Process Capability and Statistical Process Control

1. Explain what statistical quality control is. 2. Calculate the capability of a process. 3. Understand how processes are monitored with control charts for both attribute and variable data

 How many paint defects are there in the finish of a car?  How long does it take to execute market orders?  How well are we able to maintain the dimensional tolerance on our ball bearing assembly?  How long do customers wait to be served from our drive-through window? LO 1

 Assignable variation: caused by factors that can be clearly identified and possibly managed ◦ Example: a poorly trained employee that creates variation in finished product output  Common variation: variation that is inherent in the production process ◦ Example: a molding process that always leaves “burrs” or flaws on a molded item LO 1

 When variation is reduced, quality is improved  However, it is impossible to have zero variation ◦ Engineers assign acceptable limits for variation ◦ The limits are know as the upper and lower specification limits  Also know as upper and lower tolerance limits LO 1

 Traditional view is that quality within the range is good and that the cost of quality outside this range is constant  Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs LO 1

 Taguchi argues that tolerance is not a yes/no decision, but a continuous function  Other experts argue that the process should be so good the probability of generating a defect should be very low LO 2

 Process limits  Specification limits  How do the limits relate to one another? LO 2

 Capability index (C pk ) shows how well parts being produced fit into design limit specifications  Also useful to calculate probabilities LO 2

 Data ◦ Designed for an average of 60 psi  Lower limit of 55 psi, upper limit of 65 psi ◦ Sample mean of 61 psi, standard deviation of 2 psi  Calculate C pk LO 2

 We are the maker of this cereal. Consumer Reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box.  Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.  Upper Tolerance Limit = (16) = 16.8 ounces  Lower Tolerance Limit = 16 –.05(16) = 15.2 ounces  We go out and buy 1,000 boxes of cereal and find that they weight an average of ounces with a standard deviation of.529 ounces. LO 2

 Specification or Tolerance Limits ◦ Upper Spec = 16.8 oz ◦ Lower Spec = 15.2 oz  Observed Weight ◦ Mean = oz ◦ Std Dev =.529 oz LO 2

 An index that shows how well the units being produced fit within the specification limits.  This is a process that will produce a relatively high number of defects.  Many companies look for a C pk of 1.3 or better… 6-Sigma company wants 2.0! LO 2

 Attribute (Go or no-go information) ◦ Defectives refers to the acceptability of product across a range of characteristics. ◦ Defects refers to the number of defects per unit which may be higher than the number of defectives. ◦ p-chart application  Variable (Continuous) ◦ Usually measured by the mean and the standard deviation. ◦ X-bar and R chart applications LO 3

Statistical Process Control (SPC) Charts UCL LCL Samples over time UCL LCL Samples over time UCL LCL Samples over time Normal Behavior Possible problem, investigate LO 3

x z  Standard deviation units or “z” units. LO 3

We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x- bar or mean value. Based on this we can expect 99.73% of our sample observations to fall within these limits. x LCLUCL 99.73% LO 3

 Created for good/bad attributes  Use simple statistics to create the control limits LO 3

1 – Rule  1 point above UCL or 1 point below LCL  2 consecutive points near the UCL or 2 consecutive points near the LCL  5 consecutive decreasing points or 5 consecutive increasing points  7 consecutive points above the center line or 7 consecutive points below the center line LO 3

 In variable sampling, we measure actual values rather than sampling attributes  Generally want small sample size 1.Quicker 2.Cheaper  Samples of 4-5 are typical  Want 25 or so samples to set up chart LO 3