CONTROL CHART BASISBPT2423 – STATISTICAL PROCESS CONTROL

CHAPTER OUTLINE Control Chart Functions Variation Basic Principles Choice of Control Limits

Upper Control Limit (UCL) Lower Control Limit (LCL)

Sample Size and Sampling Frequency Rational Subgroups Analysis of Patterns

LESSON OUTCOMES Understand the concept of variation Explain the statistical basis of the control chart,

including control limits and rational subgroup concept

Identify some practical issues in the implementation of statistical process control

CONTROL CHART FUNCTIONS A control chart enhances the analysis of the process by

showing how the process is performing over time Serve 2 basic functions:

1. Control charts are decision making toolsProvide an economic basis for making a decision as to whether to investigate for potential problems; to adjust the process or to leave the process alone

2. Control charts are problem-solving toolsPoint out where improvement is needed and help to provide a statistical basis on which to formulate improvement actions

CONTROL CHART FUNCTIONS Control charts have had a long history of use in U.S.

industries; Five reasons for it popularity:1. Control charts are a proven technique for improving

productivity2. Control charts are effective in defect prevention3. Control charts prevent unnecessary process

adjustment4. Control charts provide diagnostic information5. Control charts provide information about process

capability

VARIATION Definition : Where no two items / services are exactly the

same The goal of most processes is to produce products or provide

services that exhibit little or no variation Several types of variation are tracked with statistical methods:

1. Within-piece : variation within a single item or surface2. Piece-to-piece : variation that occurs among pieces

produced at approximately the same item 3. Time-to-time : variation in the product produced at

different times of the day Variation in a process is studied by sampling the process;

understanding variation and its causes results in better decisions

VARIATION

Stable and Unstable Variation

BASIC PRINCIPLESThe Chart contains: Center line that represents the average value of the quality

characteristics corresponding to the in-control state Two other horizontal lines, called the upper control limit

(UCL) and the lower control limit (LCL) All the sample points on the control chart are connected

with straight-line segments, so that it’s easier to visualize how the sequence of points has evolved over time

BASIC PRINCIPLES If the process is in control, nearly all of the sample

points will fall between chosen control limits and no action is necessary

However, a point that plots outside of the control limits is interpreted as evidence that the process is out of control, investigation and corrective action are required to find and eliminate the causes

Even if all the points plot inside the control limits, if they behave in a systematic or non random manner, then this could be an indication that the process is out of control

If the process is in control, all the plotted points should have an essentially random pattern

CHOICE OF CONTROL LIMITS 99.73% of the data under a normal curve falls within ± 3σ;

because of this, control limits are established at ± 3σ from the centerline of the process

Let w be a sample statistic that measures some quality characteristic of interest, and suppose that the mean of w is µw and the standard deviation of w is σw

Formula:Upper Control Limit (UCL) = µ

w + 3σ

w

Center Line = µw

Lower Control Limit (LCL) = µw – 3σ

w

SAMPLE SIZE AND SAMPLING FREQUENCY In designing a control chart, sample size and the frequency of

sampling must be specify In general, larger samples will make easier to detect small

shifts in the process When choosing the sample size, user must keep in mind the

size of the ‘shift’ that are trying to detect The most desirable situation form the point of view of

detecting shifts would be to take large samples very frequently (not economic feasible)

General problem is one of allocating sampling effort – either take small samples at short intervals or larger samples at longer intervals

SAMPLE SIZE AND SAMPLING FREQUENCY Average run length (ARL) can be use to evaluate the

decisions regarding sample size & sampling frequency of the control chart

ARL is the average number of points that must be plotted before a point indicates an out-of-control condition by using formula:

ARL = 1/p where p is the probability that any point exceeds the

control limits

Example:Chart with 3σ limits, p=0.0027 : the probability that a single point falls outside the limits when the process is in control

ARL = 1/p = 1/0.0027 = 370

which means an out-of-control signal will be generated every 370 samples, on the average

SAMPLE SIZE AND SAMPLING FREQUENCY

RATIONAL SUBGROUPS Subgroups and the samples composing them must be

homogeneous A homogeneous subgroup will have been produced

under the same conditions, by the same machine, the same operator, the same mold and so on

Subgroups used in investigating piece-to-piece variation will not necessarily be constructed in the same manner as subgroups formed to study time-to-time variation

Subgroup formation should reflect the type of variation When constructing variables chart, keep the subgroup

sample size constant for each subgroup taken

RATIONAL SUBGROUPSSome guidelines to be followed The larger the subgroup size, the more sensitive the chart

becomes to small variations in the process average. This provide a better picture of the process since it allows the investigator to detect changes in the process quickly

While a larger subgroup size makes for a more sensitive chart, it also increases inspection costs

Destructive testing may make large subgroup sizes unfeasible

Subgroup sizes smaller than four do not create a representative distribution of subgroup averages

ANALYSIS OF PATTERNSA control chart exhibits a state of control when:

1. 2/3 of the points are near the center value2. A few of the points are on or near the center value3. The points appear to float back and forth across the centerline4. The points are balanced (in roughly equal numbers) on both

sides of the centerline5. There are no points beyond the control limits6. There are no patterns or trends on the chart

A process that is not under control or is unstable, displays patterns of variation - the process need to be investigate and determine if an assignable cause can be found for the variation

ANALYSIS OF PATTERNS

Patterns in Control Chart: Oscillating Change / Jump / Shift Runs Recurring Cycles Freaks / Drift

ANALYSIS OF PATTERNSExample : Change / Jump / Shift

Description : The process begins at one level and jump quickly to another level as the process continues to operate. Causes for sudden shifts in level tend to reflect some new and significant difference in the process.

Possible causes : New operator, new batches of raw material or changes to the process settings

ANALYSIS OF PATTERNSExample : Runs