Control Charts in Manufacturing

Control Charts

• Control charts are used to determine when to leave a process alone and prevent unnecessary adjustments.
• They are graphical representations based on statistical sampling theory.
• Control charts detect variations in the processing and warn if there is any departure from specified tolerance limits.
• They help in detecting the cause of undesired variations and removing them.
• Control charts are used to predict the future performance of a process if it is currently under control.
• They can help determine the sources of variation and eliminate them to bring the process back into control.

Purpose and Advantages of Control Charts

• Control charts indicate whether a process is in control or out of control.
• They determine process variability and detect unusual variations.
• They ensure product quality level.
• They warn in time, reducing scrap or percentage rejection.
• They provide information about the selection of process and setting of tolerance limits.
• Control charts build up the reputation of the organization through customer satisfaction.

Components of a Control Chart

• Points representing a statistic (e.g., mean, range, proportion) of measurements of a quality characteristic in samples.
• The mean of the statistic using all the samples.
• A center line drawn at the value of the mean of the statistic.
• Upper and lower control limits (natural process limits) indicating the threshold at which the process output is considered statistically 'unlikely'.
• Optional features: upper and lower warning limits, division into zones, and annotation with events of interest.

Types of Control Charts

• Control charts can be used to measure any characteristic of a product.
• Characteristics can be divided into two groups: variables and attributes.
• Control charts for variables are used to monitor characteristics that can be measured and have a continuum of values.
• Control charts for attributes are used to monitor characteristics that have discrete values and can be counted.

Comparison of Control Charts for Variables and Attributes

• Variables charts involve the measurement of job dimensions and an item is accepted or rejected based on tolerance limits.
• Attribute charts differentiate between defective and non-defective items without measuring dimensions.
• Variables charts are more detailed and contain more information.
• Attribute charts require a bigger sample size and are less expensive.
• Variables charts are more sensitive and can alert to quality problems before they occur.

Commonly Used Charts

• (X-Bar) and R charts for process control.
• P chart for analysis of fraction defectives.
• C chart for control of number of defects per unit.

Acceptance Sampling

• Acceptance sampling is concerned with the decision to accept or reject a mass of manufactured items based on standards of quality.
• It uses statistical sampling to determine whether to accept or reject a production lot of material.
• Acceptance sampling is usually done as products leave the factory or within the factory.
• The decision to accept or reject is made by determining the number of defective items in a sample from the lot.
• The lot is accepted if the number of defects falls below the acceptance number or otherwise rejected.

Operating Characteristic Curve

• The Operating Characteristic Curve (OC Curve) shows the probability of accepting lots with various levels of quality.
• It is the working plan of acceptance sampling.
• AQL (Acceptance Quality Level) is the maximum % defective that can be considered satisfactory as a process average for sampling inspection.
• RQL (Rejectable Quality Level) is the % defective, also known as the Lot Tolerance Percent Defective (LTPD).

Risks in Acceptance Sampling

• Producer's risk: the risk of rejecting a good quality lot due to a bad sample.
• Consumer's risk: the risk of accepting a bad quality lot due to a good sample.

Acceptance Sampling Plans

• A sampling plan specifies the parameters of the sampling process and the acceptance/rejection criteria.
• Variables to be specified include the size of the lot, the size of the sample inspected, the number of defects above which a lot is rejected, and the number of samples that will be taken.
• Types of sampling plans include single sampling, double sampling, and sequential sampling.
• Single sampling plan: decision is made after drawing a single sample from the lot.
• Double sampling plan: a second sample is drawn if the number of defectives in the first sample lies between two acceptance numbers.
• Sequential sampling plan: additional samples are drawn until an inference can be made, with a maximum number of samples specified.