Quality management tools

Seven Basic Tools of Quality

The Seven Basic Tools of Quality is a designation given to a fixed set of graphical techniques identified as being most helpful in troubleshooting issues related to quality.

They are called basic because they are suitable for people with little formal training in statistics and because they can be used to solve the vast majority of quality-related issues .

The seven tools are

Cause and effect diagram (also known as the "fishbone" or Ishikawa diagram)

Check sheet

Control chart

Histogram

Pareto chart

Scattered diagram

Stratification (alternately, flow chart or run chart)

The Seven Basic Tools stand in contrast to more advanced statistical methods such as

survey sampling, acceptance sampling, statistical hypothesis testing, design of experiments

, multivariate analysis, and various methods developed in the field of operations research.

Ishikawa diagrams

(also called fishbone diagrams, herringbone diagrams, cause-and-effect diagrams, or Fishikawa) are causal diagrams created by Kaoru Ishikawa (1968) that show the causes of a specific event. Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factors causing an overall effect. Each cause or reason for imperfection is a source of variation . Causes are usually grouped into major categories to identify these sources of variation.

The categories typically include:

People: Anyone involved with the process

Methods: How the process is performed and the specific requirements for doing it, such as policies, procedures, rules, regulations and laws

Machines: Any equipment, computers, tools, etc. required to accomplish the job

Materials: Raw materials, parts, pens, paper, etc. used to produce the final product

Measurements: Data generated from the process that are used to evaluate its quality

Environment: The conditions, such as location, time, temperature, and culture in which the process operates.

Cause and effect diagram for defect XXX

Check sheet

The check sheet is a form (document) used to collect data in real time at the location where the data is generated. The data it captures can be quantitative or qualitative. When the information is quantitative, the check sheet is sometimes called a tally sheet.

The check sheet is one of the so-called Seven Basic Tools of Quality Control.

Format

The defining characteristic of a check sheet is that data are recorded by making marks ("checks") on it. A typical check sheet is divided into regions, and marks made in different regions have different significance. Data are read by observing the location and number of marks on the sheet.

Check sheets typically employ a heading that answers the Five Ws:

Who filled out the check sheet

What was collected (what each check represents, an identifying batch or lot number)

Where the collection took place (facility, room, apparatus)

When the collection took place (hour, shift, day of the week)

Why the data were collected

Function

To check the shape of the probability distribution of a process

To quantify defects by type

To quantify defects by location

To quantify defects by cause (machine, worker)

To keep track of the completion of steps in a multistep procedure (in other words, as a checklist)

Frequency distribution for film coater

Quality Control Checksheet Example

Control chart

Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, in statistical process control are tools used to determine if a manufacturing or business process is in a state of statistical

control

Xbar chart for a paired xbar and R chart

Chart details

A control chart consists of:

Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic in samples taken from the process at different times [the data]

The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges, mean of the proportions)

A centre line is drawn at the value of the mean of the statistic

The standard error (e.g., standard deviation/sqrt(n) for the mean) of the statistic is also calculated using all the samples

Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely' and are drawn typically at 3 standard errors from the centre line

The chart may have other optional features, including:

Upper and lower warning or control limits, drawn as separate lines, typically two

standard errors above and below

the centre line

Division into zones, with the

addition of rules governing frequencies of observations in

each zone

Annotation with events of

interest, as determined by

the Quality Engineer in

charge of the process's quality

Types of charts

Chart Process observation Process observations relationships

Process observations

type

Size of shift to detect

Xbar and R chart

Quality characteristic measurement within one subgroup

Independent Variables Large (≥ 1.5σ)

Xbar and S chart

Quality characteristic measurement within one subgroup

Independent Variables Large (≥ 1.5σ)

Shewhart individual control chart (ImR chart or XmR chart)

Quality characteristic measurement for one observation

Independent Variables† Large (≥ 1.5σ)

Three-way chart

Quality characteristic measurement within one subgroup

Independent Variables Large (≥ 1.5σ)

p-chart Fraction nonconforming within one subgroup

Independent Attributes† Large (≥ 1.5σ)

np-chart Number nonconforming within one subgroup

IndependentAttributes† Large (≥

1.5σ)

c-chart Number of nonconformances within one subgroup

Independent Attributes† Large (≥ 1.5σ)

u-chart Nonconformances per unit within one subgroup

Independent Attributes† Large (≥ 1.5σ)

Chart Process observation Process observations relationships

Process observations

type

Size of shift to detect

EWMA chartExponentially weighted moving average of quality characteristic measurement within one subgroup Independent

Attributes or variables

Small (< 1.5σ)

CUSUM chart Cumulative sum of quality characteristic measurement within one subgroup

Independent Attributes or variables

Small (< 1.5σ)

Time series mode

Quality characteristic measurement within one subgroup

Autocorrelated Attributes or variables

N/A

Regression control chart

Quality characteristic measurement within one subgroup

Dependent of process control variables

Variables Large (≥ 1.5σ)

Histogram

In statistics, a histogram is a graphical representation of the

distribution of data. It is an estimate of the probability distribution of a continuous

variable and was first introduced by Karl Pearson

Uses

Histograms are used to plot the density of data, and

often for density estimation: estimating the probability density function of the underlying variable.

Histogram of arrivals per minute

Pareto chart

A Pareto chart is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and

the cumulative total is represented by the line.

Scattered Diagram

A scatter plot, scatterplot, or scattergraph is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data.

The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis . This kind of plot is also called a scatter chart, scattergram, scatter diagram, or scatter graph.

Stratified sampling

In statistics, stratified sampling is a method of sampling from a

population

Advantages

If the population is large and enough resources are available, usually one will use

multi-stage sampling. In such situations, usually stratified sampling will be done at

some stages. However the main advantage remains stratified sampling being the most

representative of a population.

Disadvantages

Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups.

It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes (or to their variances, if known to vary significantly.

by means of an F Test). Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroups' variances differ significantly and the data need to be stratified by variance, then there is no way to make the subgroup sample sizes proportional (at the same time) to the subgroups' sizes within the total population.

For an efficient way to partition sampling resources among groups that vary in their means, their variances, and their costs, see "optimum allocation"