Business Statistics: A Decision-Making Approach 6th Edition Chapter 17 Introduction to Quality and Statistical Process Control Business Statistics: A Decision-Making Approach, 6e © 2005 PrenticeHall, Inc Chap 17-1 Chapter Goals After completing this chapter, you should be able to: Use the seven basic tools of quality Construct and interpret x-bar and R-charts Construct and interpret p-charts Construct and interpret c-charts Business Statistics: A Decision- Chap 17-2 Chapter Overview Quality Management and Tools for Improvement Tools for Quality Improvement Philosophy of Quality Deming’s 14 Points The Basic Tools Juran’s 10 Steps to Quality Improvement Business Statistics: A Decision- Control Charts X-bar/R-charts p-charts c-charts Chap 17-3 Themes of Quality Management Primary focus is on process improvement Most variations in process are due to systems Teamwork is integral to quality management Customer satisfaction is a primary goal Organization transformation is necessary It is important to remove fear Higher quality costs less Business Statistics: A Decision- Chap 17-4 Deming’s 14 Points Create a constancy of purpose toward improvement Adopt the new philosophy Better to improve now than to react to problems later Stop depending on inspection to achieve quality build in quality from the start become more competitive, stay in business, and provide jobs Inspection to find defects at the end of production is too late Stop awarding contracts on the basis of low bids Better to build long-run purchaser/supplier relationships Business Statistics: A Decision- Chap 17-5 Deming’s 14 Points (continued) Improve the system continuously to improve quality and thus constantly reduce costs Institute training on the job Institute leadership Workers and managers must know the difference between common cause and special cause variation Know the difference between leadership and supervision Drive out fear so that everyone may work effectively Break down barriers between departments so that people can work as a team Business Statistics: A Decision- Chap 17-6 Deming’s 14 Points (continued) 10 Eliminate slogans and targets for the workforce They can create adversarial relationships 11 Eliminate quotas and management by objectives 12 Remove barriers to pride of workmanship 13 Institute a vigorous program of education and self-improvement 14 Make the transformation everyone’s job Business Statistics: A Decision- Chap 17-7 Juran’s 10 Steps to Quality Improvement Build awareness of both the need for improvement and the opportunity for improvement Set goals for improvement Organize to meet the goals that have been set Provide training Implement projects aimed at solving problems Business Statistics: A Decision- Chap 17-8 Juran’s 10 Steps to Quality Improvement (continued) Report progress Give recognition Communicate the results Keep score 10 Maintain momentum by building improvement into the company’s regular systems Business Statistics: A Decision- Chap 17-9 The Deming Cycle Plan Act The Deming Cycle Study Business Statistics: A Decision- Do The key is a continuous cycle of improvement Chap 17-10 Creating a p-Chart Calculate subgroup proportions Compute the average of the subgroup proportions Prepare graphs of the subgroup proportions as a line chart Compute the upper and lower control limits Use lines to show the control limits on the p-chart Business Statistics: A Decision- Chap 17-41 p-Chart Example Subgroup number Sample size Number of successes Proportion, p … 150 150 150 15 12 17 … 10.00 8.00 11.33 … Average subgroup proportion = Business Statistics: A Decision- p Chap 17-42 Average of Subgroup Proportions The average of subgroup proportions = p If equal sample sizes: p ∑ p= i k where: pi = sample proportion for subgroup i k = number of subgroups of size n Business Statistics: A Decision- If unequal sample sizes: np ∑ p= ∑n i i i where: ni = number of items in sample i Σni = total number of items sampled in k samples Chap 17-43 Computing Control Limits The upper and lower control limits for an p-chart are UCL = Average Proportion + Standard Deviations LCL = Average Proportion – Standard Deviations or UCL = p + 3σ LCL = p − 3σ Business Statistics: A Decision- Chap 17-44 Standard Deviation of Subgroup Proportions The estimate of the standard deviation for the subgroup proportions is If equal sample sizes: ( p )(1 − p ) sp = n where: If unequal sample sizes: Generally, s p is computed separately for each different sample size p = mean subgroup proportion n = common sample size Business Statistics: A Decision- Chap 17-45 Computing Control Limits (continued) The upper and lower control limits for the p-chart are UCL = p + 3(s p ) LCL = p + 3(s p ) If sample sizes are equal, this becomes ( p )(1 − p ) UCL = p + n ( p )(1 − p ) LCL = p − n Business Statistics: A Decision- Proportions are never negative, so if the calculated lower control limit is negative, set LCL = Chap 17-46 p-Chart Examples For equal sample sizes For unequal sample sizes UCL UCL p p LCL LCL s p is constant since n is the same for all subgroups Business Statistics: A Decision- s p varies for each subgroup since ni varies Chap 17-47 c-Chart Control chart for number of nonconformities (occurrences) per sampling unit (an area of opportunity) Also a type of attribute chart Shows total number of nonconforming items per unit examples: number of flaws per pane of glass number of errors per page of code Assume that the size of each sampling unit remains constant Business Statistics: A Decision- Chap 17-48 Mean and Standard Deviation for a c-Chart The mean for a c-chart is x ∑ c= The standard deviation for a c-chart is i k s= c where: xi = number of successes per sampling unit k = number of sampling units Business Statistics: A Decision- Chap 17-49 c-Chart Control Limits The control limits for a c-chart are UCL = c + c LCL = c − c Business Statistics: A Decision- Chap 17-50 Process Control Determine process control for p-chars and c-charts using the same rules as for x-bar and R-charts Out of control conditions: One or more points outside control limits Nine or more points in a row on one side of the center line Six or more points moving in the same direction 14 or more points alternating above and below the center line Business Statistics: A Decision- Chap 17-51 c-Chart Example A weaving machine makes cloth in a standard width Random samples of 10 meters of cloth are examined for flaws Is the process in control? Sample number Flaws found Business Statistics: A Decision- Chap 17-52 Constructing the c-Chart The mean and standard deviation are: x ∑ c= k i + 1+ + + + 1+ = = 1.7143 s = c = 1.7143 = 1.3093 The control limits are: UCL = c + c = 1.7143 + 3(1.3093) = 5.642 LCL = c − c = 1.7143 + 3(1.3093) = −2.214 Note: LCL < so set LCL = Business Statistics: A DecisionChap 17-53 The completed c-Chart UCL = 5.642 c = 1.714 LCL = 0 Sample number The process is in control Individual points are distributed around the center line without any pattern Any improvement in the process must come from reduction in common-cause variation Business Statistics: A Decision- Chap 17-54 Chapter Summary Reviewed the philosophy of quality management Demings 14 points Juran’s 10 steps Described the seven basic tools of quality Discussed the theory of control charts Common cause variation vs special cause variation Constructed and interpreted x-bar and R-charts Constructed and interpreted p-charts Constructed and interpreted c-charts Business Statistics: A Decision- Chap 17-55 ... building improvement into the company’s regular systems Business Statistics: A Decision- Chap 17-9 The Deming Cycle Plan Act The Deming Cycle Study Business Statistics: A Decision- Do The key is a continuous... Philosophy of Quality Deming’s 14 Points The Basic Tools Juran’s 10 Steps to Quality Improvement Business Statistics: A Decision- Control Charts X-bar/R-charts p-charts c-charts Chap 17-3 Themes... Organization transformation is necessary It is important to remove fear Higher quality costs less Business Statistics: A Decision- Chap 17-4 Deming’s 14 Points Create a constancy of purpose toward