Chapter 10 Quality Control

Phases of Quality Assurance Figure 10-1 Acceptance sampling Process control Continuous improvement Inspection before/after production Corrective action during Quality built into the process The least progressive The most Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control The Process (1 of 2) Over time, the output of any process shows a certain amount of natural or inherent variability This is also referred to as random variability It is due to countless minor factors and is assumed to be out of management’s control in the short run, i.e., you have to live with it Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control The Process (2 of 2) The distribution of a process’ output has a mean, , and a standard deviation, ; it can have a wide variety of shapes Process distribution Mean Management 3620 Chapter 10 Quality Control

Process Capability (1 of 3) When selecting a process to perform an operation, the inherent variability of process output should be compared to the range or tolerances allowed by the designer’s specifications Management 3620 Chapter 10 Quality Control

Process Capability (2 of 3) process distribution Lower Specification Upper Specification Much of the process output fits within specification width In other words, is the process capable of producing the item within specifications? Almost all of the process output fits within the specification width A significant portion of the process output falls outside of the specification width Management 3620 Chapter 10 Quality Control

Process Capability (3 of 3) The process capability index (cp) compares the design specifications with a measure of process variability Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Three-Sigma Quality Lower design specification Upper 1350 ppm 1350 ppm +3 Sigma -3 Sigma mean Management 3620 Chapter 10 Quality Control

Three-Sigma Quality vs. Six-Sigma Quality Lower design specification Upper 1350 ppm 1350 ppm +3 Sigma -3 Sigma mean 1.7 ppm 1.7 ppm +6 Sigma -6 Sigma mean Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Normal Distribution Figure 10-5     Mean 95.5% 99.7% Standard deviation Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (1 of 6) Once a process is in operation, a goal is to maintain the status quo, i.e., keep the process “in control” What can make the process no longer be in control, i.e., go “out of control”? The presence of an assignable cause The presence of an assignable cause may cause the process distribution to shift to the left or right, and/or increase the variability (flatten out) Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (2 of 6) If the process mean shifts, more of output falls outside the specifications upper design specification Time lower design Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (3 of 6) If the process mean shifts, more of output falls outside the specifications If process variance increases, more of the output falls outside of the specifications Time upper design specification lower design Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (4 of 6) In either case, the process is considered to be out of control It should be stopped, investigated (the assignable cause found if present) and corrected (the process brought back to the status quo) Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (5 of 6) Examples of assignable causes include operator raw material equipment environment Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Control (6 of 6) How does management detect the presence of an assignable cause? Process output is monitored to detect any changes by inspecting the output of the process Inspection means assessing some characteristic of a unit of output Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Inspection Issues Figure 10-2 How Much/How Often Where/When Centralized vs. On-site Inputs Transformation Outputs Acceptance sampling Process control Management 3620 Chapter 10 Quality Control

Optimal Amount of Inspection Figure 10-3 Cost of passing defectives Total Cost Cost Cost of inspection Inspection Effort Optimal Amount of Inspection Management 3620 Chapter 10 Quality Control

Where to Inspect in the Operations System Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process Management 3620 Chapter 10 Quality Control

Examples of Inspection Points Table 10-1 Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Inspection Options 100% inspection of the process output can be costly and/or time consuming inspection may alter or destroy unit Sample from the process output referred to as statistical process control (SPC) based on the Central Limit Theorem error possible when deciding if the process is in control Management 3620 Chapter 10 Quality Control

Overview of the Statistical Quality Control (QC) Process Sample of size n Process Output Inspect Each Item in the Sample IN CONTROL Sample Information Compare OUT OF CONTROL Decision Criteria Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Central Limit Theorem The distribution of sample means tend to be normally distributed even though the process distribution is not normal The mean of the distribution sample means (x) is equal to the mean of the process distribution( ) The standard deviation of the distribution of sample means ( ) is equal to the standard deviation of the process distribution( ) divided by Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Process Distribution Process distribution Measure lower design specification upper design specification Management 3620 Chapter 10 Quality Control

Sampling Distribution Process distribution Sample Statistic lower design specification upper design specification Management 3620 Chapter 10 Quality Control

Statistical Process Control (1 of 3) Primary purpose is to decide when the process output may be affected by an assignable cause The decision is based on an indicator of the status of the output of a process (sample statistic) the criteria placed on the distribution of the sample statistic (control limits) Management 3620 Chapter 10 Quality Control

Sampling Distribution Figure 10-4 Sampling distribution Process distribution Lower control limit Upper control limit lower design specification upper design specification sample statistic Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Control Chart (1 of 5) This information is typically displayed as a control chart upper control limit Time Sample Statistic Sampling distribution central line lower control limit Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Control Chart (2 of 5) After a sample is taken and inspected, the resulting sample statistic is computed and plotted upper control limit Sample Statistic central line lower control limit Time Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Control Chart (3 of 5) If the sample statistic falls between the control limits, the process is considered to be in control upper control limit Sample Statistic central line lower control limit Time Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Control Chart (4 of 5) If the sample statistic falls outside the control limits, the process is considered to be out of control upper control limit Sample Statistic central line lower control limit Time Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Control Chart (5 of 5) Under this arrangement, there is the possibility of making an error in determining the process’s status upper control limit Time Sample Statistic Probability of deciding the process is out of control when it is still in control Sampling distribution central line lower control limit Management 3620 Chapter 10 Quality Control

Possible Errors When Sampling (A Summary) Management 3620 Chapter 10 Quality Control

Statistical Process Control (3 of 3) Control charts for the two inspection methods will be examined Two control charts for variables inspection sample means chart (x-bar chart) sample range chart (R chart) One control chart for attributes inspection sample proportion defective chart (p chart) Management 3620 Chapter 10 Quality Control

Control Charts for Variables (1 of 3) A sample of size n is taken from the process output Each unit in the sample is inspected a variables basis Measurement of the specified value is taken on a continuous scale Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Variables (2 of 3) These data are used to calculate two sample statistics sample mean, x (the sum of measurement of each unit in the sample divided by n) sample range, R, (the highest measurement in the sample minus the lowest measurement in the sample) Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Variables (3 of 3) In this case two separate control charts are used to monitor two different aspects of the process output central tendency variability The central tendency of the output is monitored using the x-chart The variability of the output is monitored using the R-chart Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control x-Chart The central line is x, the sum of a number of sample means collected while the process was considered to be “in control” divided by the number of samples The 3 lower control limit is x - A2R The 3 upper control limit is x + A2R Factor A2 is based on sample size Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control x-Chart If the process distribution standard deviation, , or variance, is given, the upper and lower control limits can be calculated using Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control R (range)-Chart The 3 lower control limit is D3R The 3 upper control limit is D4R Factors D3 and D4 are based on sample size Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Mean and Range Charts process mean is shifting upward Shift Detected No shift detected Figure 10-10A Process Distribution UCL LCL x-Chart UCL LCL R-chart Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Mean and Range Charts process variability is increasing Figure 10-10B No shift detected Increase detected Process Distribution UCL LCL x-Chart UCL LCL R-chart Management 3620 Chapter 10 Quality Control

Control Chart for Attributes (1of 3) A sample of size n is taken from the process output Each unit in the sample is inspected a attributes basis A unit is classified in one of two categories good or bad pass or fail operates or doesn’t operate does or does not meet design specifications Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Attributes (2 of 3) These data are used to calculate the sample statistic sample percentage defective, p (the number of units found to be defective in that sample divided by n) Although the distribution of sample statistic follows a binomial distribution, that distribution can be approximated by a normal distribution with a mean of and a standard deviation of Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Attributes (3 of 3) The lower control limit is The upper control limit is Management 3620 Chapter 10 Quality Control

Chapter 10 Quality Control Use of c-Charts Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time Management 3620 Chapter 10 Quality Control