What tools and techniques can be used to shorten the production time for an existing product, while also increasing production quality.?

Lean Manufacturing has many tools that help increase productivity and quality as well like one piece flow , 5S , kaizen etc.

under the lean production there are lots of tools to be used. Example..SMED DMAIC etc, this tools are  very powerful and effective way of shortening production time including minimizing the defects and also able to detect future machine breakdowns as so.

specific tools like lean manufacturingt,FMEA and root cause analysis is the best way to optimise the production downtime

Implementation of the Lean manufacturing process to increase the productivity and to achieve the best quality Six Sigma should be implemented.

Downtime can also be minimized by making maintenance team to do the regular and repetitive maintenance of the machinery.

Implementation of the Lean manufacturing process to increase the productivity and to achieve the best quality Six Sigma should be implemented

I assume from the question that the query is for A PRODUCT  which is a final finished part and the production industry as small  / medium scale.

Your requirement is to Reduce production time and Improve Quality.

To produce that product, definitely, there will  be many number production process / stages (like machining, fabrication, assembly,etc). 

Method 1:  Take a time study in each and every process / stages. Time study need to be taken in such a way to differentiate value added activities and non-value added activities. Highlight where you are spending more time compared to other process. Focus on non-values added activities (rework, unwanted process, unwanted movement,etc) and focus on eliminating to improve the production time.

Method 2: Conduct a case study / analysis on finding major defects occurred in the past (or recent) on each and every process stage (Tools like pareto diagram can be used) . Take the top 3 defects, focus on eliminating them by doing a root cause analysis (best on using Fish Bone Diagram). This improves your quality of the product by reduction of rework / rejection percentage. 

Generally. Large scale industry focus first on customer requirement (Pre-ordered in long term) where time study will be taken to standardize for line balancing (Tack Time vs actual time) in-order to meet customer delivery. The common tool used will be VSM (Value Stream Mapping). This focus more on production time and quality of the product. In this tool, they also used to decide whether investment can be made to improve particular process. There are many techniques like Lean Management, Six Sigma, 3M report (used from Toyota Production System), etc.

In production environment, the regular processes to be monitored and best fit solution to automate it using Technology. The various servers and its connections to be automated using software with automatic logic mechanism.

The release of new functionality/bug fixes needs to be done using automated scripts rather than manual activity.

These things can shorten the time in production.

To maximize productivity, every company needs a sound production plan to ensure that materials, equipment and human resources are available when and where they are needed.

the key factors of a production plan are:-

• Forecast market expectations
• Inventory control
• Availability of equipment and human resources
• Standardized steps and time
• Risk factors

The production plan initially needs to address specific key elements well in advance of production in order to ensure an uninterrupted flow of work as it unfolds.

• Material ordering—Materials and services that require a long lead time or are at an extended shipping distance, also known as blanket orders, should be ordered in advance of production requirements. Suppliers should send you materials periodically to ensure an uninterrupted pipeline.
• Equipment procurement—Procuring specialized tools and equipment to initiate the production process may require a longer lead time. Keep in mind that the equipment may have to be custom made or simply difficult to set up. This type of equipment may also require special training.
• Bottlenecks—These are constraints or restrictions in the process flow and should be assessed in advance so you can plan around them or eliminate them before you begin production.
• Human resources acquisitions and training—Key or specialized positions may demand extensive training on specialized equipment, technical processes or regulatory requirements. These employees should be interviewed thoroughly about their skills. When hiring them, allow sufficient time for training and be sure that they are competent in their work before the job begins. This will ensure that your process or service flows smoothly.

• Communicate the plan to the employees who will implement it

• Consider change :-Changes happen every day. You will need to adjust your plan in line with these changes and advise the plant

implementation of 5s and tme management.

By making some changes at the plant according to the process by using engineering tools we can enhance the production and the quality product  

Production is a team work, and the leader must be in good communication skill n the specific technical knowledge to train the staff and a commanding power.