Chapter 9: Quality and Statistical Process Control

root cause

- A root cause for a defect is a change in an input or an environmental variable that initiated a defect. - In order for a defect to happen, we need to have some variation in outcome. But for a variation in outcome to happen, we need to have some variation either in the input variables or in the environmental variables. So when diagnosing a defect, we need to find the input or environmental variable(s) that caused that defect.

foolproofing

change the work in such a way that the operator attempting to make a mistake cannot complete the task, thereby realizing that he has done something wrong.

quality cost framework

control costs (spend money to prevent failure costs) - appraisal costs - prevention costs Failure costs - internal failure costs (inspector catches) - external failure costs (customer catches)

sources of assignable cause variation

equipment, material, environment, operater

redundancy

including a second identical component as a backup for the first component - do this for the least reliable component - new probability is prob that one of the two parts works

quality

joseph juran: fitness for use - design quality, and conformance quality

tolerance limits

limits set on a the dimensions or quality of a product/service that is ultimately defined by the customer.

Kaizen Event

members of a work cell or team meet to develop improvements in the process

run chart

plot levels of a single characteristic or dimension over time

scatter diagram

plot the relationship between two variables

six sigman program

A process that has 6 standard deviations on either side of the mean and the specification limit.

robust process

A process that is robust can tolerate variation in input variables and environmental variables without leading to a defect. ▪ a robust process is resistant against variation in input and environmental variables.

set of specifications

A set of rules that determine if the outcome variable of a unit is defective or not.

x bar charts

A special control chart in which we track the mean of a sample (also known as X-bar). - Upper control limit (UCL): A line in a control chart that provides the largest value that is still acceptable without being labeled an abnormal variation. - Lower control limit (LCL): A line in a control chart that provides the smallest value that is still acceptable without being labeled an abnormal variation. - X double bar: The average of a set of sample averages. - The control limits measure to what extent the process is behaving the same way it did in the past. - The specification limits measure to what extent the process meets the specifications of the customer.

target variation

the largest amount of variation in a process that does not exceed a given defect probability.

overengineering

we make the process so that it can do well, even under very exceptional conditions.

six sigma business strategy

• Identify core processes that drive an organization's strategic business objectives •Two ways to improve a process: mean improvement and variation reduction •All processes have variation •Common cause •Special cause •Management by fact and data •Use of a structured problem-solving approach

six sigma

Define, Measure, Analyze, Improve, Control - a measure of process capability: when the tolerance limits are each 6 standard deviations from the process mean, there will be just 3.4 defects per million opportunities - data is critical at two stages: at the measure stage, to understand the current process, and the improve stage to see if improvement has been made

outcome variables

Measures describing the quality of the output of the process. (defect rate or yield rate)

defective

Not corresponding to the specifications of the process.

robust

The ability of a process to tolerate changes in input and environmental variables without causing the outcomes to be defective.

parts per million

The expected number of defective parts in a random sample of one million.

upper specification limit (USL)

The largest outcome value that does not trigger a defective unit.

attributes data

The number or proportion of units with some characteristic is tracked (p charts and c charts)

lower specification limit (LSL)

The smallest outcome value that does not trigger a defective unit

defect probability

The statistical probability with which a randomly chosen flow unit does not meet specifications.

input variables

The variables in a process that are under the control of management.

variables data

a precise measurement of some physical dimension is taken (X and R charts)

low capability process

a process that can't meet customer's requirements

control charts

a visual representation of variation in the process. It has time on its x axis and an outcome variable on the y-axis. In each time period, we collect a sample of outcomes, which we plot in the control chart. The control chart also shows a long-run center line (called X-bar-bar), which is the average across all points. It also shows an upper and a lower control limit, which are computed based on past data.

process capability

acceptable variation / actual variation

statistical process control

- Preferable to inspection where possible: - prevention, rather than detection - more timely feedback - inspection is a non-value adding activity, but it costs a firm time and money - Goal: control process parameters and the product will take care of itself - primary tool: process control charts - In control means operating normally (only common cause variation) - out of control means not operating normally (assignable cause variation)

7 tools fro problem solving

- Process flow diagram - Checksheet - Pareto diagram - Histogram - Cause-and-effect diagram - Run chart - Scatter diagram

histogram

- a graphical representation of the variation in a data set - shows the number of observations within specified groups

improving organizational quality

- quality is defined by the customer - adopt a prevention orientation - focus on continuous improvement - get to the root cause - practice quality at the source

pareto diagram

- separate the "vital few" problem sources from the "trivial many" - "causes" sorted from most frequent to least frequent - A graphical way to identify the most important causes of process defects. To create a Pareto diagram, we need to collect data on the number of defect occurrences as well as the associated defect types. We can then plot simple bars with heights indicating the relative occurrences of the defect types. It is also common to plot the cumulative contribution of the defect types. ▪ The Pareto principle was postulated by J.M. Juran. Juran observed that managers spent too much time trying to fix "small" problems, while not paying enough attention to "big" problems. The Pareto principle, also referred to as the 80-20 rule, postulates that 20 percent of the causes account for 80 percent of the problems. In the context of quality, the Pareto principle implies that a few defect types account for the majority of defects.

process capability index

- the ratio between the width of the specification interval of the outcome variable and the variation in the outcome variable (measured by six times its estimated standard deviation). It tells us how many standard deviations we can move away from the statistical mean before causing a defect. - = USL - LSL / 6*std - Measures the allowable tolerance relative to the actual variation of the process. Both numerator and denominator are expressed in the same units, so measure is unitless. - Cp = 1 is a "three signma process"

fishbone diagram

- used to identify and organize the causes of problems - A structured way to brainstorm about the potential root causes that have led to a change in an outcome variable. This is done by mapping out all input and environmental variables. Also known as a cause-effect diagram or Ishikawa diagram. - When drawing a fishbone diagram, we typically start with a horizontal arrow that points at the name of the outcome variable we want to analyze. Diagonal lines than lead to this arrow representing main causes. Smaller arrows then lead to these causality lines creating a fishbone-like shape. Diagonal lines can capture both input variables and environmental variables.

five whys

A brainstorming technique that helps employees to find the root cause of a problem. In order to avoid stopping too early and not having found the real root cause, employees are encouraged to ask, "Why did this happen?" at least five times.

statistical process control (SPC)

A framework in operations management built around the empirical measurement and the statistical analysis of input, environmental, and outcome variables. 1. Measuring the current amount of outcome variation in the process and comparing how this variation relates to the outcome specifications and thus the likelihood of making a defect. This determines the capability of the process. 2. Monitor the process and determine if the presently observed variation conforms to the usual patterns of variation (in which case we are dealing with common cause variation). In the cases in which the presently observed variation does not conform to 3. Investigating the root cause of an assignable cause variation by finding the input or environmental variable(s) that caused the variation. 4. Avoiding the recurrence in the future of similar assignable cause variations and/or changing the process so that it is sufficiently robust to not have its quality be affected by such events in the future.

p chart

A special control chart used for dealing with binary outcomes. It has all the features of the X-bar chart, yet does not require a continuous outcome variable. However, p-charts require larger sample sizes, especially if defects occur rarely. Also known as attribute-based control charts. ▪ Sample sizes for p-charts tend to be larger, typically ranging from 50 to 200 for each period. Larger sample sizes are needed in particular if defects are relatively rare events. If you have a 1 percent defect probability, chances are that you would not find any defects with a sample size as low as 5 or 10. Samples are collected in each period, just as in the case of X-bar control charts. Within each sample, we evaluate the percentage of defective items. Let p denote this percentage (that's why we call them p-charts). We then compute the average percentage of defects over all samples, which we call pbar. This "average across averages" is the center line in our attribute control chart, just as we used X-double-bar as the center line for variable control charts. - Once we have created the center line and the lower and upper control limits, we use the p-chart in exactly the same way we use the X-bar chart. Every time period, we plot the percentage of defective items in the p-chart. If that percentage goes above the upper control limit, we expect some (negative) assignable cause to be at work. If that percentage goes below the lower control limit, we expect some (positive) assignable cause variation to be at work (after all, the percentage of defects in this case has gone down).

abnormal

A variation is abnormal if it is not behaving in line with past data; this allows us to conclude that we are dealing with an assignable cause variation and are not just facing randomness in the form of common cause variation.

deming cycle

Plan, Do, Check, Act

design specifications

Specifications that describe in close detail how the work is to be done; it is often used in construction equipment purchasing contracts or where the specifications are well defined.

environmental variables

Variables in a process that are not under the control of management but nevertheless might impact the outcome of the process.

assignable cause variation

Variation that occurs because of a specific change in input or in environmental variables.

natural variation (common cause)

Variation that occurs in a process as a result of pure randomness (also known as common cause variation).

event tree

Visual representation of binary outcome variables. It supports the defect probability calculations by connecting the defects in the process to an overall outcome measure.