Chapter 14 Methods for Quality Improvement
Quality, Processes, and Systems Quality of a good or service – the extent to which it satisfies user needs and preferences 8 Dimensions of Quality • Performance • Features • Reliability • Conformance • Durability • Serviceability • Aesthetics • Other perceptions that influence judgment of quality
Quality, Processes, and Systems Process – series of actions or operations that transforms input into outputs over time
Quality, Processes, and Systems System – collection of interacting processes with an ongoing purpose
Quality, Processes, and Systems Two important points about systems 1. No two items produced by a process are the same 2. Variability is an inherent characteristic of the output of all processes
Quality, Processes, and Systems 6 major sources of Process Variation 1. People 2. Machines 3. Materials 4. Methods 5. Measurement 6. Environment
Statistical Control Control Charts – graphical devices used for • monitoring process variation • Identifying when to take action to improve the process • Assisting in diagnosing the causes of process variation run chart, or time series plot
Statistical Control Run Chart enhanced by • Adding centerline • Connecting plot points in temporal order Enhancements aid the eye in picking out any patterns
Statistical Control Output variable of interest can be described by a probability distribution at any point in time. Particular value of output variable at time t can be thought of as being generated by these probability distributions The distribution may change over time, either the mean, the variance or both. Distribution of the process – distribution of the output variable
Statistical Control A process whose output distribution does not change over time is said to be in statistical control , or in control . Processes with changing distributions are out of statistical control , or out of control , or lacking stability .
Statistical Control Patterns of Process Variation Patterns of Process Variation – changing distributions
Statistical Control The output of processes that are in statistical control still have variability associated with them, but there is no pattern to this variability. It is random .
Statistical Control Statistical Process Control – keeping a process in statistical control or bringing a process into statistical control through monitoring and eliminating variation Common Causes of variation – methods, materials, machines, personnel and environment that constitute a process and the inputs required by the process
Statistical Control Special Causes of Variation (Assignable Causes) – events or actions that are not part of the process design. Processes in control still exhibit variation, from the common causes. Processes out of control exhibit variation from both common causes and special causes of variation Most processes are not naturally in a state of statistical control
Statistical Control
The Logic of Control Charts Control charts are used to help differentiate between variation due to common and special causes Mean when process is in control When a value falls outside the control limits, it is either a rare event or the process is out of control
The Logic of Control Charts Hypothesis testing with control charts: H 0 : Process is under control H a : Process is out of control Another view: H 0 : = centerline H a : centerline H a here indicates that the mean has shifted
The Logic of Control Charts Control limits vs. Specification limits Specification limits – set by customers, management, product designers. Determined as “acceptable values” for an output. Control limits are dependent on the process, specification limits are not.
A Control Chart for Monitoring the Mean of a Process: The x-Chart - control chart x c h a r t that plots sample means • Often used in concert with R-chart, which monitors process variation • More sensitive to changes in process mean than a chart of individual measurements
A Control Chart for Monitoring the Mean of a Process: The x-Chart To construct, you need 20 samples of a sample size of at least 2. x x x ... x 1 2 3 k C e n te r lin e x : k L o w er co n tro l lim it : x A R 2 U p p er co n tro l lim it : x A R 2 where A 2 is found in a Table of Control Chart Constants, and R is the mean range of the samples
A Control Chart for Monitoring the Mean of a Process: The x-Chart Two important decisions in Constructing an x-chart 1.Determine sample size n 2.Determine the frequency with which samples are to be drawn Rational Subgroups – subgroups chosen with sample size n and frequency to make it likely that process changes will happen between rather than within samples Rational Subgrouping strategy maximizes the chance for measurements to be similar within each sample, and for samples to differ from each other.
A Control Chart for Monitoring the Mean of a Process: The x-Chart Summary of x-chart Construction Collect at least 20 samples with sample size n ≥ 2, 1. utilizing rational subgrouping strategy 2. Calculate mean and range for each sample 3. Calculate mean of sample means x and mean of sample ranges R 4. Plot centerline and control limits 5. Plot the k sample means in the order that the samples were produced by the process
A Control Chart for Monitoring the Mean of a Process: The x-Chart Constructing Zone Boundaries These zone Using 3-sigma control limits boundaries are used 2 Upper A-B Boundary: x A R in conjunction with 2 3 2 Lower A-B Boundary: x A R Pattern-Analysis rules 2 3 1 Upper B-C Boundary: to help determine x A R 2 3 1 when a process is out Lower B-C Boundary: x A R 2 3 of control R d Using estimate standard deviation of x , n 2 R d Upper A-B Boundary: 2 x 2 n R d Lower A-B Boundary: 2 x 2 n R d Upper B-C Boundary: 2 x n R d Lower B-C Boundary: 2 x n
A Control Chart for Monitoring the Mean of a Process: The x-Chart Any of the 6 rules being broken suggests an out of control process
A Control Chart for Monitoring the Variation of a Process: The R-Chart R-chart used to detect changes in process variation R-chart plots and monitors the variation of sample ranges
A Control Chart for Monitoring the Variation of a Process: The R-Chart To construct, you need 20 samples of a sample size of at least 2. R R R R ... 1 2 3 k C e n te rlin e : R k L o w e r c o n tro l lim it : R D 3 U p p e r c o n tro l lim it : R D 4 where D 3 and D 4 are found in a Table of Control Chart Constants. When n ≤ 6, there is only an upper control limit
A Control Chart for Monitoring the Variation of a Process: The R-Chart Summary of R-Chart Construction Collect at least 20 samples with sample size n ≥ 2, 1. utilizing rational subgrouping strategy 2. Calculate the range for each sample 3. Calculate mean of sample ranges R Plot centerline and control limits. When n ≤ 6, there is 4. only an upper control limit 5. Plot the k sample ranges in the order that the samples were produced by the process
A Control Chart for Monitoring the Variation of a Process: The R-Chart Constructing Zone Boundaries R Upper A-B Boundary: R 2 d 3 d 2 R Lower A-B Boundary: R 2 d 3 d 2 R Upper B-C Boundary: R d 3 d 2 R Lower B-C Boundary: R d 3 d 2 Note: when n ≤ 6, the R -chart has no lower control limit, but boundaries can still be plotted if non-negative These zone boundaries are used in conjunction with Pattern-Analysis rules 1-4 to help determine when a process is out of control
A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart p-chart used to detect changes in process proportion when output variable is categorical As long as process proportion remains constant, process is in statistical control
A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart Sample-Size determination Choose n such that 9 1 p 0 n p 0 where n = Sample Size p 0 = an estimate of the process proportion p
A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart Calculations for p-chart Construction N u m b er o f d efective item s in sa m p le p N u m b er o f item s in sa m p le T o ta l n u m b e r o f d e fe c tiv e ite m s in a ll k sa m p le s C e n te rlin e : p T o ta l n u m b e r o f u n its in a ll k sa m p le s p 1 p U p p e r c o n tro l lim it : p 3 n p 1 p L o w e r c o n tro l lim it : p 3 n
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