >13 16% 12 completed units/hr Productivity Consistency for all workers: standard deviation of completed units/hr: 1.55 completed units/hr The previous (before trial) level of quality (one key measure) for this work area is as follows: Quality Measure 4: 12 percent rework (percent of assemblies produced that were found to have some defect that required rework) The previous (before trial) measure of worker satisfaction is as follows: Worker satisfaction is measured from the responses of workers to one question on a questionnaire given to workers once a year. The question is "What is your level of satisfaction with your overall job?" The responses are from a 7 point scale where 1 = very satisfied and 7 = very dissatisfied. The average satisfaction response score for all workers last year = 3.5 3. Process Improvement Evaluation Study Now, at the end of the six-month trial, another study of productivity, quality, and satisfaction is being undertaken. The regular year-end data collection can be used. One data set is based on a random sample of 50 workers involved in this experiment and precise measurement of each worker's productivity. A second data set gathered each year is a random sample of one key assembly (goes into most of our products) which is inspected for minor or major defects. Also, the same 50 workers from this experiment completed a worker questionnaire. Their responses to the "Satisfaction with My Overall Job" question are in the third data set. The data results may be found on the second worksheet. These data sets (from 50 workers and 123 assemblies) were collected to help answer the following questions about the new team-based production processes: (1) Has the productivity distribution of all workers changed, and if so how? (2) Has the average productivity of all workers changed? If so, how? (3) Has the consistency of productivity of workers improved? (4) Has the quality of all finished assemblies improved? (5) Has the average satisfaction level of all workers improved? (6) Does there appear to be a relationship between worker productivity and satisfaction? 4. Assignment Your team works at Green Valley in Operations. You have been asked to analyze the collected sample data to help answer the business questions above and write a business memo with your results. Use the following GVA format for your business memo. This memo is written for James Dunne, the VP of Operations, so clearly answer the business questions asked and keep most of the technical detail in the attachments. FORMAT FOR BUSINESS MEMO Use the Date, To, From, Subject memo format (Word has templates for memos you could use) Have the following sections of your memo: 1. Introduction. Explain the purpose of the study & provide the specific business questions you worked to answer. 2. Data. In this section, describe the sample data sources and data gathered. Refer to the attachments that contain the complete data. Include descriptive statistics of the sample data in one or more tables and briefly discuss. 3. Analysis Methodology. Briefly describe, in everyday business language, the methods used to analyze the data -- to answer each question. Refer to the attachments for detail. 4. Analysis Results: Provide one or more tables that show the first 5 questions, the previous values, a description of the sample, the the sample quantitative results, the p-value, and the business answer. (Note. See table template on another tab of this file.) For question 6, provide a graph and your best business answer. Provide a brief discussion of analysis results. 5. Study Conclusions & Recommendations Brief summary of the study & the most important conclusions about the team-based production processes have been developed in the study. Recommendations for management actions may be included. Attachments Attachment 1 - 6. One page for each analysis (for the five questions) showing all work & explanations. Identify any assumptions/conditions necessary to use the method & how you checked out the assumptions Attachement 7. Provide all the raw data values. Provide explanations as needed. Define all units Assemblies Inspected 2 (0=no defect, 1=minor defect, 2=major defect) 2 NOTE: all defects require rework. 2 1 Productivity Sample (units/hr) 1 12.4 1 14.0 1 10.5 1 14.4 1 14.3 1 10.8 1 12.6 0 12.0 0 12.3 0 11.1 0 14.3 0 13.6 0 13.6 0 13.5 0 13.3 0 11.8 0 10.8 0 12.6 0 13.3 0 11.6 0 10.0 0 11.5 0 10.6 0 14.8 0 11.3 0 14.4 0 12.8 0 15.3 0 11.4 0 12.6 0 11.5 0 14.6 0 12.3 0 12.4 0 12.5 0 11.1 0 13.1 0 15.3 0 13.3 0 11.0 0 10.9 0 12.9 0 13.0 0 11.8 0 13.6 0 11.4 0 12.6 0 13.2 0 13.2 0 12.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sat Score* 2 1 3 5 5 7 1 2 5 1 2 1 1 1 2 1 2 2 3 2 2 2 6 3 2 2 7 4 7 2 7 1 4 4 7 3 2 4 2 4 1 1 1 2 3 3 2 7 1 2 *7 point scale where 1=very satisfied 2-satisfied 3-somewhat satisfied 4-undecided 5-somewht dissatified 6-dissatisfied 7-very dissatisfied) TABLE XX. RESULTS: Green Valley Process Improvement Program, Evaluation Study . . . . date Business Question (1) Has the productivity distribution of all workers changed, and if so how? (2) Has the average productivity of all workers changed? If so, how? (3) Has the consistency of productivity of workers improved? (4) Has the quality of all finished assemblies improved? (5) Has the average satisfaction level of all workers improved? (6) Does there appear to be a relationship between worker productivity and satisfaction? Previous Value (s) Sample Sample Results p-value* Business Answer NAME: Daniel Schuld, Li ChongChong Business Questions Sample Data Analysis Method (1) Has the productivity distribution of all workers changed, and if so how? ChiSq Goodness fit fot Test (2) Has the average productivity of all workers changed? If so, how? t-Test for Mean (3) Has the consistency of productivity of workers improved? ChiSq Test for Varience (1 sided) (4) Has the quality of all finished assemblies improved? Normal Test for Proportion (5) Has the average satisfaction level of all workers improved? t-Test for Mean (6) Does there appear to be a relationship between worker productivity and satisfaction? Scatter Graph DSC 211 Fall 2015 BUSINESS STATISTICS II CASE 1: Green Valley Assembly (GVA) Company - Process Improvement Via Teaming 1. Green Valley. This company assembles consumer electronic products for major manufacturers. The quality of the assembly work is very important -- the major manufacturers will go elsewhere if Green Valley cannot produce high quality work. 2. Process Improvement Efforts Using Teams. The Operations Department of GVA has been encouraging the development of work teams and, within teams, building pride and cooperation towards team goals of high productivity at high levels of quality. Top managers believe that these approaches will lead not only to better worker satisfaction but also to higher levels of productivity and quality. For one area where GVA has been experimenting with these work team approaches, they have now just completed a six-month trial. There are several thousand employees involved. The purpose of this trial is to determine if team approaches lead to improved productivity, quality and satisfaction. The previous (before trial) key measures of productivity are as follows: Productivity Distribution for all workers: Completed Units/Hr: Proportion of workforce: Average Productivity for all workers: 10 -11 14% >11-12 34% >12-13 36% >13 16% 12 completed units/hr Productivity Consistency for all workers: standard deviation of completed units/hr: 1.55 completed units/hr The previous (before trial) level of quality (one key measure) for this work area is as follows: Quality Measure 4: 12 percent rework (percent of assemblies produced that were found to have some defect that required rework) The previous (before trial) measure of worker satisfaction is as follows: Worker satisfaction is measured from the responses of workers to one question on a questionnaire given to workers once a year. The question is "What is your level of satisfaction with your overall job?" The responses are from a 7 point scale where 1 = very satisfied and 7 = very dissatisfied. The average satisfaction response score for all workers last year = 3.5 3. Process Improvement Evaluation Study Now, at the end of the six-month trial, another study of productivity, quality, and satisfaction is being undertaken. The regular year-end data collection can be used. One data set is based on a random sample of 50 workers involved in this experiment and precise measurement of each worker's productivity. A second data set gathered each year is a random sample of one key assembly (goes into most of our products) which is inspected for minor or major defects. Also, the same 50 workers from this experiment completed a worker questionnaire. Their responses to the "Satisfaction with My Overall Job" question are in the third data set. The data results may be found on the second worksheet. These data sets (from 50 workers and 123 assemblies) were collected to help answer the following questions about the new team-based production processes: (1) Has the productivity distribution of all workers changed, and if so how? (2) Has the average productivity of all workers changed? If so, how? (3) Has the consistency of productivity of workers improved? (4) Has the quality of all finished assemblies improved? (5) Has the average satisfaction level of all workers improved? (6) Does there appear to be a relationship between worker productivity and satisfaction? 4. Assignment Your team works at Green Valley in Operations. You have been asked to analyze the collected sample data to help answer the business questions above and write a business memo with your results. Use the following GVA format for your business memo. This memo is written for James Dunne, the VP of Operations, so clearly answer the business questions asked and keep most of the technical detail in the attachments. FORMAT FOR BUSINESS MEMO Use the Date, To, From, Subject memo format (Word has templates for memos you could use) Have the following sections of your memo: 1. Introduction. Explain the purpose of the study & provide the specific business questions you worked to answer. 2. Data. In this section, describe the sample data sources and data gathered. Refer to the attachments that contain the complete data. Include descriptive statistics of the sample data in one or more tables and briefly discuss. 3. Analysis Methodology. Briefly describe, in everyday business language, the methods used to analyze the data -- to answer each question. Refer to the attachments for detail. 4. Analysis Results: Provide one or more tables that show the first 5 questions, the previous values, a description of the sample, the the sample quantitative results, the p-value, and the business answer. (Note. See table template on another tab of this file.) For question 6, provide a graph and your best business answer. Provide a brief discussion of analysis results. 5. Study Conclusions & Recommendations Brief summary of the study & the most important conclusions about the team-based production processes have been developed in the study. Recommendations for management actions may be included. Attachments Attachment 1 - 6. One page for each analysis (for the five questions) showing all work & explanations. Identify any assumptions/conditions necessary to use the method & how you checked out the assumptions Attachement 7. Provide all the raw data values. Provide explanations as needed. Define all units Assemblies Inspected 2 (0=no defect, 1=minor defect, 2=major defect) 2 NOTE: all defects require rework. 2 1 Productivity Sample (units/hr) 1 12.43 1 13.96 1 10.54 1 14.40 1 14.27 1 10.80 1 12.58 0 11.99 0 12.29 0 11.13 0 14.31 0 13.57 0 13.57 0 13.49 0 13.25 0 11.76 0 10.79 0 12.57 0 13.34 0 11.65 0 10.02 0 11.47 0 10.64 0 14.79 0 11.34 0 14.35 0 12.82 0 15.25 0 11.43 0 12.62 0 11.46 0 14.58 0 12.25 0 12.37 0 12.52 0 11.12 0 13.11 0 15.29 0 13.28 0 10.96 0 10.95 0 12.94 0 13.02 0 11.83 0 13.56 0 11.38 0 12.65 0 13.21 0 13.22 0 12.28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sat Score* 2 1 3 5 5 7 1 2 5 1 2 1 1 1 2 1 2 2 3 2 2 2 6 3 2 2 7 4 7 2 7 1 4 4 7 3 2 4 2 4 1 1 1 2 3 3 2 7 1 2 Productivity Sample Sat Score *7 point scale where Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1=very satisfied 2-satisfied 3-somewhat satisfied 4-undecided 5-somewht dissatified 6-dissatisfied 7-very dissatisfied) 12.59 0.19 12.58 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 1.31 1.72 -0.70 0.16 5.27 10.02 15.29 629.41 50 10 -11 >11-12 >12-13 >13 Proportion of workforce:(f's) 7.0 0.14 11.0 0.22 12.0 0.24 20 0.40 Proportion of workforce: (e's) 0.14 0.34 0.36 0.16 7 17 (1) Completed Units/Hr: Results(f's) Results(e's) (f-e)^2/e (2) (3) 0.0000 Productivity Sample n 50 mean 12.6 stdev 1.31 18 8 2.12 2.00 ChiSq = 22.12 p-value = 0.000062 t= 3.17 P-value 0.002605 ChiSq = 54.32 p valure= 0.28 (4) Assemblies Inspected n 123.0 % rework 8.94% (5) 1 2 3 4 5 6 7 a ver stderr = 0.026 P-value = 0.1174 Sat Score frequency table 12 17 6 5 3 1 6 2.94 24% 34% 12% 10% 6% 2% 12% t= -2.028 p-value= 0.0240 (6) -0.101697 7 6 5 4 3 2 1 0 10.00 2.94 0.28 2.00 2.00 1.95 3.81 -0.08 1.03 6 1 7 147 50 11.00 12.00 13.00 14.00 15.00 16.00 50.0 100% 1.00 18.00 22.12 TABLE XX. RESULTS: Green Valley Process Improvement Program, Business Question Previous Value (s) (1) Has the productivity distribution Completed Units/Hr: of all workers changed, and if so Proportion of how? workforce: 10 -11 14% Sample >11-12 >12-13 34% Evaluation Study . . . . date 36% >13 Sample Results Completed 50 Productivity Units/Hr: Measures Proportion of workforce: 16% 10 -11 >11-12 p-value* >12-13 >13 0.000062 14% 22% 24% 40% (2) Has the average productivity of Average Productivity for all workers: 12 completed units/hr all workers changed? If so, how? 50 Productivity Average Productivity for all workers: 12.6 completed units/hr Measures (3) Has the consistency of Productivity Consistency for all workers: standard productivity of workers improved? deviation of completed units/hr: 1.55 completed units/hr 50 Productivity Productivity Consistency for all workers: standard deviation of completed Measures units/hr: 1.31 completed units/hr 0.0026 0.28 (4) Has the quality of all finished assemblies improved? The previous (before trial) level of quality (one key measure) for this work area is as follows: 12% rework 123 Assemblies The previous (before trial) level of quality (one key measure) for this work Inspected area is as follows: 8.94% rework 0.12 (5) Has the average satisfaction level of all workers improved? The average satisfaction response score for all workers last year is 3.5 50 Satisfaction The average satisfaction response score for all workers last year is 2.94 Scores 0.024 (6) Does there appear to be a relationship between worker productivity and satisfaction? 50 Satisfaction Scores and Productivity Sample * p-value is likelihood of this type result if answer were no. 0.10 Business Answer NAME: CHONGCHONG LI Business Questions Sample Data Analysis Method (1) Has the productivity distribution of all workers changed, and if so how? 50 Productivity Measures, 14%, 22%, 24%, 40% ChiSq of Goodness fit for Test (2) Has the average productivity of all workers changed? If so, how? 50 Productivity Measures n=50, mean=12.6 stedv=1.31 t- Test for Mean (3) Has the consistency of productivity of workers improved? ChiSq Test for Varience (4) Has the quality of all finished assemblies improved? 123 Assemblies Inspected, p-bar=0.894 Normal Test for Proportion (5) Has the average satisfaction level of all workers improved? 50 Satisfaction Scores, t-Test for Mean (6) Does there appear to be a relationship between worker productivity and satisfac? 50 Satisfaction Scores, 50 Productivity Measures Scatter Graph Issue: Green Valley Assembly (GVA) Company - Process Improvement Via Teaming BusQues Has the productivity distribution of all workers changed, and if so how? Data: Productivity Sample (units/hr) Completed Units/Hr 10-11 Proportion of workforce: 14% >11-12 >12-13 34% 36% >13 Check 16% 100% Sample in 2013 of 220 such purchases found the following: # in samp 7 11 12 20 50 % of samp 14% 22% 24% 40% 100% AnalysisChiSq Goodness of Fit Test Hyp 1 Ho: The productivity distribution of all workers has not changed 2 Test Stat: 3 4 5 Sig Level: Reject R: Calcs: Ha: The productivity distribution of all workers has changed ChiSq = Sum of (e-f)^2/e across the 4 categories. If Ho true, this is ChiSq distributed with df = 4-1=3. alpha = 0.05 Reject Ho if ChiSq > 9.35 or < 10-11 7 7 0.000 Expected (If Ho true) Observed (e-f)^2/e >11-12 >12-13 17 18 11 12 2.118 2.000 >13 8 20 18.000 0.22 Check 50 50 22.118 ChiSq = p-value = 0.00006166 6 Concl: Results Table: Reject Ho. Has the productivity distribution changed? >13 Hours 10-11 >11-12 >12-13 Previou 14% 34% 36% 16% Sample 14% 22% 24% 40% Samp Si -value* Statistical Test p Stat Sign? 50 * 0.000062 ChiSq Goodness of Fit Likelihood of this type of sample result if answer were no. Busine units/hr provides overwhelming evidence ss that the productivity distribution of Answer workers has changed : YES Issue: Green Valley Assembly (GVA) Company - Process Improvement Via Teaming BusQues: Has the average productivity of all workers changed? Data: 50 Productivity measures Analysis: t-Test for Mean 1. Hypotheses: Ho: mu = 12 2. Test Stat: 3. Sign Level: 4. Reject Rule: 5. Calculations: samp size (n): samp mean (x-bar): samp stdev (s): 50 12.59 1.31 Ha: mu <> 12 (1) Will calcuate t = (x-bar - 12) / (s/n^.5) (2) If Ho true (m=12): this test statistic is t distributed with df = n-1 = 49 alpha = 0.05 Reject Ho if t > 2.312 or < 0.03150 (1)Value of Test Statistic: x-bar = 12.59 s= 1.31 t= 3.17 (2) p-value p-value = 0.002605 6. Conclusion: Reject Ho. Table of Results: Has the average productivity of all workers changed? samp size samp mean dif 50 12.59 49 Stat Test p-value* stat signif? t-Test for Mean 0.0026 YES *likelihood of this type sample if answer is no. Bus Answer: This sample of 50 productivity numbers in units/hr provides very strong evidence to conclude that the productivity average of workers ha as changed Bus Issue: BusQues: Data: Analysis: Has the consistency of productivity of workers improved? Sample size of 50 Productivity Measures sample s= 1.31 sample var = 1.72 Hypothesis Testing --CHI square test for variance 1. Hypothesis: Ho: var > 1.55 Ha: var =< 1.55 2.Test Stat: (1) ChiSq = (n-1)*s2/var (2) If Ho true(var >1.55), is ChiSq df =n-1=49 3. Sig level: alpha = 0.05 4. Reject Rule: Reject Ho if ChiSq= < 33.93 5. Calculation: (1)Value of Test Statistic: s = 1.31 s2 = 1.72 ChiSq= 54.32 (2) p-value P-value = 0.7212 Results Table: 6. Conclusion: Do not Reject Ho Has the consistency of productivity of workers improved? Sample size Sample varience Diff StatTest P-value* Signif? ChiSq Test for 50 1.72 0.17 0.72 NO Variance *likelihood of this type sample if answer is no. Bus Answer: Based on the sample size of 50 productivity Measures, we are unable to conlude that the consistency of productivity of workers impro ers improved. The results are inconclusive. BUS Issue: BUS QUES: Has the quality of all finished assemblies improved? Data: The sample of 123 Assemblies Inspected shows p-bar= 8.94% Analysis: Normal Test for Proportion 1. Hypotheses: Ho: p > 12% Ha: p =< 12% 2. Test Stat: (1) p-bar, the sample proportion. (2) If Ho is TURE, all p-bars are NORMAL with mean = 0.894 mean = p = 0.0894 stderr = 0.026 n = 123 3. Sing Level: alpha = 0.05 4. Reject Rule: Reject Ho if P-bar<= 0.13 5: Calculations: # of defect: 11 p-bar = 0.0894 p-value = 0.1174 6: Conclusions: Do not Reject Ho. Results Table: Has the quality of all finished assemblies improved? Samp Prop Samp Size Diff p-value* StatTest 8.94% 123 -3% 0.1174 ChiSq Test for Variance Stat Sig? NO *likelihood of this type of result if answer is NO. Answer: Based on the sample of 123 Assemblies inspectd, we are unable to conclude that he quality of all finished assemblies improved. The results are inconclusive. Issue: Green Valley Assembly (GVA) Company - Process Improvement Via Teaming BusQues: Has the average satisfaction level of all workers improved? Data: 50 Productivity measures Analysis: t-Test for Mean 1. Hypotheses: Ho: mu > 3.5 2. Test Stat: 3. Sign Level: 4. Reject Rule: 5. Calculations: samp size (n): samp mean (x-bar): samp stdev (s): Ha: mu =< 3.5 (1) Will calcuate t = (x-bar - 3.5) / (s/n^.5) (2) If Ho true (m=3.5): this test statistic is t distributed with df = n-1 = 49 alpha = 0.05 Reject Ho if t =< 2.010 (1)Value of Test Statistic: x-bar = 2.94 s= 1.95 t= -2.03 p-value = 0.024 (2) p-value 6. Conclusion: Table of Results: Reject Ho. Has the average satisfaction level of all workers improved? samp size samp mean 50 2.94 dif Stat Test p-value* stat signif? 49 t-Test for Mean 0.0240 YES *likelihood of this type sample if answer is no. Bus Answer: This sample of 50 Sat Score provides strong evidence to conclude that the the average satisfaction level of all workers improved. 50 2.94 1.95 Sat Score* 2 1 3 5 5 7 1 2 5 1 2 1 1 1 2 1 2 2 3 2 2 2 6 3 2 2 7 4 7 2 7 1 4 4 7 3 2 4 2 4 1 1 1 2 3 3 2 7 1 2 correlation -0.101697 16.0 Productvity Productivity Sample (units/hr) 12.4 14.0 10.5 14.4 14.3 10.8 12.6 12.0 12.3 11.1 14.3 13.6 13.6 13.5 13.3 11.8 10.8 12.6 13.3 11.6 10.0 11.5 10.6 14.8 11.3 14.4 12.8 15.3 11.4 12.6 11.5 14.6 12.3 12.4 12.5 11.1 13.1 15.3 13.3 11.0 10.9 12.9 13.0 11.8 13.6 11.4 12.6 13.2 13.2 12.3 15.0 14.0 13.0 12.0 11.0 10.0 9.0 0 1 2 3 Sat Score 4 5 6 7 8